\input texinfo          @c -*-texinfo-*-
@c %**start of header
@setfilename nettle.info
@settitle Nettle: a low-level cryptographic library
@documentencoding UTF-8
@footnotestyle separate
@syncodeindex fn cp
@syncodeindex tp cp
@c %**end of header

@set UPDATED-FOR 3.9
@set AUTHOR Niels Möller

@copying
This manual is for the Nettle library (version @value{UPDATED-FOR}), a
low-level cryptographic library.

Originally written 2001 by @value{AUTHOR}, updated 2023.

@quotation
This manual is placed in the public domain. You may freely copy it, in
whole or in part, with or without modification. Attribution is
appreciated, but not required.
@end quotation
@end copying

@ifnottex
@macro pmod {m} 
(mod \m\)
@end macro
@end ifnottex

@titlepage
@title Nettle Manual
@subtitle For the Nettle Library version @value{UPDATED-FOR}
@author @value{AUTHOR}
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage

@dircategory Encryption
@direntry
* Nettle: (nettle).             A low-level cryptographic library.
@end direntry

@contents

@ifnottex
@node Top
@top Nettle

This document describes the Nettle low-level cryptographic library. You
can use the library directly from your C programs, or write or use an
object-oriented wrapper for your favorite language or application.

@insertcopying

@menu
* Introduction::                What is Nettle?
* Copyright::                   Your rights.
* Conventions::                 General interface conventions.
* Example::                     An example program.
* Linking::                     Linking with libnettle and libhogweed.
* Compatibility::               On API and ABI compatibility between versions.
* Reference::                   All Nettle functions and features.
* Nettle soup::                 For the serious nettle hacker.
* Installation::                How to install Nettle.
* Index::                       Function and concept index.

@detailmenu
 --- The Detailed Node Listing ---

Reference

* Hash functions::
* Cipher functions::
* Cipher modes::
* Authenticated encryption::
* Keyed hash functions::
* Key derivation functions::
* Public-key algorithms::
* Randomness::
* ASCII encoding::
* Miscellaneous functions::
* Compatibility functions::

Hash functions

* Recommended hash functions::
* Miscellaneous hash functions::
* Legacy hash functions::
* nettle_hash abstraction::

Cipher functions

* AES::
* Arcfour::
* Arctwo::
* Blowfish::
* Camellia::
* CAST128::
* ChaCha::
* DES::
* DES3::
* Salsa20::
* Serpent::
* SM4::
* Twofish::
* nettle_cipher abstraction::

Cipher modes

* CBC::
* CTR::
* CFB and CFB8::
* XTS::

Authenticated encryption with associated data

* EAX::
* GCM::
* CCM::
* ChaCha-Poly1305::
* OCB::
* SIV-CMAC::
* SIV-GCM::
* nettle_aead abstraction::

Keyed Hash Functions

* HMAC::
* UMAC::
* CMAC::
* Poly1305::

Public-key algorithms

* RSA::                         The RSA public key algorithm.
* DSA::                         The DSA digital signature algorithm.
* Elliptic curves::             Elliptic curves and ECDSA

Elliptic curves

* Side-channel silence::
* ECDSA::
* GOSTDSA::
* Curve 25519 and Curve 448::

@end detailmenu
@end menu

@end ifnottex

@node Introduction
@chapter Introduction

Nettle is a cryptographic library that is designed to fit easily in more
or less any context: In crypto toolkits for object-oriented languages
(C++, Python, Pike, ...), in applications like LSH or GNUPG, or even in
kernel space. In most contexts, you need more than the basic
cryptographic algorithms, you also need some way to keep track of available
algorithms, their properties and variants. You often have some algorithm
selection process, often dictated by a protocol you want to implement.

And as the requirements of applications differ in subtle and not so
subtle ways, an API that fits one application well can be a pain to use
in a different context. And that is why there are so many different
cryptographic libraries around.

Nettle tries to avoid this problem by doing one thing, the low-level
crypto stuff, and providing a @emph{simple} but general interface to it.
In particular, Nettle doesn't do algorithm selection. It doesn't do
memory allocation. It doesn't do any I/O.

The idea is that one can build several application and context specific
interfaces on top of Nettle, and share the code, test cases, benchmarks,
documentation, etc. Examples are the Nettle module for the Pike
language, and LSH, which both use an object-oriented abstraction on top
of the library.

This manual explains how to use the Nettle library. It also tries to
provide some background on the cryptography, and advice on how to best
put it to use.

@node Copyright
@chapter Copyright

Nettle is dual licenced under the GNU General Public License version 2
or later, and the GNU Lesser General Public License version 3 or later.
When using Nettle, you must comply fully with all conditions of at least
one of these licenses. A few of the individual files are licensed under
more permissive terms, or in the public domain. To find the current
status of particular files, you have to read the copyright notices at
the top of the files.

This manual is in the public domain. You may freely copy it in whole or
in part, e.g., into documentation of programs that build on Nettle.
Attribution, as well as contribution of improvements to the text, is of
course appreciated, but it is not required.

@node Conventions
@chapter Conventions

For each supported algorithm, there is an include file that defines a
@emph{context struct}, a few constants, and declares functions for
operating on the context. The context struct encapsulates all information
needed by the algorithm, and it can be copied or moved in memory with no
unexpected effects.

For consistency, functions for different algorithms are very similar,
but there are some differences, for instance reflecting if the key setup
or encryption function differ for encryption and decryption, and whether
or not key setup can fail. There are also differences between algorithms
that don't show in function prototypes, but which the application must
nevertheless be aware of. There is no big difference between the
functions for stream ciphers and for block ciphers, although they should
be used quite differently by the application.

If your application uses more than one algorithm of the same type, you
should probably create an interface that is tailor-made for your needs,
and then write a few lines of glue code on top of Nettle.

By convention, for an algorithm named @code{foo}, the struct tag for the
context struct is @code{foo_ctx}, constants and functions uses prefixes
like @code{FOO_BLOCK_SIZE} (a constant) and @code{foo_set_key} (a
function).

In all functions, strings are represented with an explicit length, of
type @code{size_t}, and a pointer of type @code{uint8_t *} or
@code{const uint8_t *}. For functions that transform one string to
another, the argument order is length, destination pointer and source
pointer. Source and destination areas are usually of the same length.
When they differ, e.g., for @code{ccm_encrypt_message}, the length
argument specifies the size of the destination area. Source and
destination pointers may be equal, so that you can process strings in
place, but source and destination areas @emph{must not} overlap in any
other way.

Many of the functions lack return value and can never fail. Those
functions which can fail, return one on success and zero on failure.

@c FIXME: Say something about the name mangling.

@node Example
@chapter Example

A simple example program that reads a file from standard input and
writes its SHA1 check-sum on standard output should give the flavor of
Nettle.

@example
@verbatiminclude sha-example.c
@end example

On a typical Unix system, this program can be compiled and linked with
the command line 
@example
gcc sha-example.c -o sha-example -lnettle
@end example

@node Linking
@chapter Linking

Nettle actually consists of two libraries, @file{libnettle} and
@file{libhogweed}. The @file{libhogweed} library contains those
functions of Nettle that uses bignum operations, and depends on the GMP
library. With this division, linking works the same for both static and
dynamic libraries.

If an application uses only the symmetric crypto algorithms of Nettle
(i.e., block ciphers, hash functions, and the like), it's sufficient to
link with @code{-lnettle}. If an application also uses public-key
algorithms, the recommended linker flags are @code{-lhogweed -lnettle
-lgmp}. If the involved libraries are installed as dynamic libraries, it
may be sufficient to link with just @code{-lhogweed}, and the loader
will resolve the dependencies automatically.

@node Compatibility
@chapter Compatibility
@cindex ABI compatibility
@cindex API compatibility
@cindex Binary compatibility

When you write a program using the Nettle library, it's desirable to
have it work together not only with exactly the same version of Nettle
you had at hand, but with other current and future versions. If a
different version of Nettle is used at compile time, i.e., you recompile
it using the header and library files belonging to a different version,
we talk about API compatibility (for Application Programming Interface).
If a different version of Nettle isn't used until link time, we talk
about ABI compatibility (Application Binary Interface) or binary
compatibility. ABI compatibility matters mainly when using dynamic
linking with a shared library. E.g., a user has an executable linking at
run-time with @file{libnettle.so}, and then updates to a later version
of the shared library, without updating or recompiling the executable.

Nettle aims to provide backwards compatibility, i.e., a program written
for a particular version of the Nettle library should usually work fine
with later version of the library. Note that the opposite is not
supported: The program should @emph{not} be expected to work with older
versions of the Nettle library; and ABI breakage can be unobvious. E.g,
the later version may define a new library symbol, and let header files
redefine an old API name as an alias for the new symbol. If the later
version ensures that the old symbol is still defined in the library,
this change is backwards compatible: A program compiled using headers
from the older version can be successfully linked with either version of
the library. But if you compile the same program using headers from the
later version of the library, and attempt to link with the older
version, you'll get an undefined reference to the new symbol.

API compatibility is rarely broken; exceptions are noted in the NEWS
file. For example, the key size argument to the function
@code{cast128_set_key} was dropped in the Nettle-3.0 release, and all
programs using that function had to be updated to work with the new
version.

ABI compatibility is broken occasionally. This is also noted in the NEWS
file, and the name of the shared library is updated to prevent
accidental run-time linking with the wrong version. All programs have to
be recompiled before they can link with the new version. Since names are
different, multiple versions can be installed on the same system, with a
mix of programs linking to one version or the other.

Under some circumstances, it is possible to have a single program
linking dynamically with two binary incompatible versions of the Nettle
library, thanks to the use of symbol versioning. Consider a program
calling functions in both Nettle and GnuTLS. For the direct dependency
on Nettle, the program is linked with a particular version of the Nettle
shared library. GnuTLS uses Nettle internally, but does not expose any
Nettle data structures or the like in its own ABI. In this situation,
the GnuTLS shared library may link with a different version of the
Nettle library. Then both versions of the Nettle library will be loaded
into the program's address space, and each reference to a symbol will be
resolved to the correct version.

Finally, some of Nettle's symbols are internal. They carry a leading
underscore, and are not declared in installed header files. They can be
used for local or experimental purposes, but programs referring directly
to those symbols get neither API nor ABI compatibility, not even between
minor versions.

@node Reference
@chapter Reference

This chapter describes all the Nettle functions, grouped by family.

@menu
* Hash functions::
* Cipher functions::
* Cipher modes::
* Authenticated encryption::
* Keyed hash functions::
* Key derivation functions::
* Public-key algorithms::
* Randomness::
* ASCII encoding::
* Miscellaneous functions::
* Compatibility functions::
@end menu

@node Hash functions
@section Hash functions
@cindex Hash function

A cryptographic @dfn{hash function} is a function that takes variable
size strings, and maps them to strings of fixed, short, length. There
are naturally lots of collisions, as there are more possible 1MB files
than 20 byte strings. But the function is constructed such that is hard
to find the collisions. More precisely, a cryptographic hash function
@code{H} should have the following properties:

@table @emph

@item One-way
@cindex One-way
Given a hash value @code{H(x)} it is hard to find a string @code{x}
that hashes to that value.

@item Collision-resistant
@cindex Collision-resistant
It is hard to find two different strings, @code{x} and @code{y}, such
that @code{H(x)} = @code{H(y)}.

@end table

Hash functions are useful as building blocks for digital signatures,
message authentication codes, pseudo random generators, association of
unique ids to documents, and many other things.

The most commonly used hash functions are MD5 and SHA1. Unfortunately,
both these fail the collision-resistance requirement; cryptologists have
found ways to construct colliding inputs. The recommended hash functions
for new applications are SHA2 (with main variants SHA256 and SHA512). At
the time of this writing (Autumn 2015), SHA3 has recently been
standardized, and the new SHA3 and other top SHA3 candidates may also be
reasonable alternatives.

@menu
* Recommended hash functions::
* Miscellaneous hash functions::
* Legacy hash functions::
* nettle_hash abstraction::
@end menu

@node Recommended hash functions
@subsection Recommended hash functions

The following hash functions have no known weaknesses, and are suitable
for new applications. The SHA2 family of hash functions were specified
by @dfn{NIST}, intended as a replacement for @acronym{SHA1}.

@subsubsection @acronym{SHA256}

SHA256 is a member of the SHA2 family. It outputs hash values of 256
bits, or 32 octets. Nettle defines SHA256 in @file{<nettle/sha2.h>}.

@deftp {Context struct} {struct sha256_ctx}
@end deftp

@defvr Constant SHA256_DIGEST_SIZE
The size of a SHA256 digest, i.e. 32.
@end defvr

@defvr Constant SHA256_BLOCK_SIZE
The internal block size of SHA256. Useful for some special constructions,
in particular HMAC-SHA256.
@end defvr

@deftypefun void sha256_init (struct sha256_ctx *@var{ctx})
Initialize the SHA256 state.
@end deftypefun

@deftypefun void sha256_update (struct sha256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha256_digest (struct sha256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA256_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{sha256_init}.
@end deftypefun

@deftypefun void sha256_compress (const uint32_t *@var{state}, uint8_t *@var{input})
Perform a raw SHA256 compress on SHA256_BLOCK_SIZE bytes from@var{input}
using @var{state} as IV (an array of 8 uint32_t). The output is stored in @var{state}.
This function provides access to the underlying compression function,
for the rare applications that need that (e.g., using different IV from
standard SHA256).
@end deftypefun

Earlier versions of nettle defined SHA256 in the header file
@file{<nettle/sha.h>}, which is now deprecated, but kept for
compatibility.

@subsubsection @acronym{SHA224}

SHA224 is a variant of SHA256, with a different initial state, and with
the output truncated to 224 bits, or 28 octets. Nettle defines SHA224 in
@file{<nettle/sha2.h>} (and in @file{<nettle/sha.h>}, for backwards
compatibility).

@deftp {Context struct} {struct sha224_ctx}
@end deftp

@defvr Constant SHA224_DIGEST_SIZE
The size of a SHA224 digest, i.e. 28.
@end defvr

@defvr Constant SHA224_BLOCK_SIZE
The internal block size of SHA224. Useful for some special constructions,
in particular HMAC-SHA224.
@end defvr

@deftypefun void sha224_init (struct sha224_ctx *@var{ctx})
Initialize the SHA224 state.
@end deftypefun

@deftypefun void sha224_update (struct sha224_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha224_digest (struct sha224_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA224_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{sha224_init}.
@end deftypefun

@subsubsection @acronym{SHA512}

SHA512 is a larger sibling to SHA256, with a very similar structure but
with both the output and the internal variables of twice the size. The
internal variables are 64 bits rather than 32, making it significantly
slower on 32-bit computers. It outputs hash values of 512 bits, or 64
octets. Nettle defines SHA512 in @file{<nettle/sha2.h>} (and in
@file{<nettle/sha.h>}, for backwards compatibility).

@deftp {Context struct} {struct sha512_ctx}
@end deftp

@defvr Constant SHA512_DIGEST_SIZE
The size of a SHA512 digest, i.e. 64.
@end defvr

@defvr Constant SHA512_BLOCK_SIZE
The internal block size of SHA512, 128. Useful for some special
constructions, in particular HMAC-SHA512.
@end defvr

@deftypefun void sha512_init (struct sha512_ctx *@var{ctx})
Initialize the SHA512 state.
@end deftypefun

@deftypefun void sha512_update (struct sha512_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha512_digest (struct sha512_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA512_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{sha512_init}.
@end deftypefun

@deftypefun void sha512_compress (const uint64_t *@var{state}, uint8_t *@var{input})
Perform a raw SHA512 compress on SHA512_BLOCK_SIZE bytes from
@var{input} using @var{state} as IV (an array of 8 uint64_t). The output is stored in @var{state}.
This function provides access to the underlying compression function,
for the rare applications that need that (e.g., using different IV from
standard SHA512).
@end deftypefun

@subsubsection @acronym{SHA384 and other variants of SHA512}

Several variants of SHA512 have been defined, with a different initial
state, and with the output truncated to shorter length than 512 bits.
Naming is a bit confused, these algorithms are called SHA512-224,
SHA512-256 and SHA384, for output sizes of 224, 256 and 384 bits,
respectively. Nettle defines these in @file{<nettle/sha2.h>} (and in
@file{<nettle/sha.h>}, for backwards compatibility).

@deftp {Context struct} {struct sha512_224_ctx}
@deftpx {Context struct} {struct sha512_256_ctx}
@deftpx {Context struct} {struct sha384_ctx}
These context structs are all the same as sha512_ctx. They are defined as
simple preprocessor aliases, which may cause some problems if used as
identifiers for other purposes. So avoid doing that.
@end deftp

@defvr Constant SHA512_224_DIGEST_SIZE
@defvrx Constant SHA512_256_DIGEST_SIZE
@defvrx Constant SHA384_DIGEST_SIZE
The digest size for each variant, i.e., 28, 32, and 48, respectively.
@end defvr

@defvr Constant SHA512_224_BLOCK_SIZE
@defvrx Constant SHA512_256_BLOCK_SIZE
@defvrx Constant SHA384_BLOCK_SIZE
The internal block size, same as SHA512_BLOCK_SIZE, i.e., 128. Useful for
some special constructions, in particular HMAC-SHA384.
@end defvr

@deftypefun void sha512_224_init (struct sha512_224_ctx *@var{ctx})
@deftypefunx void sha512_256_init (struct sha512_256_ctx *@var{ctx})
@deftypefunx void sha384_init (struct sha384_ctx *@var{ctx})
Initialize the context struct.
@end deftypefun

@deftypefun void sha512_224_update (struct sha512_224_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void sha512_256_update (struct sha512_256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void sha384_update (struct sha384_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data. These are all aliases for sha512_update, which does
the same thing.
@end deftypefun

@deftypefun void sha512_224_digest (struct sha512_224_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void sha512_256_digest (struct sha512_256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void sha384_digest (struct sha384_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it to
@var{digest}. @var{length} may be smaller than the specified digest
size, in which case only the first @var{length} octets of the digest are
written.

These function also reset the context in the same way as the
corresponding init function.
@end deftypefun

@subsubsection @acronym{SHA3-224}
@cindex SHA3

The SHA3 hash functions were specified by NIST in response to weaknesses
in SHA1, and doubts about SHA2 hash functions which structurally are
very similar to SHA1. SHA3 is a result of a competition, where the
winner, also known as Keccak, was designed by Guido Bertoni, Joan
Daemen, Michaël Peeters and Gilles Van Assche. It is structurally very
different from all widely used earlier hash functions. Like SHA2, there
are several variants, with output sizes of 224, 256, 384 and 512 bits
(28, 32, 48 and 64 octets, respectively). In August 2015, it was
formally standardized by NIST, as FIPS 202,
@url{https://dx.doi.org/10.6028/NIST.FIPS.202}.

Note that the SHA3 implementation in earlier versions of Nettle was
based on the specification at the time Keccak was announced as the
winner of the competition, which is incompatible with the final standard
and hence with current versions of Nettle. The @file{nette/sha3.h}
defines a preprocessor symbol @code{NETTLE_SHA3_FIPS202} to indicate
conformance with the standard.

@defvr Constant NETTLE_SHA3_FIPS202
Defined to 1 in Nettle versions supporting FIPS 202. Undefined in
earlier versions.
@end defvr

Nettle defines SHA3-224 in @file{<nettle/sha3.h>}.

@deftp {Context struct} {struct sha3_224_ctx}
@end deftp

@defvr Constant SHA3_224_DIGEST_SIZE
The size of a SHA3_224 digest, i.e., 28.
@end defvr

@defvr Constant SHA3_224_BLOCK_SIZE
The internal block size of SHA3_224.
@end defvr

@deftypefun void sha3_224_init (struct sha3_224_ctx *@var{ctx})
Initialize the SHA3-224 state.
@end deftypefun

@deftypefun void sha3_224_update (struct sha3_224_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha3_224_digest (struct sha3_224_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA3_224_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context.
@end deftypefun

@subsubsection @acronym{SHA3-256}

This is SHA3 with 256-bit output size, and possibly the most useful
of the SHA3 hash functions.

Nettle defines SHA3-256 in @file{<nettle/sha3.h>}.

@deftp {Context struct} {struct sha3_256_ctx}
@end deftp

@defvr Constant SHA3_256_DIGEST_SIZE
The size of a SHA3_256 digest, i.e., 32.
@end defvr

@defvr Constant SHA3_256_BLOCK_SIZE
The internal block size of SHA3_256.
@end defvr

@deftypefun void sha3_256_init (struct sha3_256_ctx *@var{ctx})
Initialize the SHA3-256 state.
@end deftypefun

@deftypefun void sha3_256_update (struct sha3_256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha3_256_digest (struct sha3_256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA3_256_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context.
@end deftypefun

@subsubsection @acronym{SHA3-384}

This is SHA3 with 384-bit output size.

Nettle defines SHA3-384 in @file{<nettle/sha3.h>}.

@deftp {Context struct} {struct sha3_384_ctx}
@end deftp

@defvr Constant SHA3_384_DIGEST_SIZE
The size of a SHA3_384 digest, i.e., 48.
@end defvr

@defvr Constant SHA3_384_BLOCK_SIZE
The internal block size of SHA3_384.
@end defvr

@deftypefun void sha3_384_init (struct sha3_384_ctx *@var{ctx})
Initialize the SHA3-384 state.
@end deftypefun

@deftypefun void sha3_384_update (struct sha3_384_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha3_384_digest (struct sha3_384_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA3_384_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context.
@end deftypefun

@subsubsection @acronym{SHA3-512}

This is SHA3 with 512-bit output size.

Nettle defines SHA3-512 in @file{<nettle/sha3.h>}.

@deftp {Context struct} {struct sha3_512_ctx}
@end deftp

@defvr Constant SHA3_512_DIGEST_SIZE
The size of a SHA3_512 digest, i.e. 64.
@end defvr

@defvr Constant SHA3_512_BLOCK_SIZE
The internal block size of SHA3_512.
@end defvr

@deftypefun void sha3_512_init (struct sha3_512_ctx *@var{ctx})
Initialize the SHA3-512 state.
@end deftypefun

@deftypefun void sha3_512_update (struct sha3_512_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha3_512_digest (struct sha3_512_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA3_512_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context.
@end deftypefun

@subsubsection @acronym{SHAKE}
@cindex SHAKE

In addition to those SHA-3 hash functions, Nettle also supports a
SHA-3 extendable-output function (XOF) called SHAKE. Unlike hash
functions, SHAKE can produce an output digest of any desired
length. There are two variants, SHAKE-128 and SHAKE-256, with
different security strengths in terms of collision or preimage
resistance: SHAKE-128 internally uses a SHA-3 hash function with
128-bit security, while SHAKE-256 corresponds to SHA3-256 which
provides 256-bit security.

To use SHAKE, the context struct needs to be initialized with the
@code{init} function and data is hashed using the @code{update}
function. Afterwards, a digest can be generated using either the
@code{shake} or @code{shake_ouput} function, where the former
generates the digest at once and resets the context, while the latter
can be called multiple times to generate the digest in an incremental
manner.

For SHAKE-128 they are defined as follows.

@deftp {Context struct} {struct sha3_128_ctx}
@end deftp

@deftypefun void sha3_128_init (struct sha3_128_ctx *@var{ctx})
Initialize the SHA3-256 state.
@end deftypefun

@deftypefun void sha3_128_update (struct sha3_128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha3_128_shake (struct sha3_128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and produces a SHAKE-128 digest, writing it
to @var{digest}. @var{length} can be of arbitrary size.

This function also resets the context.
@end deftypefun

@deftypefun void sha3_128_shake_output (struct sha3_128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and produces a SHAKE-128 digest, writing it
to @var{digest}. @var{length} can be of arbitrary size.

This function does not reset the context.
@end deftypefun

For SHAKE-256, the corresponding context struct and the @code{init}
and @code{update} functions are the same as SHA3-256. To generate a
digest, use either the @code{shake} or @code{shake_output} function.

@deftypefun void sha3_256_shake (struct sha3_256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and produces a SHAKE-256 digest, writing it
to @var{digest}. @var{length} can be of arbitrary size.

This function also resets the context.
@end deftypefun

@deftypefun void sha3_256_shake_output (struct sha3_256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and produces a SHAKE-256 digest, writing it
to @var{digest}. @var{length} can be of arbitrary size.

This function does not reset the context.
@end deftypefun

@node Miscellaneous hash functions
@subsection Miscellaneous hash functions

@subsubsection @acronym{STREEBOG512}

STREEBOG512 is a member of the Streebog (GOST R 34.11-2012) family.  It outputs
hash values of 512 bits, or 64 octets. Nettle defines STREEBOG512 in
@file{<nettle/streebog.h>}.

@deftp {Context struct} {struct streebog512_ctx}
@end deftp

@defvr Constant STREEBOG512_DIGEST_SIZE
The size of a STREEBOG512 digest, i.e. 64.
@end defvr

@defvr Constant STREEBOG512_BLOCK_SIZE
The internal block size of STREEBOG512. Useful for some special constructions,
in particular HMAC-STREEBOG512.
@end defvr

@deftypefun void streebog512_init (struct streebog512_ctx *@var{ctx})
Initialize the STREEBOG512 state.
@end deftypefun

@deftypefun void streebog512_update (struct streebog512_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void streebog512_digest (struct streebog512_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{STREEBOG512_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{streebog512_init}.
@end deftypefun

@subsubsection @acronym{STREEBOG256}

STREEBOG256 is a variant of STREEBOG512, with a different initial state, and with
the output truncated to 256 bits, or 32 octets. Nettle defines STREEBOG256 in
@file{<nettle/streebog.h>}.

@deftp {Context struct} {struct streebog256_ctx}
@end deftp

@defvr Constant STREEBOG256_DIGEST_SIZE
The size of a STREEBOG256 digest, i.e. 32.
@end defvr

@defvr Constant STREEBOG256_BLOCK_SIZE
The internal block size of STREEBOG256. Useful for some special constructions,
in particular HMAC-STREEBOG256.
@end defvr

@deftypefun void streebog256_init (struct streebog256_ctx *@var{ctx})
Initialize the STREEBOG256 state.
@end deftypefun

@deftypefun void streebog256_update (struct streebog256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void streebog256_digest (struct streebog256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{STREEBOG256_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{streebog256_init}.
@end deftypefun

@subsubsection @acronym{SM3}

SM3 is a cryptographic hash function standard adopted by the government of the
People's Republic of China, which was issued by the Cryptography Standardization
Technical Committee of China on December 17, 2010. The corresponding standard
is GM/T 0004-2012 "SM3 Cryptographic Hash Algorithm".

SM3 algorithm is a hash algorithm in ShangMi cryptosystems. SM3 is mainly used
for digital signature and verification, message authentication code generation
and verification, random number generation, and the RFC 8998 specification
defines the usage of ShangMi algorithm suite in TLS 1.3, etc. According to the
State Cryptography Administration of China, its security and efficiency are
equivalent to SHA-256.

Nettle defines SM3 in @file{<nettle/sm3.h>}.

@deftp {Context struct} {struct sm3_ctx}
@end deftp

@defvr Constant SM3_DIGEST_SIZE
The size of a SM3 digest, i.e. 32.
@end defvr

@defvr Constant SM3_BLOCK_SIZE
The internal block size of SM3. Useful for some special constructions,
in particular HMAC-SM3.
@end defvr

@deftypefun void sm3_init (struct sm3_ctx *@var{ctx})
Initialize the SM3 state.
@end deftypefun

@deftypefun void sm3_update (struct sm3_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sm3_digest (struct sm3_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SM3_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{sm3_init}.
@end deftypefun


@node Legacy hash functions
@subsection Legacy hash functions

The hash functions in this section all have some known weaknesses, and
should be avoided for new applications. These hash functions are mainly
useful for compatibility with old applications and protocols. Some are
still considered safe as building blocks for particular constructions,
e.g., there seems to be no known attacks against HMAC-SHA1 or even
HMAC-MD5. In some important cases, use of a ``legacy'' hash function
does not in itself make the application insecure; if a known weakness is
relevant depends on how the hash function is used, and on the threat
model.

@subsubsection @acronym{MD5}

MD5 is a message digest function constructed by Ronald Rivest, and
described in @cite{RFC 1321}. It outputs message digests of 128 bits, or
16 octets. Nettle defines MD5 in @file{<nettle/md5.h>}.

@deftp {Context struct} {struct md5_ctx}
@end deftp

@defvr Constant MD5_DIGEST_SIZE
The size of an MD5 digest, i.e. 16.
@end defvr

@defvr Constant MD5_BLOCK_SIZE
The internal block size of MD5. Useful for some special constructions,
in particular HMAC-MD5.
@end defvr

@deftypefun void md5_init (struct md5_ctx *@var{ctx})
Initialize the MD5 state.
@end deftypefun

@deftypefun void md5_update (struct md5_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void md5_digest (struct md5_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{MD5_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{md5_init}.
@end deftypefun

@deftypefun void md5_compress (const uint32_t *@var{state}, uint8_t *@var{input})
Perform a raw MD5 compress on MD5_BLOCK_SIZE bytes from @var{input}
using @var{state} as IV (an array of 4 uint32_t). The output is stored in @var{state}.
This function provides access to the underlying compression function,
for the rare applications that need that (e.g., using different IV from
standard MD5).
@end deftypefun

The normal way to use MD5 is to call the functions in order: First
@code{md5_init}, then @code{md5_update} zero or more times, and finally
@code{md5_digest}. After @code{md5_digest}, the context is reset to
its initial state, so you can start over calling @code{md5_update} to
hash new data.

To start over, you can call @code{md5_init} at any time.

@subsubsection @acronym{MD2}

MD2 is another hash function of Ronald Rivest's, described in
@cite{RFC 1319}. It outputs message digests of 128 bits, or 16 octets.
Nettle defines MD2 in @file{<nettle/md2.h>}.

@deftp {Context struct} {struct md2_ctx}
@end deftp

@defvr Constant MD2_DIGEST_SIZE
The size of an MD2 digest, i.e. 16.
@end defvr

@defvr Constant MD2_BLOCK_SIZE
The internal block size of MD2.
@end defvr

@deftypefun void md2_init (struct md2_ctx *@var{ctx})
Initialize the MD2 state.
@end deftypefun

@deftypefun void md2_update (struct md2_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void md2_digest (struct md2_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{MD2_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{md2_init}.
@end deftypefun

@subsubsection @acronym{MD4}

MD4 is a predecessor of MD5, described in @cite{RFC 1320}. Like MD5, it
is constructed by Ronald Rivest. It outputs message digests of 128 bits,
or 16 octets. Nettle defines MD4 in @file{<nettle/md4.h>}. Use of MD4 is
not recommended, but it is sometimes needed for compatibility with
existing applications and protocols.

@deftp {Context struct} {struct md4_ctx}
@end deftp

@defvr Constant MD4_DIGEST_SIZE
The size of an MD4 digest, i.e. 16.
@end defvr

@defvr Constant MD4_BLOCK_SIZE
The internal block size of MD4.
@end defvr

@deftypefun void md4_init (struct md4_ctx *@var{ctx})
Initialize the MD4 state.
@end deftypefun

@deftypefun void md4_update (struct md4_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void md4_digest (struct md4_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{MD4_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{md4_init}.
@end deftypefun

@subsubsection @acronym{RIPEMD160}

RIPEMD160 is a hash function designed by Hans Dobbertin, Antoon
Bosselaers, and Bart Preneel, as a strengthened version of RIPEMD
(which, like MD4 and MD5, fails the collision-resistance requirement).
It produces message digests of 160 bits, or 20 octets. Nettle defined
RIPEMD160 in @file{nettle/ripemd160.h}.

@deftp {Context struct} {struct ripemd160_ctx}
@end deftp

@defvr Constant RIPEMD160_DIGEST_SIZE
The size of a RIPEMD160 digest, i.e. 20.
@end defvr

@defvr Constant RIPEMD160_BLOCK_SIZE
The internal block size of RIPEMD160.
@end defvr

@deftypefun void ripemd160_init (struct ripemd160_ctx *@var{ctx})
Initialize the RIPEMD160 state.
@end deftypefun

@deftypefun void ripemd160_update (struct ripemd160_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void ripemd160_digest (struct ripemd160_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{RIPEMD160_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{ripemd160_init}.
@end deftypefun

@subsubsection @acronym{SHA1}

SHA1 is a hash function specified by @dfn{NIST} (The U.S. National
Institute for Standards and Technology). It outputs hash values of 160
bits, or 20 octets. Nettle defines SHA1 in @file{<nettle/sha1.h>} (and
in @file{<nettle/sha.h>}, for backwards compatibility).

@deftp {Context struct} {struct sha1_ctx}
@end deftp

@defvr Constant SHA1_DIGEST_SIZE
The size of a SHA1 digest, i.e. 20.
@end defvr

@defvr Constant SHA1_BLOCK_SIZE
The internal block size of SHA1. Useful for some special constructions,
in particular HMAC-SHA1.
@end defvr

@deftypefun void sha1_init (struct sha1_ctx *@var{ctx})
Initialize the SHA1 state.
@end deftypefun

@deftypefun void sha1_update (struct sha1_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha1_digest (struct sha1_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{SHA1_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{sha1_init}.
@end deftypefun

@deftypefun void sha1_compress (const uint32_t *@var{state}, uint8_t *@var{input})
Perform a raw SHA1 compress on SHA1_BLOCK_SIZE bytes from @var{input}
using @var{state} as IV (an array of 5 uint32_t). The output is stored in @var{state}.
This function provides access to the underlying compression function,
for the rare applications that need that (e.g., using different IV from
standard SHA1).
@end deftypefun

@subsubsection @acronym{GOSTHASH94 and GOSTHASH94CP}
@cindex GOST hash

@anchor{GOSTHASH94CP}
The GOST94 or GOST R 34.11-94 hash algorithm is a Soviet-era algorithm 
used in Russian government standards (see @cite{RFC 4357}).
It outputs message digests of 256 bits, or 32 octets. The standard itself
does not fix the S-box used by the hash algorith, so there are two popular
variants (the testing S-box from the standard itself and the S-box defined
by CryptoPro company, see RFC 4357). Nettle provides support for the former
S-box in the form of GOSTHASH94 hash algorithm and for the latter in the
form of GOSTHASH94CP hash algorithm.
Nettle defines GOSTHASH94 and GOSTHASH94CP in @file{<nettle/gosthash94.h>}.

@deftp {Context struct} {struct gosthash94_ctx}
@end deftp

@defvr Constant GOSTHASH94_DIGEST_SIZE
The size of a GOSTHASH94 digest, i.e. 32.
@end defvr

@defvr Constant GOSTHASH94_BLOCK_SIZE
The internal block size of GOSTHASH94, i.e., 32.
@end defvr

@deftypefun void gosthash94_init (struct gosthash94_ctx *@var{ctx})
Initialize the GOSTHASH94 state.
@end deftypefun

@deftypefun void gosthash94_update (struct gosthash94_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void gosthash94_digest (struct gosthash94_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{GOSTHASH94_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{gosthash94_init}.
@end deftypefun

@deftp {Context struct} {struct gosthash94cp_ctx}
@end deftp

@defvr Constant GOSTHASH94CP_DIGEST_SIZE
The size of a GOSTHASH94CP digest, i.e. 32.
@end defvr

@defvr Constant GOSTHASH94CP_BLOCK_SIZE
The internal block size of GOSTHASH94CP, i.e., 32.
@end defvr

@deftypefun void gosthash94cp_init (struct gosthash94cp_ctx *@var{ctx})
Initialize the GOSTHASH94CP state.
@end deftypefun

@deftypefun void gosthash94cp_update (struct gosthash94cp_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void gosthash94cp_digest (struct gosthash94cp_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Performs final processing and extracts the message digest, writing it
to @var{digest}. @var{length} may be smaller than
@code{GOSTHASH94CP_DIGEST_SIZE}, in which case only the first @var{length}
octets of the digest are written.

This function also resets the context in the same way as
@code{gosthash94cp_init}.
@end deftypefun

@node nettle_hash abstraction
@subsection The @code{struct nettle_hash} abstraction
@cindex nettle_hash

Nettle includes a struct including information about the supported hash
functions. It is defined in @file{<nettle/nettle-meta.h>}, and is used
by Nettle's implementation of @acronym{HMAC} (@pxref{Keyed hash
functions}).

@deftp {Meta struct} @code{struct nettle_hash} name context_size digest_size block_size init update digest
The last three attributes are function pointers, of types
@code{nettle_hash_init_func *}, @code{nettle_hash_update_func *}, and
@code{nettle_hash_digest_func *}. The first argument to these functions is
@code{void *} pointer to a context struct, which is of size
@code{context_size}.
@end deftp

@deftypevr {Constant Struct} {struct nettle_hash} nettle_md2
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_md4
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_md5
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_ripemd160
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha1
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha224
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha256
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha384
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha512
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sha3_256
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_gosthash94
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_gosthash94cp
@deftypevrx {Constant Struct} {struct nettle_hash} nettle_sm3
These are all the hash functions that Nettle implements.
@end deftypevr

Nettle also exports a list of all these hashes.

@deftypefun {const struct nettle_hash **} nettle_get_hashes (void)
Returns a NULL-terminated list of pointers to supported hash functions.
This list can be used to dynamically enumerate or search the supported
algorithms.
@end deftypefun

@deffn Macro nettle_hashes
A macro expanding to a call to nettle_get_hashes, so that one could
write, e.g., @code{nettle_hashes[0]->name} for the name of the first
hash function on the list. In earlier versions, this was not a macro but
the actual array of pointers. However, referring directly to the array
makes the array size leak into the ABI in some cases.
@end deffn

@node Cipher functions
@section Cipher functions
@cindex Cipher

A @dfn{cipher} is a function that takes a message or @dfn{plaintext}
and a secret @dfn{key} and transforms it to a @dfn{ciphertext}. Given
only the ciphertext, but not the key, it should be hard to find the
plaintext. Given matching pairs of plaintext and ciphertext, it should
be hard to find the key.

@cindex Block Cipher
@cindex Stream Cipher

There are two main classes of ciphers: Block ciphers and stream ciphers.

A block cipher can process data only in fixed size chunks, called
@dfn{blocks}. Typical block sizes are 8 or 16 octets. To encrypt
arbitrary messages, you usually have to pad it to an integral number of
blocks, split it into blocks, and then process each block. The simplest
way is to process one block at a time, independent of each other. That
mode of operation is called @dfn{ECB}, Electronic Code Book mode.
However, using @acronym{ECB} is usually a bad idea. For a start, plaintext blocks
that are equal are transformed to ciphertext blocks that are equal; that
leaks information about the plaintext. Usually you should apply the
cipher is some ``feedback mode'', @dfn{CBC} (Cipher Block Chaining) and
@dfn{CTR} (Counter mode) being two of
of the most popular. See @xref{Cipher modes}, for information on
how to apply @acronym{CBC} and @acronym{CTR} with Nettle.

A stream cipher can be used for messages of arbitrary length. A typical
stream cipher is a keyed pseudo-random generator. To encrypt a plaintext
message of @var{n} octets, you key the generator, generate @var{n}
octets of pseudo-random data, and XOR it with the plaintext. To decrypt,
regenerate the same stream using the key, XOR it to the ciphertext, and
the plaintext is recovered.

@strong{Caution:} The first rule for this kind of cipher is the
same as for a One Time Pad: @emph{never} ever use the same key twice.

A common misconception is that encryption, by itself, implies
authentication. Say that you and a friend share a secret key, and you
receive an encrypted message. You apply the key, and get a plaintext
message that makes sense to you. Can you then be sure that it really was
your friend that wrote the message you're reading? The answer is no. For
example, if you were using a block cipher in ECB mode, an attacker may
pick up the message on its way, and reorder, delete or repeat some of
the blocks. Even if the attacker can't decrypt the message, he can
change it so that you are not reading the same message as your friend
wrote. If you are using a block cipher in @acronym{CBC} mode rather than
ECB, or are using a stream cipher, the possibilities for this sort of
attack are different, but the attacker can still make predictable
changes to the message.

It is recommended to @emph{always} use an authentication mechanism in
addition to encrypting the messages. Popular choices are Message
Authentication Codes like @acronym{HMAC-SHA1} (@pxref{Keyed hash
functions}), or digital signatures like @acronym{RSA}.

Some ciphers have so called ``weak keys'', keys that results in
undesirable structure after the key setup processing, and should be
avoided. In Nettle, most key setup functions have no return value, but
for ciphers with weak keys, the return value indicates whether or not
the given key is weak. For good keys, key setup returns 1, and for weak
keys, it returns 0. When possible, avoid algorithms that
have weak keys. There are several good ciphers that don't have any weak
keys.

To encrypt a message, you first initialize a cipher context for
encryption or decryption with a particular key. You then use the context
to process plaintext or ciphertext messages. The initialization is known
as @dfn{key setup}. With Nettle, it is recommended to use each
context struct for only one direction, even if some of the ciphers use a
single key setup function that can be used for both encryption and
decryption.

@menu
* AES::
* Arcfour::
* Arctwo::
* Blowfish::
* Camellia::
* CAST128::
* ChaCha::
* DES::
* DES3::
* Salsa20::
* Serpent::
* SM4::
* Twofish::
* nettle_cipher abstraction::
@end menu

@node AES
@subsection AES
@cindex AES

AES is a block cipher, specified by NIST as a replacement for
the older DES standard. The standard is the result of a competition
between cipher designers. The winning design, also known as RIJNDAEL,
was constructed by Joan Daemen and Vincent Rijnmen.

Like all the AES candidates, the winning design uses a block size of 128
bits, or 16 octets, and three possible key-size, 128, 192 and 256 bits
(16, 24 and 32 octets) being the allowed key sizes. It does not have any
weak keys. Nettle defines AES in @file{<nettle/aes.h>}, and there is one
context struct for each key size. (Earlier versions of Nettle used a
single context struct, @code{struct aes_ctx}, for all key sizes. This
interface kept for backwards compatibility).
 
@deftp {Context struct} {struct aes128_ctx}
@deftpx {Context struct} {struct aes192_ctx}
@deftpx {Context struct} {struct aes256_ctx}
@end deftp

@deftp {Context struct} {struct aes_ctx}
Alternative struct, for the old AES interface.
@end deftp

@defvr Constant AES_BLOCK_SIZE
The AES block-size, 16.
@end defvr

@defvr Constant AES128_KEY_SIZE
@defvrx Constant AES192_KEY_SIZE
@defvrx Constant AES256_KEY_SIZE
@defvrx Constant AES_MIN_KEY_SIZE
@defvrx Constant AES_MAX_KEY_SIZE
@end defvr

@defvr Constant AES_KEY_SIZE
Default AES key size, 32.
@end defvr

@deftypefun void aes128_set_encrypt_key (struct aes128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes128_set_decrypt_key (struct aes128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes192_set_encrypt_key (struct aes192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes192_set_decrypt_key (struct aes192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes256_set_encrypt_key (struct aes256_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes256_set_decrypt_key (struct aes256_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void aes_set_encrypt_key (struct aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
@deftypefunx void aes_set_decrypt_key (struct aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher, for encryption or decryption, respectively.
@end deftypefun

@deftypefun void aes128_invert_key (struct aes128_ctx *@var{dst}, const struct aes128_ctx *@var{src})
@deftypefunx void aes192_invert_key (struct aes192_ctx *@var{dst}, const struct aes192_ctx *@var{src})
@deftypefunx void aes256_invert_key (struct aes256_ctx *@var{dst}, const struct aes256_ctx *@var{src})
@deftypefunx void aes_invert_key (struct aes_ctx *@var{dst}, const struct aes_ctx *@var{src})
Given a context @var{src} initialized for encryption, initializes the
context struct @var{dst} for decryption, using the same key. If the same
context struct is passed for both @code{src} and @code{dst}, it is
converted in place. These functions are mainly useful for applications
which needs to both encrypt and decrypt using the @emph{same} key,
because calling, e.g., @code{aes128_set_encrypt_key} and
@code{aes128_invert_key}, is more efficient than calling
@code{aes128_set_encrypt_key} and @code{aes128_set_decrypt_key}.
@end deftypefun

@deftypefun void aes128_encrypt (struct aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes192_encrypt (struct aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes256_encrypt (struct aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes_encrypt (struct aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void aes128_decrypt (struct aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes192_decrypt (struct aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes256_decrypt (struct aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void aes_decrypt (struct aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to the encryption functions above.
@end deftypefun

@node Arcfour
@subsection Arcfour
@cindex Arcfour
@cindex RC4

ARCFOUR is a historic stream cipher, also known under the trade marked
name RC4, and was a widely used fast stream cipher.

We do not recommend the use of ARCFOUR; the Nettle implementation is
provided primarily for interoperability with existing applications and
standards.

One problem is that the key setup of ARCFOUR is quite weak, you should
never use keys with structure, keys that are ordinary passwords, or
sequences of keys like ``secret:1'', ``secret:2'', @enddots{}. If you
have keys that don't look like random bit strings, and you want to use
ARCFOUR, always hash the key before feeding it to ARCFOUR.

Another problem is that the output is distinguishable from random data,
and that the initial bytes of the generated key stream leak information
about the key; for this reason, it was sometimes recommended to discard
the first 512, 768 or 1024 bytes of the key stream.

@example
/* A more robust key setup function for ARCFOUR */
void
arcfour_set_key_hashed(struct arcfour_ctx *ctx,
                       size_t length, const uint8_t *key)
@{
  struct sha256_ctx hash;
  uint8_t digest[SHA256_DIGEST_SIZE];
  uint8_t buffer[0x200];

  sha256_init(&hash);
  sha256_update(&hash, length, key);
  sha256_digest(&hash, SHA256_DIGEST_SIZE, digest);

  arcfour_set_key(ctx, SHA256_DIGEST_SIZE, digest);
  arcfour_crypt(ctx, sizeof(buffer), buffer, buffer);
@}
@end example

Nettle defines ARCFOUR in @file{<nettle/arcfour.h>}.

@deftp {Context struct} {struct arcfour_ctx}
@end deftp

@defvr Constant ARCFOUR_MIN_KEY_SIZE
Minimum key size, 1.
@end defvr

@defvr Constant ARCFOUR_MAX_KEY_SIZE
Maximum key size, 256.
@end defvr

@defvr Constant ARCFOUR_KEY_SIZE
Default ARCFOUR key size, 16.
@end defvr

@deftypefun void arcfour_set_key (struct arcfour_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. 
@end deftypefun

@deftypefun void arcfour_crypt (struct arcfour_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypt some data. The same function is used for both encryption and
decryption. Unlike the block ciphers, this function modifies the
context, so you can split the data into arbitrary chunks and encrypt
them one after another. The result is the same as if you had called
@code{arcfour_crypt} only once with all the data.
@end deftypefun

@node Arctwo
@subsection Arctwo
@cindex Arctwo
@cindex RC2

ARCTWO (also known as the trade marked name RC2) is a block cipher
specified in RFC 2268. Nettle also include a variation of the ARCTWO
set key operation that lack one step, to be compatible with the
reverse engineered RC2 cipher description, as described in a Usenet
post to @code{sci.crypt} by Peter Gutmann.

ARCTWO uses a block size of 64 bits, and variable key-size ranging
from 1 to 128 octets. Besides the key, ARCTWO also has a second
parameter to key setup, the number of effective key bits, @code{ekb}.
This parameter can be used to artificially reduce the key size. In
practice, @code{ekb} is usually set equal to the input key size.
Nettle defines ARCTWO in @file{<nettle/arctwo.h>}.

We do not recommend the use of ARCTWO; the Nettle implementation is
provided primarily for interoperability with existing applications and
standards.

@deftp {Context struct} {struct arctwo_ctx}
@end deftp

@defvr Constant ARCTWO_BLOCK_SIZE
The ARCTWO block-size, 8.
@end defvr

@defvr Constant ARCTWO_MIN_KEY_SIZE
@end defvr

@defvr Constant ARCTWO_MAX_KEY_SIZE
@end defvr

@defvr Constant ARCTWO_KEY_SIZE
Default ARCTWO key size, 8.
@end defvr

@deftypefun void arctwo_set_key_ekb (struct arctwo_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key}, unsigned @var{ekb})
@deftypefunx void arctwo_set_key (struct arctwo_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
@deftypefunx void arctwo_set_key_gutmann (struct arctwo_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption
and decryption. The first function is the most general one, which lets
you provide both the variable size key, and the desired effective key
size (in bits). The maximum value for @var{ekb} is 1024, and for
convenience, @code{ekb = 0} has the same effect as @code{ekb = 1024}.

@code{arctwo_set_key(ctx, length, key)} is equivalent to
@code{arctwo_set_key_ekb(ctx, length, key, 8*length)}, and
@code{arctwo_set_key_gutmann(ctx, length, key)} is equivalent to
@code{arctwo_set_key_ekb(ctx, length, key, 1024)}
@end deftypefun

@deftypefun void arctwo_encrypt (struct arctwo_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not
overlap in any other way.
@end deftypefun

@deftypefun void arctwo_decrypt (struct arctwo_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{arctwo_encrypt}
@end deftypefun

@node Blowfish
@subsection Blowfish
@cindex Blowfish

BLOWFISH is a block cipher designed by Bruce Schneier. It uses a block
size of 64 bits (8 octets), and a variable key size, up to 448 bits. It
has some weak keys. Nettle defines BLOWFISH in @file{<nettle/blowfish.h>}.

@deftp {Context struct} {struct blowfish_ctx}
@end deftp

@defvr Constant BLOWFISH_BLOCK_SIZE
The BLOWFISH block-size, 8.
@end defvr

@defvr Constant BLOWFISH_MIN_KEY_SIZE
Minimum BLOWFISH key size, 8.
@end defvr

@defvr Constant BLOWFISH_MAX_KEY_SIZE
Maximum BLOWFISH key size, 56.
@end defvr

@defvr Constant BLOWFISH_KEY_SIZE
Default BLOWFISH key size, 16.
@end defvr

@deftypefun int blowfish_set_key (struct blowfish_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. Checks for weak keys, returning 1
for good keys and 0 for weak keys. Applications that don't care about
weak keys can ignore the return value.

@code{blowfish_encrypt} or @code{blowfish_decrypt} with a weak key will
crash with an assert violation.
@end deftypefun

@deftypefun void blowfish_encrypt (struct blowfish_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void blowfish_decrypt (struct blowfish_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{blowfish_encrypt}
@end deftypefun

@deftypefun int blowfish_bcrypt_hash (char *@var{dst}, size_t @var{lenkey}, const char *@var{key}, size_t @var{lenscheme}, const char *@var{scheme}, int @var{log2rounds}, const uint8_t *@var{salt})
Compute the bcrypt password hash.
The function will return @code{0} if the hash cannot be computed
due to invalid input.
The function will return @code{1} and store the computed hash
in the array pointed to by @var{dst}.  The hash is computed based
on the chosen @var{scheme}, number of rounds @var{log2rounds} and
specified @var{salt}.

@var{dst} must point to a character array of at least
 @code{BLOWFISH_BCRYPT_HASH_SIZE} bytes.

@var{key} contains the plaintext password string of size @var{lenkey}.

@var{scheme} is of size @var{lenscheme} and contains either just the
chosen scheme (valid schemes
are: @code{2a}, @code{2b}, @code{2x} or @code{2y}), or
(the prefix of) an existing hashed password (typically @code{$2b$10$...}).

@var{log2rounds} contains the log2 of the number of encryption rounds
that must be used to compute the hash.  If it is @code{-1} the value
will be extracted from @var{scheme}.

@var{salt} should point to an array of @code{BLOWFISH_BCRYPT_BINSALT_SIZE}
random bytes to be used to perturb the hash computation.  If it is @code{NULL}
the salt will be extracted from @var{scheme}.

Sample code to generate a bcrypt hash:
@example
char password[] = "ExamplePassword";
char scheme[] = "2b";
uint8_t salt[BLOWFISH_BCRYPT_BINSALT_SIZE];
@dots{}
/* Make sure that salt is filled with random bytes */
@dots{}
char hash[BLOWFISH_BCRYPT_HASH_SIZE];
int result = blowfish_bcrypt(hash,
                             sizeof(password) - 1, password,
                             sizeof(scheme) - 1, scheme, 10, salt);
if (result)
  printf("%s\n", hash);
@end example
@end deftypefun

@deftypefun int blowfish_bcrypt_verify (size_t @var{lenkey}, const char *@var{key}, size_t @var{lenhashed}, const char *@var{hashed})
Verifies the bcrypt password hash against the supplied plaintext password.
The function will return @code{0} if the password does not match.
The function will return @code{1} if the password matches.

@var{key} contains the plaintext password string of size @var{lenkey}.

@var{hashed} contains the hashed string of size @var{lenhashed} to compare with.

Sample code to verify a bcrypt hash:
@example
char password[] = "ExamplePassword";
char hash[] =
  "$2y$"  /* Hash algorithm version */
  "10"   /* 2^10 hash rounds (strength) */
  "$"   /* separator */
  "1b2lPgo4XumibnJGN3r3sO" /* base64 encoded 16-byte salt */
  "u7wE7xNfYDKlAxZffJDCJdVfFTAyevu"; /* Hashedpart */
if (blowfish_bcrypt_verify(sizeof(password) - 1, password,
                           sizeof(hash) - 1, hash))
  printf("Password is correct.");
else
  printf("Password is incorrect.");
@end example
@end deftypefun

@node Camellia
@subsection Camellia
@cindex Camellia

Camellia is a block cipher developed by Mitsubishi and Nippon Telegraph
and Telephone Corporation, described in @cite{RFC3713}. It is
recommended by some Japanese and European authorities as an alternative
to AES, and it is one of the selected algorithms in the New European
Schemes for Signatures, Integrity and Encryption (NESSIE) project. The
algorithm is patented. The implementation in Nettle is derived from the
implementation released by NTT under the GNU LGPL (v2.1 or later), and
relies on the implicit patent license of the LGPL. There is also a
statement of royalty-free licensing for Camellia at
@url{https://www.ntt.co.jp/news/news01e/0104/010417.html}, but this
statement has some limitations which seem problematic for free software.

Camellia uses a the same block size and key sizes as AES: The block size
is 128 bits (16 octets), and the supported key sizes are 128, 192, and
256 bits. The variants with 192 and 256 bit keys are identical, except
for the key setup. Nettle defines Camellia in
@file{<nettle/camellia.h>}, and there is one context struct for each key
size. (Earlier versions of Nettle used a single context struct,
@code{struct camellia_ctx}, for all key sizes. This interface kept for
backwards compatibility).

@deftp {Context struct} {struct camellia128_ctx}
@deftpx {Context struct} {struct camellia192_ctx}
@deftpx {Context struct} {struct camellia256_ctx}
Contexts structs. Actually, @code{camellia192_ctx} is an alias for
@code{camellia256_ctx}.
@end deftp

@deftp {Context struct} {struct camellia_ctx}
Alternative struct, for the old Camellia interface.
@end deftp

@defvr Constant CAMELLIA_BLOCK_SIZE
The CAMELLIA block-size, 16.
@end defvr

@defvr Constant CAMELLIA128_KEY_SIZE
@defvrx Constant CAMELLIA192_KEY_SIZE
@defvrx Constant CAMELLIA256_KEY_SIZE
@defvrx Constant CAMELLIA_MIN_KEY_SIZE
@defvrx Constant CAMELLIA_MAX_KEY_SIZE
@end defvr

@defvr Constant CAMELLIA_KEY_SIZE
Default CAMELLIA key size, 32.
@end defvr

@deftypefun void camellia128_set_encrypt_key (struct camellia128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia128_set_decrypt_key (struct camellia128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia192_set_encrypt_key (struct camellia192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia192_set_decrypt_key (struct camellia192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia256_set_encrypt_key (struct camellia256_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia256_set_decrypt_key (struct camellia256_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void camellia_set_encrypt_key (struct camellia_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
@deftypefunx void camellia_set_decrypt_key (struct camellia_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher, for encryption or decryption, respectively.
@end deftypefun

@deftypefun void camellia128_invert_key (struct camellia128_ctx *@var{dst}, const struct camellia128_ctx *@var{src})
@deftypefunx void camellia192_invert_key (struct camellia192_ctx *@var{dst}, const struct camellia192_ctx *@var{src})
@deftypefunx void camellia256_invert_key (struct camellia256_ctx *@var{dst}, const struct camellia256_ctx *@var{src})
@deftypefunx void camellia_invert_key (struct camellia_ctx *@var{dst}, const struct camellia_ctx *@var{src})
Given a context @var{src} initialized for encryption, initializes the
context struct @var{dst} for decryption, using the same key. If the same
context struct is passed for both @code{src} and @code{dst}, it is
converted in place. These functions are mainly useful for applications
which needs to both encrypt and decrypt using the @emph{same} key.
@end deftypefun

@deftypefun void camellia128_crypt (struct camellia128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void camellia192_crypt (struct camellia192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void camellia256_crypt (struct camellia256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void camellia_crypt (struct camellia_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
The same function is used for both encryption and decryption.
@var{length} must be an integral multiple of the block size. If it is
more than one block, the data is processed in ECB mode. @code{src} and
@code{dst} may be equal, but they must not overlap in any other way.
@end deftypefun

@node CAST128
@subsection CAST128
@cindex CAST

CAST-128 is a block cipher, specified in @cite{RFC 2144}. It uses a 64
bit (8 octets) block size, and a key size of 128 bits. It is possible,
but discouraged, to use the same algorithm with shorter keys. Nettle
refers to the variant with variable key size as CAST-5. Keys for CAST-5
are zero padded to 128 bits, and with very short keys, less than 80
bits, encryption also uses fewer rounds than CAST128. Nettle defines
cast128 in @file{<nettle/cast128.h>}.

@deftp {Context struct} {struct cast128_ctx}
@end deftp

@defvr Constant CAST128_BLOCK_SIZE
The CAST128 block-size, 8.
@end defvr

@defvr Constant CAST128_KEY_SIZE
The CAST128 key size, 16.
@end defvr

@defvr Constant CAST5_MIN_KEY_SIZE
Minimum CAST5 key size, 5.
@end defvr

@defvr Constant CAST5_MAX_KEY_SIZE
Maximum CAST5 key size, 16. With 16 octets key (128 bits), CAST-5 is the
same as CAST-128.
@end defvr

@deftypefun void cast128_set_key (struct cast128_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. 
@end deftypefun

@deftypefun void cast128_encrypt (struct cast128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void cast128_decrypt (struct cast128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{cast128_encrypt}
@end deftypefun

@deftypefun void cast5_set_key (struct cast128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. This variant of the key setup takes the key size
as argument. The same function is used for both encryption and
decryption.
@end deftypefun

@node ChaCha
@subsection ChaCha
@cindex ChaCha

ChaCha is a variant of the stream cipher Salsa20 (@pxref{Salsa20}),
below, also designed by D. J. Bernstein. Nettle defines ChaCha in
@file{<nettle/chacha.h>}.

@deftp {Context struct} {struct chacha_ctx}
@end deftp

@defvr Constant CHACHA_KEY_SIZE
ChaCha key size, 32.
@end defvr

@defvr Constant CHACHA_BLOCK_SIZE
ChaCha block size, 64.
@end defvr

@defvr Constant CHACHA_NONCE_SIZE
Size of the nonce, 8.
@end defvr

@defvr Constant CHACHA_COUNTER_SIZE
Size of the counter, 8.
@end defvr

@deftypefun void chacha_set_key (struct chacha_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. Before using the cipher,
you @emph{must} also call @code{chacha_set_nonce}, see below.
@end deftypefun

@deftypefun void chacha_set_nonce (struct chacha_ctx *@var{ctx}, const uint8_t *@var{nonce})
Sets the nonce. It is always of size @code{CHACHA_NONCE_SIZE}, 8
octets. This function also initializes the block counter, setting it to
zero.
@end deftypefun

@deftypefun void chacha_set_counter (struct chacha_ctx *@var{ctx}, const uint8_t *@var{counter})
Sets the block counter. It is always of size @code{CHACHA_COUNTER_SIZE},
8 octets. This is rarely needed since @code{chacha_set_nonce}
initializes the block counter to zero. When it is still necessary, this
function must be called after @code{chacha_set_nonce}.

@end deftypefun

@deftypefun void chacha_crypt (struct chacha_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message, using ChaCha. When a
message is encrypted using a sequence of calls to @code{chacha_crypt},
all but the last call @emph{must} use a length that is a multiple of
@code{CHACHA_BLOCK_SIZE}.
@end deftypefun

@subsubsection 32-bit counter variant

While the original paper uses 64-bit counter value, the variant defined
in @cite{RFC 8439} uses 32-bit counter value. This variant is
particularly useful for @pxref{ChaCha-Poly1305} AEAD construction, which
supports 12-octet nonces.

@defvr Constant CHACHA_NONCE96_SIZE
Size of the nonce, 12.
@end defvr

@defvr Constant CHACHA_COUNTER32_SIZE
Size of the counter, 4.
@end defvr

@deftypefun void chacha_set_nonce96 (struct chacha_ctx *@var{ctx}, const uint8_t *@var{nonce})
Sets the nonce. This is similar to the above @code{chacha_set_nonce},
but the input is always of size @code{CHACHA_NONCE96_SIZE}, 12 octets.
@end deftypefun

@deftypefun void chacha_set_counter32 (struct chacha_ctx *@var{ctx}, const uint8_t *@var{counter})
Sets the block counter. This is similar to the above @code{chacha_set_counter},
but the input is always of size @code{CHACHA_COUNTER32_SIZE}, 4 octets.
@end deftypefun

@deftypefun void chacha_crypt32 (struct chacha_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message, using ChaCha. This is similar to the
above @code{chacha_crypt}, but it assumes the internal counter value is 32-bit
long and the nonce is 96-bit long.
@end deftypefun

@node DES
@subsection DES
@cindex DES

DES is the old Data Encryption Standard, specified by NIST. It uses a
block size of 64 bits (8 octets), and a key size of 56 bits. However,
the key bits are distributed over 8 octets, where the least significant
bit of each octet may be used for parity. A common way to use DES is to
generate 8 random octets in some way, then set the least significant bit
of each octet to get odd parity, and initialize DES with the resulting
key.

The key size of DES is so small that keys can be found by brute force,
using specialized hardware or lots of ordinary work stations in
parallel. One shouldn't be using plain DES at all today, if one uses
DES at all one should be using ``triple DES'', see DES3 below.

DES also has some weak keys. Nettle defines DES in @file{<nettle/des.h>}.

@deftp {Context struct} {struct des_ctx}
@end deftp

@defvr Constant DES_BLOCK_SIZE
The DES block-size, 8.
@end defvr

@defvr Constant DES_KEY_SIZE
DES key size, 8.
@end defvr

@deftypefun int des_set_key (struct des_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. Parity bits are ignored. Checks for weak keys, returning 1
for good keys and 0 for weak keys. Applications that don't care about
weak keys can ignore the return value.
@end deftypefun

@deftypefun void des_encrypt (struct des_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void des_decrypt (struct des_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{des_encrypt}
@end deftypefun

@deftypefun int des_check_parity (size_t @var{length}, const uint8_t *@var{key})
Checks that the given key has correct, odd, parity. Returns 1 for
correct parity, and 0 for bad parity.
@end deftypefun

@deftypefun void des_fix_parity (size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Adjusts the parity bits to match DES's requirements. You need this
function if you have created a random-looking string by a key agreement
protocol, and want to use it as a DES key. @var{dst} and @var{src} may
be equal.
@end deftypefun

@node DES3
@subsection DES3
@cindex DES3
@cindex 3DES
@cindex Triple-DES

The inadequate key size of DES has already been mentioned. One way to
increase the key size is to pipe together several DES boxes with
independent keys. It turns out that using two DES ciphers is not as
secure as one might think, even if the key size of the combination is a
respectable 112 bits.

The standard way to increase DES's key size is to use three DES boxes.
The mode of operation is a little peculiar: the middle DES box is wired
in the reverse direction. To encrypt a block with DES3, you encrypt it
using the first 56 bits of the key, then @emph{decrypt} it using the
middle 56 bits of the key, and finally encrypt it again using the last
56 bits of the key. This is known as ``ede'' triple-DES, for
``encrypt-decrypt-encrypt''.

The ``ede'' construction provides some backward compatibility, as you get
plain single DES simply by feeding the same key to all three boxes. That
should help keeping down the gate count, and the price, of hardware
circuits implementing both plain DES and DES3.

DES3 has a key size of 168 bits, but just like plain DES, useless parity
bits are inserted, so that keys are represented as 24 octets (192 bits).
As a 112 bit key is large enough to make brute force attacks
impractical, some applications uses a ``two-key'' variant of triple-DES.
In this mode, the same key bits are used for the first and the last DES
box in the pipe, while the middle box is keyed independently. The
two-key variant is believed to be secure, i.e. there are no known
attacks significantly better than brute force.

Naturally, it's simple to implement triple-DES on top of Nettle's DES
functions. Nettle includes an implementation of three-key ``ede''
triple-DES, it is defined in the same place as plain DES,
@file{<nettle/des.h>}.

@deftp {Context struct} {struct des3_ctx}
@end deftp

@defvr Constant DES3_BLOCK_SIZE
The DES3 block-size is the same as DES_BLOCK_SIZE, 8.
@end defvr

@defvr Constant DES3_KEY_SIZE
DES key size, 24.
@end defvr

@deftypefun int des3_set_key (struct des3_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. Parity bits are ignored. Checks for weak keys, returning 1
if all three keys are good keys, and 0 if one or more key is weak.
Applications that don't care about weak keys can ignore the return
value.
@end deftypefun

For random-looking strings, you can use @code{des_fix_parity} to adjust
the parity bits before calling @code{des3_set_key}.

@deftypefun void des3_encrypt (struct des3_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void des3_decrypt (struct des3_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{des_encrypt}
@end deftypefun

@node Salsa20
@subsection Salsa20
@cindex Salsa20

Salsa20 is a fairly recent stream cipher designed by D. J. Bernstein. It
is built on the observation that a cryptographic hash function can be
used for encryption: Form the hash input from the secret key and a
counter, xor the hash output and the first block of the plaintext, then
increment the counter to process the next block (similar to CTR mode,
@pxref{CTR}). Bernstein defined an encryption algorithm, Snuffle,
in this way to ridicule United States export restrictions which treated hash
functions as nice and harmless, but ciphers as dangerous munitions.

Salsa20 uses the same idea, but with a new specialized hash function to
mix key, block counter, and a couple of constants. It's also designed
for speed; on x86_64, it is currently the fastest cipher offered by
nettle. It uses a block size of 512 bits (64 octets) and there are two
specified key sizes, 128 and 256 bits (16 and 32 octets).

@strong{Caution:} The hash function used in Salsa20 is @emph{not}
directly applicable for use as a general hash function. It's @emph{not}
collision resistant if arbitrary inputs are allowed, and furthermore,
the input and output is of fixed size.

When using Salsa20 to process a message, one specifies both a key and a
@dfn{nonce}, the latter playing a similar rôle to the initialization
vector (@acronym{IV}) used with @acronym{CBC} or @acronym{CTR} mode. One
can use the same key for several messages, provided one uses a unique
random @acronym{iv} for each message. The @acronym{iv} is 64 bits (8
octets). The block counter is initialized to zero for each message, and
is also 64 bits (8 octets). Nettle defines Salsa20 in
@file{<nettle/salsa20.h>}.

@deftp {Context struct} {struct salsa20_ctx}
@end deftp

@defvr Constant SALSA20_128_KEY_SIZE
@defvrx Constant SALSA20_256_KEY_SIZE
The two supported key sizes, 16 and 32 octets.
@end defvr

@defvr Constant SALSA20_KEY_SIZE
Recommended key size, 32.
@end defvr

@defvr Constant SALSA20_BLOCK_SIZE
Salsa20 block size, 64.
@end defvr

@defvr Constant SALSA20_NONCE_SIZE
Size of the nonce, 8.
@end defvr

@deftypefun void salsa20_128_set_key (struct salsa20_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void salsa20_256_set_key (struct salsa20_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void salsa20_set_key (struct salsa20_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. @code{salsa20_128_set_key} and @code{salsa20_128_set_key}
use a fix key size each, 16 and 32 octets, respectively. The function
@code{salsa20_set_key} is provided for backwards compatibility, and the
@var{length} argument must be either 16 or 32. Before using the cipher,
you @emph{must} also call @code{salsa20_set_nonce}, see below.
@end deftypefun

@deftypefun void salsa20_set_nonce (struct salsa20_ctx *@var{ctx}, const uint8_t *@var{nonce})
Sets the nonce. It is always of size @code{SALSA20_NONCE_SIZE}, 8
octets. This function also initializes the block counter, setting it to
zero.
@end deftypefun

@deftypefun void salsa20_crypt (struct salsa20_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message, using salsa20. When a
message is encrypted using a sequence of calls to @code{salsa20_crypt},
all but the last call @emph{must} use a length that is a multiple of
@code{SALSA20_BLOCK_SIZE}.
@end deftypefun

The full salsa20 cipher uses 20 rounds of mixing. Variants of Salsa20
with fewer rounds are possible, and the 12-round variant is specified by
eSTREAM, see @url{https://www.ecrypt.eu.org/stream/finallist.html}.
Nettle calls this variant @code{salsa20r12}. It uses the same context
struct and key setup as the full salsa20 cipher, but a separate function
for encryption and decryption.

@deftypefun void salsa20r12_crypt (struct salsa20_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message, using salsa20 reduced to 12
rounds.
@end deftypefun

@node Serpent
@subsection Serpent
@cindex Serpent

SERPENT is one of the AES finalists, designed by Ross Anderson, Eli
Biham and Lars Knudsen. Thus, the interface and properties are similar
to AES'. One peculiarity is that it is quite pointless to use it with
anything but the maximum key size, smaller keys are just padded to
larger ones. Nettle defines SERPENT in @file{<nettle/serpent.h>}.

@deftp {Context struct} {struct serpent_ctx}
@end deftp

@defvr Constant SERPENT_BLOCK_SIZE
The SERPENT block-size, 16.
@end defvr

@defvr Constant SERPENT_MIN_KEY_SIZE
Minimum SERPENT key size, 16.
@end defvr

@defvr Constant SERPENT_MAX_KEY_SIZE
Maximum SERPENT key size, 32.
@end defvr

@defvr Constant SERPENT_KEY_SIZE
Default SERPENT key size, 32.
@end defvr

@deftypefun void serpent_set_key (struct serpent_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. 
@end deftypefun

@deftypefun void serpent_encrypt (struct serpent_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void serpent_decrypt (struct serpent_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{serpent_encrypt}
@end deftypefun

@node SM4
@subsection SM4
@cindex SM4

SM4 is a block cipher standard adopted by the government of the People's
Republic of China, and it was issued by the State Cryptography Administration
on March 21, 2012. The standard is GM/T 0002-2012 "SM4 block cipher algorithm".
Nettle defines it in @file{<nettle/sm4.h>}.

@deftp {Context struct} {struct sm4_ctx}
@end deftp

@defvr Constant SM4_BLOCK_SIZE
The SM4 block-size, 16.
@end defvr

@defvr Constant SM4_KEY_SIZE
Default SM4 key size, 16.
@end defvr

@deftypefun void sm4_set_encrypt_key (struct sm4_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The function is used for encryption.
@end deftypefun

@deftypefun void sm4_set_decrypt_key (struct sm4_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the cipher. The function is used for decryption.
@end deftypefun

@deftypefun void sm4_crypt (const struct sm4_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Cryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way. The same function is used for both encryption and
decryption.
@end deftypefun

@node Twofish
@subsection Twofish
@cindex Twofish

Another AES finalist, this one designed by Bruce Schneier and others.
Nettle defines it in @file{<nettle/twofish.h>}.

@deftp {Context struct} {struct twofish_ctx}
@end deftp

@defvr Constant TWOFISH_BLOCK_SIZE
The TWOFISH block-size, 16.
@end defvr

@defvr Constant TWOFISH_MIN_KEY_SIZE
Minimum TWOFISH key size, 16.
@end defvr

@defvr Constant TWOFISH_MAX_KEY_SIZE
Maximum TWOFISH key size, 32.
@end defvr

@defvr Constant TWOFISH_KEY_SIZE
Default TWOFISH key size, 32.
@end defvr

@deftypefun void twofish_set_key (struct twofish_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. 
@end deftypefun

@deftypefun void twofish_encrypt (struct twofish_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encryption function. @var{length} must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. @code{src} and @code{dst} may be equal, but they must not overlap
in any other way.
@end deftypefun

@deftypefun void twofish_decrypt (struct twofish_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Analogous to @code{twofish_encrypt}
@end deftypefun

@node nettle_cipher abstraction
@subsection The @code{struct nettle_cipher} abstraction
@cindex nettle_cipher

Nettle includes a struct including information about some of the more
regular cipher functions. It can be useful for applications that need a
simple way to handle various algorithms. Nettle defines these structs in
@file{<nettle/nettle-meta.h>}.

@deftp {Meta struct} @code{struct nettle_cipher} name context_size block_size key_size set_encrypt_key set_decrypt_key encrypt decrypt
The last four attributes are function pointers, of types
@code{nettle_set_key_func *} and @code{nettle_cipher_func *}. The first
argument to these functions is a @code{const void *} pointer to a context
struct, which is of size @code{context_size}.
@end deftp

@deftypevr {Constant Struct} {struct nettle_cipher} nettle_aes128
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_aes192
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_aes256

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_arctwo40
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_arctwo64
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_arctwo128
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_arctwo_gutmann128

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_arcfour128

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_camellia128
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_camellia192
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_camellia256

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_cast128

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_serpent128
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_serpent192
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_serpent256

@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_twofish128
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_twofish192
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_twofish256
Nettle includes such structs for all the @emph{regular} ciphers, i.e.
ones without weak keys or other oddities.
@end deftypevr

Nettle also exports a list of all these ciphers without weak keys or
other oddities.

@deftypefun {const struct nettle_cipher **} nettle_get_ciphers (void)
Returns a NULL-terminated list of pointers to supported block ciphers.
This list can be used to dynamically enumerate or search the supported
algorithms.
@end deftypefun

@deffn Macro nettle_ciphers
A macro expanding to a call to nettle_get_ciphers. In earlier versions,
this was not a macro but the actual array of pointers.
@end deffn

@node Cipher modes
@section Cipher modes

Cipher modes of operation specifies the procedure to use when encrypting
a message that is larger than the cipher's block size. As explained in
@xref{Cipher functions}, splitting the message into blocks and
processing them independently with the block cipher (Electronic Code
Book mode, @acronym{ECB}), leaks information.

Besides @acronym{ECB}, Nettle provides several other modes of operation:
Cipher Block Chaining (@acronym{CBC}), Counter mode (@acronym{CTR}), Cipher
Feedback (@acronym{CFB} and @acronym{CFB8}), XEX-based tweaked-codebook mode
with ciphertext stealing (@acronym{XTS}) and a couple of @acronym{AEAD}
modes (@pxref{Authenticated encryption}).  @acronym{CBC} is widely used, but
there are a few subtle issues of information leakage, see, e.g.,
@url{https://www.kb.cert.org/vuls/id/958563, @acronym{SSH} @acronym{CBC}
vulnerability}. Today, @acronym{CTR} is usually preferred over @acronym{CBC}.

Modes like @acronym{CBC}, @acronym{CTR}, @acronym{CFB} and @acronym{CFB8}
provide @emph{no} message authentication, and should always be used together
with a @acronym{MAC} (@pxref{Keyed hash functions}) or signature to
authenticate the message.

@menu
* CBC::
* CTR::
* CFB and CFB8::
* XTS::
@end menu

@node CBC
@subsection Cipher Block Chaining

@cindex Cipher Block Chaining
@cindex CBC Mode

When using @acronym{CBC} mode, plaintext blocks are not encrypted
independently of each other, like in Electronic Cook Book mode. Instead,
when encrypting a block in @acronym{CBC} mode, the previous ciphertext
block is XORed with the plaintext before it is fed to the block cipher.
When encrypting the first block, a random block called an @dfn{IV}, or
Initialization Vector, is used as the ``previous ciphertext block''. The
IV should be chosen randomly, but it need not be kept secret, and can
even be transmitted in the clear together with the encrypted data.

In symbols, if @code{E_k} is the encryption function of a block cipher,
and @code{IV} is the initialization vector, then @code{n} plaintext blocks
@code{M_1},@dots{} @code{M_n} are transformed into @code{n} ciphertext blocks
@code{C_1},@dots{} @code{C_n} as follows:

@example
C_1 = E_k(IV  XOR M_1)
C_2 = E_k(C_1 XOR M_2)

@dots{}

C_n = E_k(C_(n-1) XOR M_n)
@end example

Nettle provides two main functions for applying a block cipher in
Cipher Block Chaining (@acronym{CBC}) mode, one for encryption and one
for decryption. These functions uses @code{const void *} to pass cipher
contexts around. The @acronym{CBC} interface is defined in
@file{<nettle/cbc.h>}.

@deftypefun {void} cbc_encrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx {void} cbc_decrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})

Applies the encryption or decryption function @var{f} in @acronym{CBC}
mode. The final ciphertext block processed is copied into @var{iv}
before returning, so that a large message can be processed by a sequence of
calls to @code{cbc_encrypt}. The function @var{f} is of type

@code{void @var{f} (const void *@var{ctx}, size_t @var{length}, uint8_t @var{dst},
const uint8_t *@var{src})},

@noindent and the @code{cbc_encrypt} and @code{cbc_decrypt} functions pass their
argument @var{ctx} on to @var{f}.
@end deftypefun

@subsubsection Utility macros

There are also some macros to help use these functions correctly.

@deffn Macro CBC_CTX (@var{context_type}, @var{block_size})
Expands to
@example
@{
   context_type ctx;
   uint8_t iv[block_size];
@}
@end example
@end deffn

It can be used to define a @acronym{CBC} context struct, either directly,

@example
struct CBC_CTX(struct aes_ctx, AES_BLOCK_SIZE) ctx;
@end example

or to give it a struct tag,

@example
struct aes_cbc_ctx CBC_CTX (struct aes_ctx, AES_BLOCK_SIZE);
@end example

@deffn Macro CBC_SET_IV (@var{ctx}, @var{iv})
First argument is a pointer to a context struct as defined by @code{CBC_CTX},
and the second is a pointer to an Initialization Vector (IV) that is
copied into that context.
@end deffn

@deffn Macro CBC_ENCRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
@deffnx Macro CBC_DECRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{cbc_encrypt} and @code{cbc_decrypt}. The
first argument is a pointer to a context struct as defined by
@code{CBC_CTX}, and the second argument is an encryption or decryption
function following Nettle's conventions. The last three arguments define
the source and destination area for the operation.
@end deffn

These macros use some tricks to make the compiler display a warning if
the types of @var{f} and @var{ctx} don't match, e.g. if you try to use
an @code{struct aes_ctx} context with the @code{des_encrypt} function.

@subsubsection Cipher-specific functions

Encryption in @acronym{CBC} mode (but not decryption!) is inherently
serial. It can pass only one block at a time to the block cipher's
encrypt function. Optimizations to process several blocks in parallel
can't be applied, and on platforms where the underlying cipher is fast,
per-function-call overhead, e.g., loading subkeys from memory into
registers, can be significant. Depending on platform and cipher used,
@code{cbc_encrypt} can be considerably slower than both
@code{cbc_decrypt} and @acronym{CTR} mode. The second reason for poor
performance can be addressed by having a combined @acronym{CBC} and
encrypt function, for ciphers where the overhead is significant.

Nettle currently includes such special functions only for AES.

@deftypefun void cbc_aes128_encrypt (const struct aes128_ctx *@var{ctx}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void cbc_aes192_encrypt (const struct aes192_ctx *@var{ctx}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void cbc_aes256_encrypt (const struct aes256_ctx *@var{ctx}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Calling @code{cbc_aes128_encrypt(ctx, iv, length, dst, src)} does the
same thing as calling @code{cbc_encrypt(ctx, aes128_encrypt,
AES_BLOCK_SIZE, iv, length, dst, src)}, but is more efficient on certain
platforms.
@end deftypefun

@node CTR
@subsection Counter mode

@cindex Counter Mode
@cindex CTR Mode

Counter mode (@acronym{CTR}) uses the block cipher as a keyed
pseudo-random generator. The output of the generator is XORed with the
data to be encrypted. It can be understood as a way to transform a block
cipher to a stream cipher.

The message is divided into @code{n} blocks @code{M_1},@dots{}
@code{M_n}, where @code{M_n} is of size @code{m} which may be smaller
than the block size. Except for the last block, all the message blocks
must be of size equal to the cipher's block size.

If @code{E_k} is the encryption function of a block cipher, @code{IC} is
the initial counter, then the @code{n} plaintext blocks are
transformed into @code{n} ciphertext blocks @code{C_1},@dots{}
@code{C_n} as follows:

@example
C_1 = E_k(IC) XOR M_1
C_2 = E_k(IC + 1) XOR M_2

@dots{}

C_(n-1) = E_k(IC + n - 2) XOR M_(n-1)
C_n = E_k(IC + n - 1) [1..m] XOR M_n
@end example

The @acronym{IC} is the initial value for the counter, it plays a
similar rôle as the @acronym{IV} for @acronym{CBC}. When adding,
@code{IC + x}, @acronym{IC} is interpreted as an integer, in network
byte order. For the last block, @code{E_k(IC + n - 1) [1..m]} means that
the cipher output is truncated to @code{m} bytes.

@deftypefun {void} ctr_crypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{ctr}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})

Applies the encryption function @var{f} in @acronym{CTR} mode. Note that
for @acronym{CTR} mode, encryption and decryption is the same operation,
and hence @var{f} should always be the encryption function for the
underlying block cipher.

When a message is encrypted using a sequence of calls to
@code{ctr_crypt}, all but the last call @emph{must} use a length that is
a multiple of the block size.
@end deftypefun

Like for @acronym{CBC}, there are also a couple of helper macros.

@deffn Macro CTR_CTX (@var{context_type}, @var{block_size})
Expands to
@example
@{
   context_type ctx;
   uint8_t ctr[block_size];
@}
@end example
@end deffn

@deffn Macro CTR_SET_COUNTER (@var{ctx}, @var{iv})
First argument is a pointer to a context struct as defined by
@code{CTR_CTX}, and the second is a pointer to an initial counter that
is copied into that context.
@end deffn

@deffn Macro CTR_CRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{ctr_crypt}. The first argument is a
pointer to a context struct as defined by @code{CTR_CTX}, and the second
argument is an encryption function following Nettle's conventions. The
last three arguments define the source and destination area for the
operation.
@end deffn

@node CFB and CFB8
@subsection Cipher Feedback mode

@cindex Cipher Feedback Mode
@cindex Cipher Feedback 8-bit Mode
@cindex CFB Modes
@cindex CFB8 Mode


Cipher Feedback mode (@acronym{CFB}) and Cipher Feedback 8-bit mode
(@acronym{CFB8}) being close relatives to both @acronym{CBC} mode and
@acronym{CTR} mode borrow some characteristics from stream ciphers.

For CFB the message is divided into @code{n} blocks @code{M_1},@dots{}
@code{M_n}, where @code{M_n} is of size @code{m} which may be smaller
than the block size. Except for the last block, all the message blocks
must be of size equal to the cipher's block size.

If @code{E_k} is the encryption function of a block cipher, @code{IV} is
the initialization vector, then the @code{n} plaintext blocks are
transformed into @code{n} ciphertext blocks @code{C_1},@dots{}
@code{C_n} as follows:

@example
C_1 = E_k(IV) XOR M_1
C_2 = E_k(C_1) XOR M_2

@dots{}

C_(n-1) = E_k(C_(n - 2)) XOR M_(n-1)
C_n = E_k(C_(n - 1)) [1..m] XOR M_n
@end example

Cipher Feedback 8-bit mode (@acronym{CFB8}) transforms block cipher into a stream
cipher. The message is encrypted byte after byte, not requiring any padding.

If @code{E_k} is the encryption function of a block cipher, @code{b} is
@code{E_k} block size, @code{IV} is the initialization vector, then the
@code{n} plaintext bytes are transformed into @code{n} ciphertext bytes
@code{C_1},@dots{} @code{C_n} as follows:

@example
I_1 = IV
C_1 = E_k(I_1) [1..8] XOR M_1
I_2 = I_1 [9..b] << 8 | C_1
C_2 = E_k(I_2) [1..8] XOR M_2

@dots{}

I_(n-1) = I_(n-2) [9..b] << 8 | C_(n-2)
C_(n-1) = E_k(I_(n-1)) [1..8] XOR M_(n-1)
I_n = I_(n-1) [9..b] << 8 | C_(n-1)
C_n = E_k(I_n) [1..8] XOR M_n
@end example

Nettle's includes functions for applying a block cipher in Cipher
Feedback (@acronym{CFB}) and Cipher Feedback 8-bit (@acronym{CFB8})
modes. These functions uses @code{void *} to pass cipher contexts around.

@deftypefun {void} cfb_encrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx {void} cfb_decrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})

Applies the encryption or decryption function @var{f} in @acronym{CFB}
mode. The final ciphertext block processed is copied into @var{iv}
before returning, so that a large message can be processed by a sequence
of calls to @code{cfb_encrypt}. Note that for @acronym{CFB} mode
internally uses encryption only function and hence @var{f} should always
be the encryption function for the underlying block cipher.

When a message is encrypted using a sequence of calls to
@code{cfb_encrypt}, all but the last call @emph{must} use a length that
is a multiple of the block size.
@end deftypefun

@deftypefun {void} cfb8_encrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx {void} cfb8_decrypt (const void *@var{ctx}, nettle_cipher_func *@var{f}, size_t @var{block_size}, uint8_t *@var{iv}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})

Applies the encryption or decryption function @var{f} in @acronym{CFB8}
mode. The final IV block processed is copied into @var{iv}
before returning, so that a large message can be processed by a sequence of
calls to @code{cfb8_encrypt}. Note that for @acronym{CFB8} mode internally
uses encryption only function and hence @var{f} should always be the
encryption function for the underlying block cipher.

@end deftypefun

Like for @acronym{CBC}, there are also a couple of helper macros.

@deffn Macro CFB_CTX (@var{context_type}, @var{block_size})
Expands to
@example
@{
   context_type ctx;
   uint8_t iv[block_size];
@}
@end example
@end deffn

@deffn Macro CFB_SET_IV(@var{ctx}, @var{iv})
First argument is a pointer to a context struct as defined by
@code{CFB_CTX}, and the second is a pointer to an initialization vector
that is copied into that context.
@end deffn

@deffn Macro CFB_ENCRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{cfb_encrypt}. The first argument is a
pointer to a context struct as defined by @code{CFB_CTX}, and the second
argument is an encryption function following Nettle's conventions. The
last three arguments define the source and destination area for the
operation.
@end deffn

@deffn Macro CFB_DECRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{cfb_decrypt}. The first argument is a
pointer to a context struct as defined by @code{CFB_CTX}, and the second
argument is an encryption function following Nettle's conventions. The
last three arguments define the source and destination area for the
operation.
@end deffn

@deffn Macro CFB8_CTX (@var{context_type}, @var{block_size})
Expands to
@example
@{
   context_type ctx;
   uint8_t iv[block_size];
@}
@end example
@end deffn

@deffn Macro CFB8_SET_IV (@var{ctx}, @var{iv})
First argument is a pointer to a context struct as defined by
@code{CFB8_CTX}, and the second is a pointer to an initialization vector
that is copied into that context.
@end deffn

@deffn Macro CFB8_ENCRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{cfb8_encrypt}. The first argument is a
pointer to a context struct as defined by @code{CFB8_CTX}, and the
second argument is an encryption function following Nettle's
conventions. The last three arguments define the source and destination
area for the operation.
@end deffn

@deffn Macro CFB8_DECRYPT (@var{ctx}, @var{f}, @var{length}, @var{dst}, @var{src})
A simpler way to invoke @code{cfb8_decrypt}. The first argument is a
pointer to a context struct as defined by @code{CFB8_CTX}, and the
second argument is an encryption function following Nettle's
conventions. The last three arguments define the source and destination
area for the operation.
@end deffn

@node XTS
@subsection XEX-based tweaked-codebook mode with ciphertext stealing

@cindex XEX-based tweaked-codebook mode with ciphertext stealing
@cindex XTS Mode


XEX-based tweaked-codebook mode with ciphertext stealing (@acronym{XTS}) is
a block mode like (@acronym{CBC}) but tweaked to be able to encrypt partial
blocks via a technique called ciphertext stealing, where the last complete
block of ciphertext is split and part returned as the last block and part
used as plaintext for the second to last block.
This mode is principally used to encrypt data at rest where it is not possible
to store additional metadata or blocks larger than the plain text. The most
common usage is for disk encryption. Due to the fact that ciphertext expansion
is not possible, data is not authenticated. This mode should not be used where
authentication is critical.

The message is divided into @code{n} blocks @code{M_1},@dots{} @code{M_n},
where @code{M_n} is of size @code{m} which may be smaller than the block size.
XTS always uses a fixed blocksize of 128 bit (16 bytes) length.

Unlike other modes, the key is double the size of that for the used cipher mode
(for example 256bit for AES-128 and 512bit for AES-256).

@acronym{XTS} encryption mode operates given:
@itemize
@item A multiplication by a primitive element alpha.
@code{MUL a^j} here represents the multiplication, where @code{j} is the power
of alpha, and the input value is converted into a 16 bytes array
@code{a_0[k], k = 0,1,..,15}. The multiplication is calculated as
@code{a_(j+1)[0] = (2(a_j[0] mod 128)) XOR (135 * floor(a_j[15]/128)}
@code{a_(j+1)[k] = (2(a_j[k] mod 128)) XOR (floor(a_j[k-1]/128), k = 1,2,..15}
Note that this operation is practically a 1 bit left shift operation with carry
propagating from one byte to the next, and if the last bit shift results in a
carry the decimal value 135 is XORed into the first byte.

@item The encryption key is provided as the @code{Key = K1 | K2}, where @code{|}
denotes string concatenation.
@code{E_k1} is the encryption function of the block cipher using @code{K1} as
the key, and @code{E_k2} is the same encryption function using @code{K2}

@item A 128 bit tweak value is provided as input and is denoted as @code{IV}
@end itemize

The @code{n} plaintext blocks are transformed into @code{n} ciphertext blocks
@code{C_1},@dots{} @code{C_n} as follows.

For a plaintext length that is a perfect multiple of the XTS block size:
@example
T_1 = E_k2(IV)
C_1 = E_k1(P_1 XOR T_1) XOR T_1

@dots{}

T_n = T_(n-1) MUL a
C_n = E_k1(P_n XOR T_n) XOR T_n
@end example

For any other plaintext lengths:
@example
T_1 = E_k2(IV)
C_1 = E_k1(P_1 XOR T_1) XOR T_1

@dots{}

T_(n-2) = T_(n-3) MUL a
C_(n-2) = E_k1(P_(n-2) XOR T_(n-2)) XOR T_(n-2)

T_(n-1) = T_(n-2) MUL a
CC_(n-1) = E_k1(P_(n-1) XOR T_(n-1)) XOR T_(n-1)

T_n = T_(n-1) MUL a
PP = [1..m]Pn | [m+1..128]CC_(n-1)
C_(n-1) = E_k1(PP XOR T_n) XOR T_n

C_n = [1..m]CC_(n-1)
@end example

@subsubsection General (@acronym{XTS}) interface.

The two general functions to encrypt and decrypt using the @acronym{XTS} block
cipher mode are the following:

@deftypefun void xts_encrypt_message (const void *@var{enc_ctx}, const void *@var{twk_ctx}, nettle_cipher_func *@var{encf}, const uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void xts_decrypt_message (const void *@var{dec_ctx}, const void *@var{twk_ctx}, nettle_cipher_func *@var{decf}, nettle_cipher_func *@var{encf}, const uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})

Applies the encryption function @var{encf} or the decryption function
@var{decf} in @acronym{XTS} mode. At least one block (16 bytes) worth
of data must be available therefore specifying a length less than 16
bytes is illegal.

The functions @var{encf} @var{decf} are of type

@code{void f (const void *@var{ctx}, size_t @var{length}, uint8_t *@var{dst},
const uint8_t *@var{src})},

@noindent and the @code{xts_encrypt_message} and @code{xts_decrypt_message}
functions pass their arguments @var{enc_ctx}, @var{twk_ctx} and @var{dec_ctx}
to the functions @var{encf}, @var{decf} as @var{ctx}.
@end deftypefun

@subsubsection @acronym{XTS}-@acronym{AES} interface

The @acronym{AES} @acronym{XTS} functions provide an API for using the
@acronym{XTS} mode with the @acronym{AES} block ciphers. The parameters
all have the same meaning as the general interface, except that the
@var{enc_ctx}, @var{dec_ctx}, @var{twk_ctx}, @var{encf} and @var{decf} are
replaced with an @acronym{AES} context structure called @var{ctx}, and a
appropriate set-key function must be called before using any of the encryption
or decryption functions in this interface.

@deftp {Context struct} {struct xts_aes128_key}
Holds state corresponding to the AES-128 block cipher.
@end deftp

@deftp {Context struct} {struct xts_aes256_key}
Holds state corresponding to the AES-256 block cipher.
@end deftp

@deftypefun void xts_aes128_set_encrypt_key (struct xts_aes128_key *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void xts_aes256_set_encrypt_key (struct xts_aes256_key *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void xts_aes128_set_decrypt_key (struct xts_aes128_key *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void xts_aes256_set_decrypt_key (struct xts_aes256_key *@var{ctx}, const uint8_t *@var{key})
Initializes the encryption or decryption key for the AES block cipher. The
length of the key must be double the size of the key for the corresponding
cipher (256 bits for AES-128 and 512 bits for AES-256). One of
these functions must be called before any of the other functions.
@end deftypefun

@deftypefun void xts_aes128_encrypt_message (struct xts_aes128_key *@var{ctx}, uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void xts_aes256_encrypt_message (struct xts_aes256_key *@var{ctx}, uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void xts_aes128_decrypt_message (struct xts_aes128_key *@var{ctx}, uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void xts_aes256_decrypt_message (struct xts_aes256_key *@var{ctx}, uint8_t *@var{tweak}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
These are identical to @code{xts_encrypt_message} and
@code{xts_decrypt_message}, except that @var{enc_ctx}, @var{dec_ctx},
@var{twk_ctx}, @var{encf} and @var{decf} are replaced by the @var{ctx} context
structure.
@end deftypefun

@node Authenticated encryption
@section Authenticated encryption with associated data
@cindex AEAD
@cindex Authenticated encryption

Since there are some subtle design choices to be made when combining a
block cipher mode with out authentication with a @acronym{MAC}. In
recent years, several constructions that combine encryption and
authentication have been defined. These constructions typically also
have an additional input, the ``associated data'', which is
authenticated but not included with the message. A simple example is an
implicit message number which is available at both sender and receiver,
and which needs authentication in order to detect deletions or replay of
messages. This family of building blocks are therefore called
@acronym{AEAD}, Authenticated encryption with associated data.

The aim is to provide building blocks that it is easier for designers of
protocols and applications to use correctly. There is also some
potential for improved performance, if encryption and authentication can
be done in a single step, although that potential is not realized for
the constructions currently supported by Nettle.

For encryption, the inputs are:

@itemize
@item
The key, which can be used for many messages.
@item 
A nonce, which must be unique for each message using the same key.
@item
Additional associated data to be authenticated, but not included in the
message.
@item
The cleartext message to be encrypted.
@end itemize

The outputs are:

@itemize
@item
The ciphertext, of the same size as the cleartext.
@item
A digest or ``authentication tag''.
@end itemize

Decryption works the same, but with cleartext and ciphertext
interchanged. All currently supported @acronym{AEAD} algorithms always
use the encryption function of the underlying block cipher, for both
encryption and decryption.

Usually, the authentication tag should be appended at the end of the
ciphertext, producing an encrypted message which is slightly longer than
the cleartext. However, Nettle's low level @acronym{AEAD} functions
produce the authentication tag as a separate output for both encryption
and decryption.

Both associated data and the message data (cleartext or ciphertext) can
be processed incrementally. In general, all associated data must be
processed before the message data, and all calls but the last one must
use a length that is a multiple of the block size, although some
@acronym{AEAD} may implement more liberal conventions. The @acronym{CCM}
mode is a bit special in that it requires the message lengths up front,
other @acronym{AEAD} constructions don't have this restriction.

The supported @acronym{AEAD} constructions are Galois/Counter mode
(@acronym{GCM}), @acronym{EAX}, ChaCha-Poly1305, and Counter with
@acronym{CBC}-@acronym{MAC} (@acronym{CCM}). There are some weaknesses
in @acronym{GCM} authentication, see
@url{https://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments@//CWC-GCM/Ferguson2.pdf}.
@acronym{CCM} and @acronym{EAX} use the same building blocks, but the
@acronym{EAX} design is cleaner and avoids a couple of inconveniences of
@acronym{CCM}. Therefore, @acronym{EAX} seems like a good conservative
choice. The more recent ChaCha-Poly1305 may also be an attractive but
more adventurous alternative, in particular if performance is important.

@menu
* EAX::
* GCM::
* CCM::
* ChaCha-Poly1305::
* OCB::
* SIV-CMAC::
* SIV-GCM::
* nettle_aead abstraction::
@end menu

@node EAX
@subsection EAX

The @acronym{EAX} mode is an @acronym{AEAD} mode which combines
@acronym{CTR} mode encryption, @xref{CTR}, with a message authentication
based on @acronym{CBC}, @xref{CBC}. The implementation in Nettle is
restricted to ciphers with a block size of 128 bits (16 octets).
@acronym{EAX} was defined as a reaction to the @acronym{CCM} mode,
@xref{CCM}, which uses the same primitives but has some undesirable and
inelegant properties.

@acronym{EAX} supports arbitrary nonce size; it's even possible to use
an empty nonce in case only a single message is encrypted for each key. 

Nettle's support for @acronym{EAX} consists of a low-level general
interface, some convenience macros, and specific functions for
@acronym{EAX} using @acronym{AES}-128 as the underlying cipher. These
interfaces are defined in @file{<nettle/eax.h>}

@subsubsection General @acronym{EAX} interface

@deftp {Context struct} {struct eax_key}
@acronym{EAX} state which depends only on the key, but not on the nonce
or the message.
@end deftp

@deftp {Context struct} {struct eax_ctx}
Holds state corresponding to a particular message.
@end deftp

@defvr Constant EAX_BLOCK_SIZE
@acronym{EAX}'s block size, 16.
@end defvr

@defvr Constant EAX_DIGEST_SIZE
Size of the @acronym{EAX} digest, also 16.
@end defvr

@deftypefun void eax_set_key (struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f})
Initializes @var{key}. @var{cipher} gives a context struct for the
underlying cipher, which must have been previously initialized for
encryption, and @var{f} is the encryption function.
@end deftypefun

@deftypefun void eax_set_nonce (struct eax_ctx *@var{eax}, const struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{nonce_length}, const uint8_t *@var{nonce})
Initializes @var{ctx} for processing a new message, using the given
nonce.
@end deftypefun

@deftypefun void eax_update (struct eax_ctx *@var{eax}, const struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{data_length}, const uint8_t *@var{data})
Process associated data for authentication. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size. Unlike many other @acronym{AEAD} constructions, for @acronym{EAX}
it's not necessary to complete the processing of all associated data
before encrypting or decrypting the message data.
@end deftypefun

@deftypefun void eax_encrypt (struct eax_ctx *@var{eax}, const struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void eax_decrypt (struct eax_ctx *@var{eax}, const struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. @var{cipher} is the context
struct for the underlying cipher and @var{f} is the encryption function.
All but the last call for each message @emph{must} use a length that is
a multiple of the block size.
@end deftypefun

@deftypefun void eax_digest (struct eax_ctx *@var{eax}, const struct eax_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. If @var{length} is
smaller than @code{EAX_DIGEST_SIZE}, only the first @var{length} octets
of the digest are written.
@end deftypefun


@subsubsection @acronym{EAX} helper macros

The following macros are defined.

@deffn Macro EAX_CTX (@var{context_type})
This defines an all-in-one context struct, including the context of the
underlying cipher and all @acronym{EAX} state. It expands
to
@example
@{
   struct eax_key key;
   struct eax_ctx eax;
   context_type cipher;
@}
@end example
@end deffn

For all these macros, @var{ctx}, is a context struct as defined by
@code{EAX_CTX}, and @var{encrypt} is the encryption function of the
underlying cipher.

@deffn Macro EAX_SET_KEY (@var{ctx}, @var{set_key}, @var{encrypt}, @var{key})
@var{set_key} is the function for setting the encryption key for the
underlying cipher, and @var{key} is the key.
@end deffn

@deffn Macro EAX_SET_NONCE (@var{ctx}, @var{encrypt}, @var{length}, @var{nonce})
Sets the nonce to be used for the message.
@end deffn

@deffn Macro EAX_UPDATE (@var{ctx}, @var{encrypt}, @var{length}, @var{data})
Process associated data for authentication.
@end deffn

@deffn Macro EAX_ENCRYPT (@var{ctx}, @var{encrypt}, @var{length}, @var{dst}, @var{src})
@deffnx Macro EAX_DECRYPT (@var{ctx}, @var{encrypt}, @var{length}, @var{dst}, @var{src})
Process message data for encryption or decryption.
@end deffn

@deffn Macro EAX_DIGEST (@var{ctx}, @var{encrypt}, @var{length}, @var{digest})
Extract the authentication tag for the message.
@end deffn


@subsubsection @acronym{EAX}-@acronym{AES}128 interface

The following functions implement @acronym{EAX} using @acronym{AES}-128
as the underlying cipher.

@deftp {Context struct} {struct eax_aes128_ctx}
The context struct, defined using @code{EAX_CTX}.
@end deftp

@deftypefun void eax_aes128_set_key (struct eax_aes128_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes @var{ctx} using the given key.
@end deftypefun

@deftypefun void eax_aes128_set_nonce (struct eax_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
Initializes the per-message state, using the given nonce.
@end deftypefun

@deftypefun void eax_aes128_update (struct eax_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process associated data for authentication. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void eax_aes128_encrypt (struct eax_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void eax_aes128_decrypt (struct eax_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void eax_aes128_digest (struct eax_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. If @var{length} is
smaller than @code{EAX_DIGEST_SIZE}, only the first @var{length} octets
of the digest are written.
@end deftypefun

@node GCM
@subsection Galois counter mode

@cindex Galois Counter Mode
@cindex GCM

Galois counter mode is an @acronym{AEAD} constructions combining counter
mode with message authentication based on universal hashing. The main
objective of the design is to provide high performance for hardware
implementations, where other popular @acronym{MAC} algorithms
(@pxref{Keyed hash functions}) become a bottleneck for high-speed
hardware implementations. It was proposed by David A. McGrew and John
Viega in 2005, and recommended by NIST in 2007,
@url{https://csrc.nist.gov/publications/nistpubs/800-38D/SP-800-38D.pdf,
NIST Special Publication 800-38D}. It is constructed on top of a block
cipher which must have a block size of 128 bits.

The authentication in @acronym{GCM} has some known weaknesses, see
@url{https://csrc.nist.gov@//groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf}.
In particular, don't use @acronym{GCM} with short authentication tags.

Nettle's support for @acronym{GCM} consists of a low-level general
interface, some convenience macros, and specific functions for
@acronym{GCM} using @acronym{AES} or Camellia as the underlying cipher.
These interfaces are defined in @file{<nettle/gcm.h>}

@subsubsection General @acronym{GCM} interface

@deftp {Context struct} {struct gcm_key}
Message independent hash sub-key, and related tables.
@end deftp

@deftp {Context struct} {struct gcm_ctx}
Holds state corresponding to a particular message.
@end deftp

@defvr Constant GCM_BLOCK_SIZE
@acronym{GCM}'s block size, 16.
@end defvr

@defvr Constant GCM_DIGEST_SIZE
Size of the @acronym{GCM} digest, also 16.
@end defvr

@defvr Constant GCM_IV_SIZE
Recommended size of the @acronym{IV}, 12. Arbitrary sizes are allowed.
@end defvr

@deftypefun void gcm_set_key (struct gcm_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f})
Initializes @var{key}. @var{cipher} gives a context struct for the
underlying cipher, which must have been previously initialized for
encryption, and @var{f} is the encryption function.
@end deftypefun

@deftypefun void gcm_set_iv (struct gcm_ctx *@var{ctx}, const struct gcm_key *@var{key}, size_t @var{length}, const uint8_t *@var{iv})
Initializes @var{ctx} using the given @acronym{IV}. The @var{key}
argument is actually needed only if @var{length} differs from
@code{GCM_IV_SIZE}.
@end deftypefun

@deftypefun void gcm_update (struct gcm_ctx *@var{ctx}, const struct gcm_key *@var{key}, size_t @var{length}, const uint8_t *@var{data})
Provides associated data to be authenticated. If used, must be called
before @code{gcm_encrypt} or @code{gcm_decrypt}. All but the last call
for each message @emph{must} use a length that is a multiple of the
block size.
@end deftypefun

@deftypefun void gcm_encrypt (struct gcm_ctx *@var{ctx}, const struct gcm_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_decrypt (struct gcm_ctx *@var{ctx}, const struct gcm_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. @var{cipher} is the context
struct for the underlying cipher and @var{f} is the encryption function.
All but the last call for each message @emph{must} use a length that is
a multiple of the block size.
@end deftypefun

@deftypefun void gcm_digest (struct gcm_ctx *@var{ctx}, const struct gcm_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. It's strongly recommended
that @var{length} is @code{GCM_DIGEST_SIZE}, but if you provide a smaller
value, only the first @var{length} octets of the digest are written.
@end deftypefun

To encrypt a message using @acronym{GCM}, first initialize a context for
the underlying block cipher with a key to use for encryption. Then call
the above functions in the following order: @code{gcm_set_key},
@code{gcm_set_iv}, @code{gcm_update}, @code{gcm_encrypt},
@code{gcm_digest}. The decryption procedure is analogous, just calling
@code{gcm_decrypt} instead of @code{gcm_encrypt} (note that
@acronym{GCM} decryption still uses the encryption function of the
underlying block cipher). To process a new message, using the same key,
call @code{gcm_set_iv} with a new @acronym{iv}.

@subsubsection @acronym{GCM} helper macros

The following macros are defined.

@deffn Macro GCM_CTX (@var{context_type})
This defines an all-in-one context struct, including the context of the
underlying cipher, the hash sub-key, and the per-message state. It expands
to
@example
@{
   struct gcm_key key; 
   struct gcm_ctx gcm;
   context_type cipher;
@}
@end example
@end deffn

Example use:
@example
struct gcm_aes128_ctx GCM_CTX(struct aes128_ctx);
@end example

The following macros operate on context structs of this form.

@deffn Macro GCM_SET_KEY (@var{ctx}, @var{set_key}, @var{encrypt}, @var{key})
First argument, @var{ctx}, is a context struct as defined
by @code{GCM_CTX}. @var{set_key} and @var{encrypt} are functions for
setting the encryption key and for encrypting data using the underlying
cipher.
@end deffn

@deffn Macro GCM_SET_IV (@var{ctx}, @var{length}, @var{data})
First argument is a context struct as defined by
@code{GCM_CTX}. @var{length} and @var{data} give the initialization
vector (@acronym{IV}).
@end deffn

@deffn Macro GCM_UPDATE (@var{ctx}, @var{length}, @var{data})
Simpler way to call @code{gcm_update}. First argument is a context
struct as defined by @code{GCM_CTX}
@end deffn

@deffn Macro GCM_ENCRYPT (@var{ctx}, @var{encrypt}, @var{length}, @var{dst}, @var{src})
@deffnx Macro GCM_DECRYPT (@var{ctx}, @var{encrypt}, @var{length}, @var{dst}, @var{src})
@deffnx Macro GCM_DIGEST (@var{ctx}, @var{encrypt}, @var{length}, @var{digest})
Simpler way to call @code{gcm_encrypt}, @code{gcm_decrypt} or
@code{gcm_digest}. First argument is a context struct as defined by
@code{GCM_CTX}. Second argument, @var{encrypt}, is the encryption
function of the underlying cipher.
@end deffn

@subsubsection @acronym{GCM}-@acronym{AES} interface

The following functions implement the common case of @acronym{GCM} using
@acronym{AES} as the underlying cipher. The variants with a specific
@acronym{AES} flavor are recommended, while the fucntinos using
@code{struct gcm_aes_ctx} are kept for compatibility with older versiosn
of Nettle.

@deftp {Context struct} {struct gcm_aes128_ctx}
@deftpx {Context struct} {struct gcm_aes192_ctx}
@deftpx {Context struct} {struct gcm_aes256_ctx}
Context structs, defined using @code{GCM_CTX}.
@end deftp

@deftp {Context struct} {struct gcm_aes_ctx}
Alternative context struct, using the old @acronym{AES} interface.
@end deftp

@deftypefun void gcm_aes128_set_key (struct gcm_aes128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void gcm_aes192_set_key (struct gcm_aes192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void gcm_aes256_set_key (struct gcm_aes256_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes @var{ctx} using the given key.
@end deftypefun

@deftypefun void gcm_aes_set_key (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{key})
Corresponding function, using the old @acronym{AES} interface. All valid
@acronym{AES} key sizes can be used.
@end deftypefun

@deftypefun void gcm_aes128_set_iv (struct gcm_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
@deftypefunx void gcm_aes192_set_iv (struct gcm_aes192_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
@deftypefunx void gcm_aes256_set_iv (struct gcm_aes256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
@deftypefunx void gcm_aes_set_iv (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
Initializes the per-message state, using the given @acronym{IV}.
@end deftypefun

@deftypefun void gcm_aes128_update (struct gcm_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void gcm_aes192_update (struct gcm_aes192_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void gcm_aes256_update (struct gcm_aes256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void gcm_aes_update (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Provides associated data to be authenticated. If used, must be called
before @code{gcm_aes_encrypt} or @code{gcm_aes_decrypt}. All but the
last call for each message @emph{must} use a length that is a multiple
of the block size.
@end deftypefun

@deftypefun void gcm_aes128_encrypt (struct gcm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes192_encrypt (struct gcm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes256_encrypt (struct gcm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes_encrypt (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes128_decrypt (struct gcm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes192_decrypt (struct gcm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes256_decrypt (struct gcm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_aes_decrypt (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void gcm_aes128_digest (struct gcm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_aes192_digest (struct gcm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_aes256_digest (struct gcm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_aes_digest (struct gcm_aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. It's strongly recommended
that @var{length} is @code{GCM_DIGEST_SIZE}, but if you provide a smaller
value, only the first @var{length} octets of the digest are written.
@end deftypefun

@subsubsection @acronym{GCM}-Camellia interface

The following functions implement the case of @acronym{GCM} using
Camellia as the underlying cipher.

@deftp {Context struct} {struct gcm_camellia128_ctx}
@deftpx {Context struct} {struct gcm_camellia256_ctx}
Context structs, defined using @code{GCM_CTX}.
@end deftp

@deftypefun void gcm_camellia128_set_key (struct gcm_camellia128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void gcm_camellia256_set_key (struct gcm_camellia256_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes @var{ctx} using the given key.
@end deftypefun

@deftypefun void gcm_camellia128_set_iv (struct gcm_camellia128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
@deftypefunx void gcm_camellia256_set_iv (struct gcm_camellia256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
Initializes the per-message state, using the given @acronym{IV}.
@end deftypefun

@deftypefun void gcm_camellia128_update (struct gcm_camellia128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void gcm_camellia256_update (struct gcm_camellia256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Provides associated data to be authenticated. If used, must be called
before @code{gcm_camellia_encrypt} or @code{gcm_camellia_decrypt}. All but the
last call for each message @emph{must} use a length that is a multiple
of the block size.
@end deftypefun

@deftypefun void gcm_camellia128_encrypt (struct gcm_camellia128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_camellia256_encrypt (struct gcm_camellia256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_camellia128_decrypt (struct gcm_camellia128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_camellia256_decrypt (struct gcm_camellia256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void gcm_camellia128_digest (struct gcm_camellia128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_camellia192_digest (struct gcm_camellia192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_camellia256_digest (struct gcm_camellia256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void gcm_camellia_digest (struct gcm_camellia_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. It's strongly recommended
that @var{length} is @code{GCM_DIGEST_SIZE}, but if you provide a smaller
value, only the first @var{length} octets of the digest are written.
@end deftypefun

@subsubsection @acronym{GCM}-SM4 interface

The following functions implement the case of @acronym{GCM} using
SM4 as the underlying cipher.

@deftp {Context struct} {struct gcm_sm4_ctx}
Context structs, defined using @code{GCM_CTX}.
@end deftp

@deftypefun void gcm_sm4_set_key (struct gcm_sm4_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes @var{ctx} using the given key.
@end deftypefun

@deftypefun void gcm_sm4_set_iv (struct gcm_sm4_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{iv})
Initializes the per-message state, using the given @acronym{IV}.
@end deftypefun

@deftypefun void gcm_sm4_update (struct gcm_sm4_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Provides associated data to be authenticated. If used, must be called
before @code{gcm_sm4_encrypt} or @code{gcm_sm4_decrypt}. All but the
last call for each message @emph{must} use a length that is a multiple
of the block size.
@end deftypefun

@deftypefun void gcm_sm4_encrypt (struct gcm_sm4_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void gcm_sm4_decrypt (struct gcm_sm4_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void gcm_sm4_digest (struct gcm_sm4_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. It's strongly recommended
that @var{length} is @code{GCM_DIGEST_SIZE}, but if you provide a smaller
value, only the first @var{length} octets of the digest are written.
@end deftypefun

@node CCM
@subsection Counter with CBC-MAC mode

@cindex Counter with CBC-MAC Mode
@cindex CCM Mode

@acronym{CCM} mode is a combination of counter mode with message
authentication based on cipher block chaining, the same building blocks
as @acronym{EAX}, @pxref{EAX}. It is constructed on top of a block cipher
which must have a block size of 128 bits. @acronym{CCM} mode is
recommended by NIST in
@url{https://csrc.nist.gov/publications/nistpubs/800-38C/SP800-38C_updated-July20_2007.pdf,
NIST Special Publication 800-38C}. Nettle's support for CCM consists of
a low-level general interface, a message encryption and authentication
interface, and specific functions for CCM using AES as the underlying
block cipher. These interfaces are defined in @file{<nettle/ccm.h>}.

In @acronym{CCM}, the length of the message must be known before
processing. The maximum message size depends on the size of the nonce,
since the message size is encoded in a field which must fit in a single
block, together with the nonce and a flag byte. E.g., with a nonce size
of 12 octets, there are three octets left for encoding the message
length, the maximum message length is @math{2^24 - 1} octets.

@acronym{CCM} mode encryption operates as follows:
@itemize
@item The nonce and message length are concatenated to create
@code{B_0 = flags | nonce | mlength}

@item The authenticated data and plaintext is formatted into the string
@code{B = L(adata) | adata | padding | plaintext | padding} with
@code{padding} being the shortest string of zero bytes such that the
length of the string is a multiple of the block size, and
@code{L(adata)} is an encoding of the length of @code{adata}.

@item The string @code{B} is separated into blocks @code{B_1} ...
@code{B_n}
@item The authentication tag @code{T} is calculated as
@code{T=0, for i=0 to n, do T = E_k(B_i XOR T)}

@item An initial counter is then initialized from the nonce to create
@code{IC = flags | nonce | padding}, where @code{padding} is the
shortest string of zero bytes such that @code{IC} is exactly one block
in length.

@item The authentication tag is encrypted using using @acronym{CTR} mode:
@code{MAC = E_k(IC) XOR T}

@item The plaintext is then encrypted using @acronym{CTR} mode with an
initial counter of @code{IC+1}.
@end itemize

@acronym{CCM} mode decryption operates similarly, except that the
ciphertext and @acronym{MAC} are first decrypted using CTR mode to
retrieve the plaintext and authentication tag. The authentication tag
can then be recalculated from the authenticated data and plaintext, and
compared to the value in the message to check for authenticity.

@subsubsection General @acronym{CCM} interface

For all of the functions in the @acronym{CCM} interface, @var{cipher} is
the context struct for the underlying cipher and @var{f} is the
encryption function. The cipher's encryption key must be set before
calling any of the @acronym{CCM} functions. The cipher's decryption
function and key are never used.

@deftp {Context struct} {struct ccm_ctx}
Holds state corresponding to a particular message.
@end deftp

@defvr Constant CCM_BLOCK_SIZE
@acronym{CCM}'s block size, 16.
@end defvr

@defvr Constant CCM_DIGEST_SIZE
Size of the @acronym{CCM} digest, 16.
@end defvr

@defvr Constant CCM_MIN_NONCE_SIZE
@defvrx Constant CCM_MAX_NONCE_SIZE
The the minimum and maximum sizes for an @acronym{CCM} nonce, 7 and 14,
respectively.
@end defvr

@deffn Macro CCM_MAX_MSG_SIZE (@var{nonce_size})
The largest allowed plaintext length, when using @acronym{CCM} with a
nonce of the given size.
@end deffn

@deftypefun void ccm_set_nonce (struct ccm_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{noncelen}, const uint8_t *@var{nonce}, size_t @var{authlen}, size_t @var{msglen}, size_t @var{taglen})
Initializes @var{ctx} using the given nonce and the sizes of the
authenticated data, message, and @acronym{MAC} to be processed.
@end deftypefun

@deftypefun void ccm_update (struct ccm_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, const uint8_t *@var{data})
Provides associated data to be authenticated. Must be called after
@code{ccm_set_nonce}, and before @code{ccm_encrypt}, @code{ccm_decrypt}, or
@code{ccm_digest}.
@end deftypefun

@deftypefun void ccm_encrypt (struct ccm_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_decrypt (struct ccm_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the message data. Must be called after
@code{ccm_set_nonce} and before @code{ccm_digest}. All but the last call
for each message @emph{must} use a length that is a multiple of the
block size.
@end deftypefun

@deftypefun void ccm_digest (struct ccm_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. @var{length} is usually
equal to the @var{taglen} parameter supplied to @code{ccm_set_nonce},
but if you provide a smaller value, only the first @var{length} octets
of the digest are written.
@end deftypefun

To encrypt a message using the general @acronym{CCM} interface, set the
message nonce and length using @code{ccm_set_nonce} and then call
@code{ccm_update} to generate the digest of any authenticated data.
After all of the authenticated data has been digested use
@code{ccm_encrypt} to encrypt the plaintext. Finally, use
@code{ccm_digest} to return the encrypted @acronym{MAC}.

To decrypt a message, use @code{ccm_set_nonce} and @code{ccm_update} the
same as you would for encryption, and then call @code{ccm_decrypt} to
decrypt the ciphertext. After decrypting the ciphertext
@code{ccm_digest} will return the encrypted @acronym{MAC} which should
be identical to the @acronym{MAC} in the received message.

@subsubsection @acronym{CCM} message interface

The @acronym{CCM} message fuctions provides a simple interface that will
perform authentication and message encryption in a single function call.
The length of the cleartext is given by @var{mlength} and the length of
the ciphertext is given by @var{clength}, always exactly @var{tlength}
bytes longer than the corresponding plaintext. The length argument
passed to a function is always the size for the result, @var{clength}
for the encryption functions, and @var{mlength} for the decryption
functions.

@deftypefun void ccm_encrypt_message (void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, appends the encrypted
@acronym{MAC} to ciphertext and outputs it to @var{dst}.
@end deftypefun

@deftypefun int ccm_decrypt_message (void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}, recalculates the @acronym{MAC} from @var{adata} and the
plaintext, and compares it to the final @var{tlength} bytes of
@var{src}. If the values of the received and calculated @acronym{MAC}s
are equal, this will return 1 indicating a valid and authenticated
message. Otherwise, this function will return zero.
@end deftypefun

@subsubsection @acronym{CCM}-@acronym{AES} interface

The @acronym{AES} @acronym{CCM} functions provide an API for using
@acronym{CCM} mode with the @acronym{AES} block ciphers. The parameters
all have the same meaning as the general and message interfaces, except
that the @var{cipher}, @var{f}, and @var{ctx} parameters are replaced
with an @acronym{AES} context structure, and a set-key function must be
called before using any of the other functions in this interface.

@deftp {Context struct} {struct ccm_aes128_ctx}
Holds state corresponding to a particular message encrypted using the
AES-128 block cipher.
@end deftp

@deftp {Context struct} {struct ccm_aes192_ctx}
Holds state corresponding to a particular message encrypted using the
AES-192 block cipher.
@end deftp

@deftp {Context struct} {struct ccm_aes256_ctx}
Holds state corresponding to a particular message encrypted using the
AES-256 block cipher.
@end deftp

@deftypefun void ccm_aes128_set_key (struct ccm_aes128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void ccm_aes192_set_key (struct ccm_aes192_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void ccm_aes256_set_key (struct ccm_aes256_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes the encryption key for the AES block cipher. One of these
functions must be called before any of the other functions in the
@acronym{AES} @acronym{CCM} interface.
@end deftypefun

@deftypefun void ccm_aes128_set_nonce (struct ccm_aes128_ctx *@var{ctx}, size_t @var{noncelen}, const uint8_t *@var{nonce}, size_t @var{authlen}, size_t @var{msglen}, size_t @var{taglen})
@deftypefunx void ccm_aes192_set_nonce (struct ccm_aes192_ctx *@var{ctx}, size_t @var{noncelen}, const uint8_t *@var{nonce}, size_t @var{authlen}, size_t @var{msglen}, size_t @var{taglen})
@deftypefunx void ccm_aes256_set_nonce (struct ccm_aes256_ctx *@var{ctx}, size_t @var{noncelen}, const uint8_t *@var{nonce}, size_t @var{authlen}, size_t @var{msglen}, size_t @var{taglen})
These are identical to @code{ccm_set_nonce}, except that @var{cipher},
@var{f}, and @var{ctx} are replaced with a context structure.
@end deftypefun

@deftypefun void ccm_aes128_update (struct ccm_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void ccm_aes192_update (struct ccm_aes192_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void ccm_aes256_update (struct ccm_aes256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
These are identical to @code{ccm_set_update}, except that @var{cipher},
@var{f}, and @var{ctx} are replaced with a context structure.
@end deftypefun

@deftypefun void ccm_aes128_encrypt (struct ccm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes192_encrypt (struct ccm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes256_encrypt (struct ccm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes128_decrypt (struct ccm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes192_decrypt (struct ccm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes256_decrypt (struct ccm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
These are identical to @code{ccm_set_encrypt} and @code{ccm_set_decrypt}, except
that @var{cipher}, @var{f}, and @var{ctx} are replaced with a context structure.
@end deftypefun

@deftypefun void ccm_aes128_digest (struct ccm_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void ccm_aes192_digest (struct ccm_aes192_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void ccm_aes256_digest (struct ccm_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
These are identical to @code{ccm_set_digest}, except that @var{cipher},
@var{f}, and @var{ctx} are replaced with a context structure.
@end deftypefun

@deftypefun void ccm_aes128_encrypt_message (struct ccm_aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes192_encrypt_message (struct ccm_aes192_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void ccm_aes256_encrypt_message (struct ccm_aes256_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx int ccm_aes128_decrypt_message (struct ccm_aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx int ccm_aes192_decrypt_message (struct ccm_aes192_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx int ccm_aes192_decrypt_message (struct ccm_aes256_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
These are identical to @code{ccm_encrypt_message} and @code{ccm_decrypt_message}
except that @var{cipher} and @var{f} are replaced with a context structure.
@end deftypefun

@node ChaCha-Poly1305
@subsection ChaCha-Poly1305

ChaCha-Poly1305 is a combination of the ChaCha stream cipher and the
poly1305 message authentication code (@pxref{Poly1305}). It originates
from the NaCl cryptographic library by D. J. Bernstein et al, which
defines a similar construction but with Salsa20 instead of ChaCha.

Nettle's implementation of ChaCha-Poly1305 follows @cite{RFC 8439},
where the ChaCha cipher is initialized with a 12-byte nonce and a 4-byte
block counter. This allows up to 256 gigabytes of data to be encrypted
using the same key and nonce.

For ChaCha-Poly1305, the ChaCha cipher is initialized with a key, of 256
bits, and a per-message nonce. The first block of the key stream
(counter all zero) is set aside for the authentication subkeys. Of this
64-octet block, the first 16 octets specify the poly1305 evaluation
point, and the next 16 bytes specify the value to add in for the final
digest. The final 32 bytes of this block are unused. Note that unlike
poly1305-aes, the evaluation point depends on the nonce. This is
preferable, because it leaks less information in case the attacker for
some reason is lucky enough to forge a valid authentication tag, and
observe (from the receiver's behaviour) that the forgery succeeded.

The ChaCha key stream, starting with counter value 1, is then used to
encrypt the message. For authentication, poly1305 is applied to the
concatenation of the associated data, the cryptotext, and the lengths of
the associated data and the message, each a 64-bit number (eight octets,
little-endian). Nettle defines ChaCha-Poly1305 in
@file{<nettle/chacha-poly1305.h>}.

@defvr Constant CHACHA_POLY1305_BLOCK_SIZE
Same as the ChaCha block size, 64.
@end defvr

@defvr Constant CHACHA_POLY1305_KEY_SIZE
ChaCha-Poly1305 key size, 32.
@end defvr

@defvr Constant CHACHA_POLY1305_NONCE_SIZE
ChaCha-Poly1305 nonce size, 12.
@end defvr

@defvr Constant CHACHA_POLY1305_DIGEST_SIZE
Digest size, 16.
@end defvr

@deftp {Context struct} {struct chacha_poly1305_ctx}
@end deftp

@deftypefun void chacha_poly1305_set_key (struct chacha_poly1305_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes @var{ctx} using the given key. Before using the context, you
@emph{must} also call @code{chacha_poly1305_set_nonce}, see below.
@end deftypefun

@deftypefun void chacha_poly1305_set_nonce (struct chacha_poly1305_ctx *@var{ctx}, const uint8_t *@var{nonce})
Initializes the per-message state, using the given nonce.
@end deftypefun

@deftypefun void chacha_poly1305_update (struct chacha_poly1305_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process associated data for authentication.
@end deftypefun

@deftypefun void chacha_poly1305_encrypt (struct chacha_poly1305_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void chacha_poly1305_decrypt (struct chacha_poly1305_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts or decrypts the data of a message. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void chacha_poly1305_digest (struct chacha_poly1305_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. If @var{length} is
smaller than @code{CHACHA_POLY1305_DIGEST_SIZE}, only the first
@var{length} octets of the digest are written.
@end deftypefun

@node OCB
@subsection @acronym{OCB} (Offset Code Book) Mode

@cindex OCB
@cindex OCB mode
@cindex Offset Code Book

The @acronym{OCB} mode is an @acronym{AEAD} construction, featuring
particularly fast and simple authentication; it needs one block cipher
operation per data block, and almost free authentication. It is
constructed on top of a block cipher which must have a block size of 128
bits.

There have been several versions of the OCB scheme, the implementation
in Nettle follows @cite{RFC 7253}, which is almost the same as the
scheme OCB3.

@subsubsection General interface

@deftp {Context struct} {struct ocb_key}
@acronym{OCB} state which depends only on the key, but not on the nonce
or the message.
@end deftp

@deftp {Context struct} {struct ocb_ctx}
Holds state corresponding to a particular message.
@end deftp

@defvr Constant OCB_BLOCK_SIZE
The block size for @acronym{OCB}'s block size, 16.
@end defvr

@defvr Constant OCB_MAX_NONCE_SIZE
The maximum nonce size for @acronym{OCB}, 15.
@end defvr

@defvr Constant OCB_DIGEST_SIZE
Size of the @acronym{OCB} authentication tag.
@end defvr

@deftypefun void ocb_set_key (struct ocb_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f})
Initializes the @var{key} struct. The @var{cipher} context must be
initialized for encryption, and @var{f} should be the corresponding
encryption function.
@end deftypefun

@deftypefun void ocb_set_nonce (struct ocb_ctx *@var{ctx}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{tag_length}, size_t @var{nonce_length}, const uint8_t *@var{nonce})
Initializes @var{ctx} for processing a new message, using the given
nonce. The @var{cipher} must be initialized for encryption, and @var{f}
should be the corresponding encryption function. The @var{tag_length}
(non-zero, and at most 16) is included when initializing the state, and
should be the same value later passed to @code{ocb_digest}. Nonce is
optional, and length at most 15 bytes.
@end deftypefun

@deftypefun void ocb_update (struct ocb_ctx *@var{ctx}, const struct ocb_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, const uint8_t *@var{data})
Process associated data for authentication. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void ocb_encrypt (struct ocb_ctx *@var{ctx}, const struct ocb_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts the data of a message. @var{cipher} is the context struct for
the underlying cipher and @var{f} is the encryption function. All but
the last call for each message @emph{must} use a length that is a
multiple of the block size.
@end deftypefun

@deftypefun void ocb_decrypt (struct ocb_ctx *@var{ctx}, const struct ocb_key *@var{key}, const void *@var{encrypt_ctx}, nettle_cipher_func *@var{encrypt}, const void *@var{decrypt_ctx}, nettle_cipher_func *@var{decrypt}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the data of a message. @var{encrypt_ctx} and @var{encrypt}
define the encryption operation of the underlying cipher, while
@var{decrypt_ctx} and @var{decrypt} represent the decryption operation
(for some ciphers, one of context pointer and function pointer may be
the same). All but the last call for each message @emph{must} use a
length that is a multiple of the block size.
@end deftypefun

@deftypefun void ocb_digest (const struct ocb_ctx *@var{ctx}, const struct ocb_key *@var{key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. The @var{length} value
@emph{should} be the same as the tag length passed to the preceding
@code{ocb_set_nonce} call (using a different length is possible, but
incompatible with @cite{RFC 7253}).
@end deftypefun

@deftypefun void ocb_encrypt_message (const struct ocb_key *@var{ocb_key}, const void *@var{cipher}, nettle_cipher_func *@var{f}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, appends the tag to
the ciphertext and writes it to @var{dst}. The @var{clength} variable
must be equal to the length of @var{src} plus @var{tlength}.
@end deftypefun

@deftypefun int ocb_decrypt_message (const struct ocb_key *@var{ocb_key}, const void *@var{encrypt_ctx}, nettle_cipher_func *@var{encrypt}, const void *@var{decrypt_ctx}, nettle_cipher_func *@var{decrypt}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}. Like @code{ocb_decrypt}, it needs both the encrypt and the
decrypt function of the underlying cipher. It also recalculates the
authentication tag from @var{adata} and the plaintext, and compares it
to the final @var{tlength} bytes of @var{src}. If the values of the
received and calculated tags are equal, this will return 1 indicating a
valid and authenticated message. Otherwise, this function will return
zero.
@end deftypefun

@subsubsection @acronym{OCB-AES} interface


@deftp {Context struct} {struct ocb_aes128_encrypt_key}
Key-dependent state for encryption using @acronym{OCB-AES128}. For
decryption, a separate @code{struct aes128_ctx}, initialized for
decryption, is needed as well.
@end deftp

@deftypefun void ocb_aes128_set_encrypt_key (struct ocb_aes128_encrypt_key *@var{ocb}, const uint8_t *@var{key})
Initializes @var{ocb} and the underlying AES cipher with the given key.
@end deftypefun

@deftypefun void ocb_aes128_set_decrypt_key (struct ocb_aes128_encrypt_key *@var{ocb}, struct aes128_ctx *@var{decrypt}, const uint8_t *@var{key})
Initializes @var{ocb} and the underlying AES cipher with the given key.
In addition, initialize @var{decrypt} for decryption using the same key;
this is needed for @code{ocb_aes128_decrypt} and
@code{ocb_aes128_decrypt_message}.
@end deftypefun

@deftypefun void ocb_aes128_set_nonce (struct ocb_ctx *@var{ctx}, const struct ocb_aes128_encrypt_key *@var{key}, size_t @var{tag_length}, size_t @var{nonce_length}, const uint8_t *@var{nonce})
Initializes @var{ctx} for processing a new message, using the given
nonce and key. The @var{tag_length} (non-zero, and at most 16) is
included when initializing the state, and should be the same value later
passed to @code{ocb_digest}. Nonce is optional, and length at most 15
bytes.
@end deftypefun

@deftypefun void ocb_aes128_update (struct ocb_ctx *@var{ctx}, const struct ocb_aes128_encrypt_key *@var{key}, size_t @var{length}, const uint8_t *@var{data})
Process associated data for authentication. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void ocb_aes128_encrypt (struct ocb_ctx *@var{ctx}, const struct ocb_aes128_encrypt_key *@var{key}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Encrypts the data of a message. All but the last call for each message
@emph{must} use a length that is a multiple of the block size.
@end deftypefun

@deftypefun void ocb_aes128_decrypt (struct ocb_ctx *@var{ctx}, const struct ocb_aes128_encrypt_key *@var{key}, const struct aes128_ctx *@var{decrypt}, size_t @var{length}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the data of a message. @var{decrypt} is an AES context
initialized for decryption using the same key. All but the last call for
each message @emph{must} use a length that is a multiple of the block
size.
@end deftypefun

@deftypefun void ocb_aes128_digest (struct ocb_ctx *@var{ctx}, const struct ocb_aes128_encrypt_key *@var{key}, size_t @var{length}, uint8_t *@var{digest})
Extracts the message digest (also known ``authentication tag''). This is
the final operation when processing a message. The @var{length} value
@emph{should} be the same as the tag length passed to the preceding
@code{ocb_aes128_set_nonce} call (using a different length is possible, but
incompatible with @cite{RFC 7253}).
@end deftypefun

@deftypefun void ocb_aes128_encrypt_message (const struct ocb_aes128_encrypt_key *@var{key}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, appends the tag to
the ciphertext and writes it to @var{dst}. The @var{clength} variable
must be equal to the length of @var{src} plus @var{tlength}.
@end deftypefun

@deftypefun int ocb_aes128_decrypt_message (const struct ocb_aes128_encrypt_key *@var{key}, const struct aes128_ctx *@var{decrypt}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{tlength}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}. Like @code{ocb_aes128_decrypt}, it needs an AES context
initialized for decryption using the same key. It also recalculates the
authentication tag from @var{adata} and the plaintext, and compares it
to the final @var{tlength} bytes of @var{src}. If the values of the
received and calculated tags are equal, this will return 1 indicating a
valid and authenticated message. Otherwise, this function will return
zero.
@end deftypefun

@node SIV-CMAC
@subsection Synthetic Initialization Vector AEAD

@cindex SIV mode
@cindex SIV-CMAC mode

@acronym{SIV-CMAC} mode is a combination of counter mode with message
authentication based on @acronym{CMAC}. Unlike other counter @acronym{AEAD}
modes, it provides protection against accidental nonce misuse, making it
a good choice for stateless-servers that cannot ensure nonce uniqueness.
It is constructed on top of a block cipher which must have a block size of
128 bits. Nettle's support for @acronym{SIV-CMAC} consists of
a message encryption and authentication interface, for
@acronym{SIV-CMAC} using AES as the underlying block cipher.
When a nonce is re-used with this mode, message authenticity is retained
however an attacker can determine whether the same plaintext was protected
with the two messages sharing the nonce.
These interfaces are defined in @file{<nettle/siv-cmac.h>}.

Unlike other @acronym{AEAD} mode in @acronym{SIV-CMAC} the initialization
vector serves as the tag. That means that in the generated ciphertext
the tag precedes the ciphertext.

Note also, that the @acronym{SIV-CMAC} algorithm, as specified in
@cite{RFC 5297}, introduces the notion of authenticated data which
consist of multiple components. For example with @acronym{SIV-CMAC} the
authentication tag of data @code{X} followed by @code{Y}, is different
than the concatenated data @code{X || Y}. The interfaces described below
follow the @acronym{AEAD} paradigm and do not allow access to this
feature and also require the use of a non-empty nonce. In the
terminology of the RFC, the input to the S2V function is always a vector
of three elements, where S1 is the authenticated data, S2 is the nonce,
and S3 is the plaintext.


@subsubsection General interface

@defvr Constant SIV_BLOCK_SIZE
@acronym{SIV-CMAC}'s block size, 16.
@end defvr

@defvr Constant SIV_DIGEST_SIZE
Size of the @acronym{SIV-CMAC} digest or initialization vector, 16.
@end defvr

@defvr Constant SIV_MIN_NONCE_SIZE
The the minimum size for an @acronym{SIV-CMAC} nonce, 1.
@end defvr

@subsubsection @acronym{SIV-CMAC}-@acronym{AES} interface

The @acronym{AES} @acronym{SIV-CMAC} functions provide an API for using
@acronym{SIV-CMAC} mode with the @acronym{AES} block ciphers. The parameters
all have the same meaning as the general and message interfaces, except
that the @var{cipher}, @var{f}, and @var{ctx} parameters are replaced
with an @acronym{AES} context structure, and a set-key function must be
called before using any of the other functions in this interface.

@deftp {Context struct} {struct siv_cmac_aes128_ctx}
Holds state corresponding to a particular message encrypted using the
AES-128 block cipher.
@end deftp

@deftp {Context struct} {struct siv_cmac_aes256_ctx}
Holds state corresponding to a particular message encrypted using the
AES-256 block cipher.
@end deftp

@deftypefun void siv_cmac_aes128_set_key (struct siv_cmac_aes128_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void siv_cmac_aes256_set_key (struct siv_cmac_aes256_ctx *@var{ctx}, const uint8_t *@var{key})
Initializes the encryption key for the AES block cipher. One of these
functions must be called before any of the other functions in the
@acronym{AES} @acronym{SIV-CMAC} interface.
@end deftypefun

@deftypefun void siv_cmac_aes128_encrypt_message (struct siv_cmac_aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void siv_cmac_aes256_encrypt_message (struct siv_cmac_aes256_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, prepends the
initialization vector to the ciphertext and outputs it to @var{dst}.
The @var{clength} variable must be equal to the length of @var{src}
plus @code{SIV_DIGEST_SIZE}.
@end deftypefun

@deftypefun int siv_cmac_aes128_decrypt_message (struct siv_cmac_aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx int siv_cmac_aes256_decrypt_message (struct siv_cmac_aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}, recalculates the initialization vector from @var{adata} and the
plaintext. If the values of the received and calculated initialization vector
are equal, this will return 1 indicating a valid and authenticated
message. Otherwise, this function will return zero.
@end deftypefun

@node SIV-GCM
@subsection SIV-GCM

@acronym{SIV-GCM}, described in @cite{RFC 8452}, is an @acronym{AEAD}
construction similar to @acronym{AES-GCM}, but provides protection against
accidental nonce misuse like @acronym{SIV-CMAC} mode.

It is constructed on top of a block cipher which must have a block size of 128
bits and a nonce size of 12 bytes. Nettle's support for @acronym{SIV-GCM}
consists of a message encryption and authentication interface, for
@acronym{SIV-GCM} using AES as the underlying block cipher.  These
interfaces are defined in @file{<nettle/siv-gcm.h>}.

Unlike other @acronym{AEAD} mode in @acronym{SIV-GCM} the tag is calculated
over the encoded additional authentication data and plaintext instead of the
ciphertext.

@subsubsection General interface

@defvr Constant SIV_GCM_BLOCK_SIZE
@acronym{SIV-GCM}'s block size, 16.
@end defvr

@defvr Constant SIV_GCM_DIGEST_SIZE
Size of the @acronym{SIV-GCM} digest for tags, 16.
@end defvr

@defvr Constant SIV_GCM_NONCE_SIZE
Size of the @acronym{SIV-GCM} nonce, 12.
@end defvr

@deftypefun void siv_gcm_encrypt_message (const struct nettle_cipher *@var{nc}, const void *@var{ctx}, void *@var{ctr_ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, appends the
authentication tag to the ciphertext and outputs it to @var{dst}.  The
@var{clength} variable must be equal to the length of @var{src} plus
@code{SIV_GCM_DIGEST_SIZE}.
@end deftypefun

@deftypefun int siv_gcm_decrypt_message (const struct nettle_cipher *@var{nc}, const void *@var{ctx}, void *@var{ctr_ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}, recalculates the initialization vector from @var{adata} and the
plaintext. If the values of the received and calculated initialization vector
are equal, this will return 1 indicating a valid and authenticated
message. Otherwise, this function will return zero.
@end deftypefun

In the above interface, @var{nc} must point to a cipher that works
with 16-byte block size and the key sizes that are multiple of
8-bytes.  The @var{ctx} context structure must be initialized for
encryption mode using a set-key function, before using any of the
functions in this interface.  While the @var{ctr_ctx} context
structure must have the same size as @var{ctx}, it does not need to be
initialized before calling those functions as it is used as working
storage.  These structures can point to the same area; in that case
the contents of *@var{ctx} is destroyed by the call.

For convenience, Nettle provides wrapper functions that works with
@acronym{AES} described in the following section.

@subsubsection @acronym{SIV-GCM}-@acronym{AES} interface

The @acronym{SIV-GCM} functions provide an API for using @acronym{SIV-GCM}
mode with the @acronym{AES} block ciphers. The parameters all have the same
meaning as the general and message interfaces, except that the @var{cipher},
@var{f}, and @var{ctx} parameters are replaced with an @acronym{AES} context
structure. The @acronym{AES} context structure must be initialized for
encryption mode using a set-key function, before using any of the functions in
this interface.

@deftypefun void siv_gcm_aes128_encrypt_message (const struct aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx void siv_gcm_aes256_encrypt_message (const struct aes256_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{clength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Computes the message digest from the @var{adata} and @var{src}
parameters, encrypts the plaintext from @var{src}, appends the
authentication tag to the ciphertext and outputs it to @var{dst}.
The @var{clength} variable must be equal to the length of @var{src}
plus @code{SIV_GCM_DIGEST_SIZE}.

@end deftypefun

@deftypefun int siv_gcm_aes128_decrypt_message (const struct aes128_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
@deftypefunx int siv_gcm_aes256_decrypt_message (const struct aes256_ctx *@var{ctx}, size_t @var{nlength}, const uint8_t *@var{nonce}, size_t @var{alength}, const uint8_t *@var{adata}, size_t @var{mlength}, uint8_t *@var{dst}, const uint8_t *@var{src})
Decrypts the ciphertext from @var{src}, outputs the plaintext to
@var{dst}, recalculates the initialization vector from @var{adata} and the
plaintext. If the values of the received and calculated initialization vector
are equal, this will return 1 indicating a valid and authenticated
message. Otherwise, this function will return zero.
@end deftypefun

@node nettle_aead abstraction
@subsection The @code{struct nettle_aead} abstraction
@cindex nettle_aead

Nettle includes a struct including information about the supported hash
functions. It is defined in @file{<nettle/nettle-meta.h>}.

@deftp {Meta struct} @code{struct nettle_aead} name context_size block_size key_size nonce_size digest_size set_encrypt_key set_decrypt_key set_nonce update encrypt decrypt digest
The last seven attributes are function pointers.
@end deftp

@deftypevr {Constant Struct} {struct nettle_aead} nettle_gcm_aes128
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_gcm_aes192
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_gcm_aes256
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_gcm_camellia128
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_gcm_camellia256
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_eax_aes128
@deftypevrx {Constant Struct} {struct nettle_aead} nettle_chacha_poly1305
These are most of the @acronym{AEAD} constructions that Nettle
implements. Note that @acronym{CCM} is missing; it requirement that the
message size is specified in advance makes it incompatible with the
@code{nettle_aead} abstraction.
@end deftypevr

Nettle also exports a list of all these constructions.

@deftypefun {const struct nettle_aead **} nettle_get_aeads (void)
Returns a NULL-terminated list of pointers to supported algorithms.This
list can be used to dynamically enumerate or search the supported
algorithms.
@end deftypefun

@deffn Macro nettle_aeads
A macro expanding to a call to nettle_get_aeads. In earlier versions,
this was not a macro but the actual array of pointers.
@end deffn

@node Keyed hash functions
@section Keyed Hash Functions

@cindex Keyed Hash Function
@cindex Message Authentication Code
@cindex MAC

A @dfn{keyed hash function}, or @dfn{Message Authentication Code}
(@acronym{MAC}) is a function that takes a key and a message, and
produces fixed size @acronym{MAC}. It should be hard to compute a
message and a matching @acronym{MAC} without knowledge of the key. It
should also be hard to compute the key given only messages and
corresponding @acronym{MAC}s.

Keyed hash functions are useful primarily for message authentication,
when Alice and Bob shares a secret: The sender, Alice, computes the
@acronym{MAC} and attaches it to the message. The receiver, Bob, also computes
the @acronym{MAC} of the message, using the same key, and compares that
to Alice's value. If they match, Bob can be assured that
the message has not been modified on its way from Alice.

However, unlike digital signatures, this assurance is not transferable.
Bob can't show the message and the @acronym{MAC} to a third party and
prove that Alice sent that message. Not even if he gives away the key to
the third party. The reason is that the @emph{same} key is used on both
sides, and anyone knowing the key can create a correct @acronym{MAC} for
any message. If Bob believes that only he and Alice knows the key, and
he knows that he didn't attach a @acronym{MAC} to a particular message,
he knows it must be Alice who did it. However, the third party can't
distinguish between a @acronym{MAC} created by Alice and one created by
Bob.

Keyed hash functions are typically a lot faster than digital signatures
as well.

@menu
* HMAC::
* UMAC::
* CMAC::
* Poly1305::
@end menu

@node HMAC
@subsection @acronym{HMAC}
@cindex HMAC

One can build keyed hash functions from ordinary hash functions. Older
constructions simply concatenate secret key and message and hashes that, but
such constructions have weaknesses. A better construction is
@acronym{HMAC}, described in @cite{RFC 2104}.

For an underlying hash function @code{H}, with digest size @code{l} and
internal block size @code{b}, @acronym{HMAC-H} is constructed as
follows: From a given key @code{k}, two distinct subkeys @code{k_i} and
@code{k_o} are constructed, both of length @code{b}. The
@acronym{HMAC-H} of a message @code{m} is then computed as @code{H(k_o |
H(k_i | m))}, where @code{|} denotes string concatenation.

@acronym{HMAC} keys can be of any length, but it is recommended to use
keys of length @code{l}, the digest size of the underlying hash function
@code{H}. Keys that are longer than @code{b} are shortened to length
@code{l} by hashing with @code{H}, so arbitrarily long keys aren't
very useful. 

Nettle's @acronym{HMAC} functions are defined in @file{<nettle/hmac.h>}.
There are abstract functions that use a pointer to a @code{struct
nettle_hash} to represent the underlying hash function and @code{void *}
pointers that point to three different context structs for that hash
function. There are also concrete functions for @acronym{HMAC-MD5},
@acronym{HMAC-RIPEMD160} @acronym{HMAC-SHA1}, @acronym{HMAC-SHA256},
@acronym{HMAC-SHA512}, and @acronym{HMAC-SM3}. First, the abstract functions:

@deftypefun void hmac_set_key (void *@var{outer}, void *@var{inner}, void *@var{state}, const struct nettle_hash *@var{H}, size_t @var{length}, const uint8_t *@var{key})
Initializes the three context structs from the key. The @var{outer} and
@var{inner} contexts corresponds to the subkeys @code{k_o} and
@code{k_i}. @var{state} is used for hashing the message, and is
initialized as a copy of the @var{inner} context.
@end deftypefun

@deftypefun void hmac_update (void *@var{state}, const struct nettle_hash *@var{H}, size_t @var{length}, const uint8_t *@var{data})
This function is called zero or more times to process the message.
Actually, @code{hmac_update(state, H, length, data)} is equivalent to
@code{H->update(state, length, data)}, so if you wish you can use the
ordinary update function of the underlying hash function instead.
@end deftypefun

@deftypefun void hmac_digest (const void *@var{outer}, const void *@var{inner}, void *@var{state}, const struct nettle_hash *@var{H}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC} of the message, writing it to @var{digest}.
@var{outer} and @var{inner} are not modified. @var{length} is usually
equal to @code{H->digest_size}, but if you provide a smaller value,
only the first @var{length} octets of the @acronym{MAC} are written.

This function also resets the @var{state} context so that you can start
over processing a new message (with the same key).
@end deftypefun

Like for @acronym{CBC}, there are some macros to help use these
functions correctly.

@deffn Macro HMAC_CTX (@var{type})
Expands to
@example
@{
   type outer;
   type inner;
   type state;
@}
@end example
@end deffn

It can be used to define a @acronym{HMAC} context struct, either
directly,

@example
struct HMAC_CTX(struct md5_ctx) ctx;
@end example

or to give it a struct tag,

@example
struct hmac_md5_ctx HMAC_CTX (struct md5_ctx);
@end example

@deffn Macro HMAC_SET_KEY (@var{ctx}, @var{H}, @var{length}, @var{key})
@var{ctx} is a pointer to a context struct as defined by
@code{HMAC_CTX}, @var{H} is a pointer to a @code{const struct
nettle_hash} describing the underlying hash function (so it must match
the type of the components of @var{ctx}). The last two arguments specify
the secret key.
@end deffn

@deffn Macro HMAC_DIGEST (@var{ctx}, @var{H}, @var{length}, @var{digest})
@var{ctx} is a pointer to a context struct as defined by
@code{HMAC_CTX}, @var{H} is a pointer to a @code{const struct
nettle_hash} describing the underlying hash function. The last two
arguments specify where the digest is written.
@end deffn

Note that there is no @code{HMAC_UPDATE} macro; simply call
@code{hmac_update} function directly, or the update function of the
underlying hash function.

Now we come to the specialized @acronym{HMAC} functions, which are
easier to use than the general @acronym{HMAC} functions.

@subsubsection @acronym{HMAC-MD5}

@deftp {Context struct} {struct hmac_md5_ctx}
@end deftp

@deftypefun void hmac_md5_set_key (struct hmac_md5_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_md5_update (struct hmac_md5_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_md5_digest (struct hmac_md5_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{MD5_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun

@subsubsection @acronym{HMAC-RIPEMD160}

@deftp {Context struct} {struct hmac_ripemd160_ctx}
@end deftp

@deftypefun void hmac_ripemd160_set_key (struct hmac_ripemd160_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_ripemd160_update (struct hmac_ripemd160_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_ripemd160_digest (struct hmac_ripemd160_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{RIPEMD160_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun

@subsubsection @acronym{HMAC-SHA1}

@deftp {Context struct} {struct hmac_sha1_ctx}
@end deftp

@deftypefun void hmac_sha1_set_key (struct hmac_sha1_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_sha1_update (struct hmac_sha1_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sha1_digest (struct hmac_sha1_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{SHA1_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun


@subsubsection @acronym{HMAC-SHA256}

@deftp {Context struct} {struct hmac_sha256_ctx}
@end deftp

@deftypefun void hmac_sha256_set_key (struct hmac_sha256_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_sha256_update (struct hmac_sha256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sha256_digest (struct hmac_sha256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{SHA256_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun


@subsubsection @acronym{HMAC-SHA512}

@deftp {Context struct} {struct hmac_sha512_ctx}
@end deftp

@deftypefun void hmac_sha512_set_key (struct hmac_sha512_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_sha512_update (struct hmac_sha512_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sha512_digest (struct hmac_sha512_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{SHA512_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun


@subsubsection @acronym{HMAC-SM3}

@deftp {Context struct} {struct hmac_sm3_ctx}
@end deftp

@deftypefun void hmac_sm3_set_key (struct hmac_sm3_ctx *@var{ctx}, size_t @var{key_length}, const uint8_t *@var{key})
Initializes the context with the key.
@end deftypefun

@deftypefun void hmac_sm3_update (struct hmac_sm3_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sm3_digest (struct hmac_sm3_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC}, writing it to @var{digest}. @var{length} may be smaller than
@code{SM3_DIGEST_SIZE}, in which case only the first @var{length}
octets of the @acronym{MAC} are written.

This function also resets the context for processing new messages, with
the same key.
@end deftypefun

@node UMAC
@subsection @acronym{UMAC}
@cindex UMAC

@acronym{UMAC} is a message authentication code based on universal
hashing, and designed for high performance on modern processors (in
contrast to GCM, @xref{GCM}, which is designed primarily for hardware
performance). On processors with good integer multiplication
performance, it can be 10 times faster than SHA256 and SHA512.
@acronym{UMAC} is specified in @cite{RFC 4418}.

The secret key is always 128 bits (16 octets). The key is used as an
encryption key for the @acronym{AES} block cipher. This cipher is used
in counter mode to generate various internal subkeys needed in
@acronym{UMAC}. Messages are of arbitrary size, and for each message,
@acronym{UMAC} also needs a unique nonce. Nonce values must not be
reused for two messages with the same key, but they need not be kept
secret.

The nonce must be at least one octet, and at most 16; nonces shorter
than 16 octets are zero-padded. Nettle's implementation of
@acronym{UMAC} increments the nonce automatically for each message, so
explicitly setting the nonce for each message is optional. This
auto-increment uses network byte order and it takes the length of the
nonce into account. E.g., if the initial nonce is ``abc'' (3 octets),
this value is zero-padded to 16 octets for the first message. For the
next message, the nonce is incremented to ``abd'', and this incremented
value is zero-padded to 16 octets.

@acronym{UMAC} is defined in four variants, for different output sizes:
32 bits (4 octets), 64 bits (8 octets), 96 bits (12 octets) and 128 bits
(16 octets), corresponding to different trade-offs between speed and
security. Using a shorter output size sometimes (but not always!) gives
the same result as using a longer output size and truncating the result.
So it is important to use the right variant. For consistency with other
hash and @acronym{MAC} functions, Nettle's @code{_digest} functions for
@acronym{UMAC} accept a length parameter so that the output can be
truncated to any desired size, but it is recommended to stick to the
specified output size and select the @acronym{umac} variant
corresponding to the desired size.

The internal block size of @acronym{UMAC} is 1024 octets, and it also
generates more than 1024 bytes of subkeys. This makes the size of the
context struct quite a bit larger than other hash functions and
@acronym{MAC} algorithms in Nettle.

Nettle defines @acronym{UMAC} in @file{<nettle/umac.h>}.

@deftp {Context struct} {struct umac32_ctx}
@deftpx {Context struct} {struct umac64_ctx}
@deftpx {Context struct} {struct umac96_ctx}
@deftpx {Context struct} {struct umac128_ctx}
Each @acronym{UMAC} variant uses its own context struct.
@end deftp

@defvr Constant UMAC_KEY_SIZE
The UMAC key size, 16.
@end defvr
@defvr Constant UMAC_MIN_NONCE_SIZE
@defvrx Constant UMAC_MAX_NONCE_SIZE
The the minimum and maximum sizes for an UMAC nonce, 1 and 16,
respectively.
@end defvr
@defvr Constant UMAC32_DIGEST_SIZE
The size of an UMAC32 digest, 4.
@end defvr
@defvr Constant UMAC64_DIGEST_SIZE
The size of an UMAC64 digest, 8.
@end defvr
@defvr Constant UMAC96_DIGEST_SIZE
The size of an UMAC96 digest, 12.
@end defvr
@defvr Constant UMAC128_DIGEST_SIZE
The size of an UMAC128 digest, 16.
@end defvr
@defvr Constant UMAC_BLOCK_SIZE
The internal block size of UMAC.
@end defvr

@deftypefun void umac32_set_key (struct umac32_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void umac64_set_key (struct umac64_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void umac96_set_key (struct umac96_ctx *@var{ctx}, const uint8_t *@var{key})
@deftypefunx void umac128_set_key (struct umac128_ctx *@var{ctx}, const uint8_t *@var{key})
These functions initialize the @acronym{UMAC} context struct. They also
initialize the nonce to zero (with length 16, for auto-increment).
@end deftypefun

@deftypefun void umac32_set_nonce (struct umac32_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{nonce})
@deftypefunx void umac64_set_nonce (struct umac64_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{nonce})
@deftypefunx void umac96_set_nonce (struct umac96_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{nonce})
@deftypefunx void umac128_set_nonce (struct umac128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{nonce})
Sets the nonce to be used for the next message. In general, nonces
should be set before processing of the message. This is not strictly
required for @acronym{UMAC} (the nonce only affects the final processing
generating the digest), but it is nevertheless recommended that this
function is called @emph{before} the first @code{_update} call for the
message.
@end deftypefun

@deftypefun void umac32_update (struct umac32_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void umac64_update (struct umac64_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void umac96_update (struct umac96_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
@deftypefunx void umac128_update (struct umac128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
These functions are called zero or more times to process the message.
@end deftypefun

@deftypefun void umac32_digest (struct umac32_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void umac64_digest (struct umac64_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void umac96_digest (struct umac96_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
@deftypefunx void umac128_digest (struct umac128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC} of the message, writing it to @var{digest}.
@var{length} is usually equal to the specified output size, but if you
provide a smaller value, only the first @var{length} octets of the
@acronym{MAC} are written. These functions reset the context for
processing of a new message with the same key. The nonce is incremented
as described above, the new value is used unless you call the
@code{_set_nonce} function explicitly for each message.
@end deftypefun

@node CMAC
@subsection @acronym{CMAC}
@cindex CMAC
@cindex CMAC-128
@cindex CMAC-64

@acronym{CMAC} is a message authentication code based on CBC encryption
mode. It is suitable for systems where block ciphers are preferrable
and perform better than hash functions. @acronym{CMAC-128} is specified in
@cite{RFC4493}. The block size is always 128 bits (16 octets).
@acronym{CMAC-64} is specified by
@url{https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38B.pdf,
NIST Special Publication 800-38B}. The block size is always 64 bits
(8 octets).

Nettle provides helper functions for @acronym{CMAC-128} with
the @acronym{AES} block cipher and for @acronym{CMAC-64} with
the @acronym{Tripple-DES} block cipher.

Nettle defines @acronym{CMAC} in @file{<nettle/cmac.h>}.

@deftp {Context struct} {struct cmac_aes128_ctx}
@deftpx {Context struct} {struct cmac_aes256_ctx}
@end deftp

@defvr Constant CMAC128_DIGEST_SIZE
The size of an CMAC-128 digest, 16.
@end defvr

@deftypefun void cmac_aes128_set_key (struct cmac_aes128_ctx *@var{ctx}, const uint8_t *@var{key})
This function initializes the @acronym{CMAC} context struct for AES-128.
@end deftypefun

@deftypefun void cmac_aes128_update (struct cmac_aes128_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
This function is called zero or more times to process the message.
@end deftypefun

@deftypefun void cmac_aes128_digest (struct cmac_aes128_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC} of the message, writing it to @var{digest}.
@var{length} is usually equal to the specified output size, but if you
provide a smaller value, only the first @var{length} octets of the
@acronym{MAC} are written. This function resets the context for
processing of a new message with the same key.
@end deftypefun

@deftypefun void cmac_aes256_set_key (struct cmac_aes256_ctx *@var{ctx}, const uint8_t *@var{key})
This function initializes the @acronym{CMAC} context struct for AES-256.
@end deftypefun

@deftypefun void cmac_aes256_update (struct cmac_aes256_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
This function is called zero or more times to process the message.
@end deftypefun

@deftypefun void cmac_aes256_digest (struct cmac_aes256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC} of the message, writing it to @var{digest}.
@var{length} is usually equal to the specified output size, but if you
provide a smaller value, only the first @var{length} octets of the
@acronym{MAC} are written. This function resets the context for
processing of a new message with the same key.
@end deftypefun

@deftp {Context struct} {struct cmac_des3_ctx}
@end deftp

@defvr Constant CMAC64_DIGEST_SIZE
The size of an CMAC-64 digest, 8.
@end defvr

@deftypefun void cmac_des3_set_key (struct cmac_des3_ctx *@var{ctx}, const uint8_t *@var{key})
This function initializes the @acronym{CMAC} context struct for @acronym{Tripple-DES}.
@end deftypefun

@deftypefun void cmac_des3_update (struct cmac_des3_ctx *@var{ctx},size_t @var{length}, const uint8_t *@var{data})
This function is called zero or more times to process the message.
@end deftypefun

@deftypefun void cmac_des3_digest (struct cmac_des3_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the @acronym{MAC} of the message, writing it to @var{digest}.
@var{length} is usually equal to the specified output size, but if you
provide a smaller value, only the first @var{length} octets of the
@acronym{MAC} are written. This function resets the context for
processing of a new message with the same key.
@end deftypefun

@node Poly1305
@subsection Poly1305

Poly1305-@acronym{AES} is a message authentication code designed by D. J.
Bernstein. It treats the message as a polynomial modulo the prime number
@math{2^130 - 5}.

The key, 256 bits, consists of two parts, where the first half is an
@acronym{AES}-128 key, and the second half specifies the point where the
polynomial is evaluated. Of the latter half, 22 bits are set to zero, to
enable high-performance implementation, leaving 106 bits for specifying
an evaluation point @code{r}. For each message, one must also provide a
128-bit nonce. The nonce is encrypted using the @acronym{AES} key, and
that's the only thing @acronym{AES} is used for.

The message is split into 128-bit chunks (with final chunk possibly
being shorter), each read as a little-endian integer. Each chunk has a
one-bit appended at the high end. The resulting integers are treated as
polynomial coefficients modulo @math{2^130 - 5}, and the polynomial is
evaluated at the point @code{r}. Finally, this value is reduced modulo
@math{2^128}, and added (also modulo @math{2^128}) to the encrypted
nonce, to produce an 128-bit authenticator for the message. See
@url{https://cr.yp.to/mac/poly1305-20050329.pdf} for further details.

Clearly, variants using a different cipher than @acronym{AES} could be
defined. Another variant is the ChaCha-Poly1305 @acronym{AEAD}
construction (@pxref{ChaCha-Poly1305}). Nettle defines
Poly1305-@acronym{AES} in @file{nettle/poly1305.h}.

@defvr Constant POLY1305_AES_KEY_SIZE
Key size, 32 octets.
@end defvr

@defvr Constant POLY1305_AES_DIGEST_SIZE
Size of the digest or ``authenticator'', 16 octets.
@end defvr

@defvr Constant POLY1305_AES_NONCE_SIZE
Nonce size, 16 octets.
@end defvr

@deftp {Context struct} {struct poly1305_aes_ctx}
The poly1305-aes context struct.
@end deftp

@deftypefun void poly1305_aes_set_key (struct poly1305_aes_ctx *@var{ctx}, const uint8_t *@var{key})
Initialize the context struct. Also sets the nonce to zero.
@end deftypefun

@deftypefun void poly1305_aes_set_nonce (struct poly1305_aes_ctx *@var{ctx}, const uint8_t *@var{nonce})
Sets the nonce. Calling this function is optional, since the nonce is
incremented automatically for each message.
@end deftypefun

@deftypefun void poly1305_aes_update (struct poly1305_aes_ctx *@var{ctx}, size_t @var{length}, const uint8_t *@var{data})
Process more data.
@end deftypefun

@deftypefun void poly1305_aes_digest (struct poly1305_aes_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{digest})
Extracts the digest. If @var{length} is smaller than
@code{POLY1305_AES_DIGEST_SIZE}, only the first @var{length} octets are
written. Also increments the nonce, and prepares the context for
processing a new message.
@end deftypefun


@node Key derivation functions
@section Key derivation Functions
@cindex Key Derivation Function

A @dfn{key derivation function} (@acronym{KDF}) is a function that from
a given symmetric key derives other symmetric keys.  A sub-class of KDFs
is the @dfn{password-based key derivation functions} (@acronym{PBKDFs}),
which take as input a password or passphrase, and its purpose is
typically to strengthen it and protect against certain pre-computation
attacks by using salting and expensive computation.

@subsection HKDF: HMAC-based Extract-and-Expand
@cindex HKDF

HKDF is a key derivation function used as a building block of
higher-level protocols like TLS 1.3. It is a derivation function
based on HMAC described in @cite{RFC 5869},
and is split into two logical modules, called 'extract' and 'expand'.
The extract module takes an initial secret and a random
salt to "extract" a fixed-length pseudorandom key (PRK). The second stage
takes as input the previous PRK and some informational data (e.g.,
text) and expands them into multiple keys.

Nettle's @acronym{HKDF} functions are defined in
@file{<nettle/hkdf.h>}.  There are two abstract functions for the extract
and expand operations that operate on any HMAC implemented via the @code{nettle_hash_update_func},
and @code{nettle_hash_digest_func} interfaces.

@deftypefun void hkdf_extract (void *mac_ctx, nettle_hash_update_func *update, nettle_hash_digest_func *digest, size_t digest_size,size_t secret_size, const uint8_t *secret, uint8_t *dst)
Extract a Pseudorandom Key (PRK) from a secret and a salt according
to HKDF. The HMAC must have been initialized, with its key being the
salt for the Extract operation. This function will call the
@var{update} and @var{digest} functions passing the @var{mac_ctx}
context parameter as an argument in order to compute digest of size
@var{digest_size}.  Inputs are the secret @var{secret} of length
@var{secret_length}. The output length is fixed to @var{digest_size} octets,
thus the output buffer @var{dst} must have room for at least @var{digest_size} octets.
@end deftypefun

@deftypefun void hkdf_expand (void *mac_ctx, nettle_hash_update_func *update, nettle_hash_digest_func *digest, size_t digest_size, size_t info_size, const uint8_t *info, size_t length, uint8_t *dst)
Expand a Pseudorandom Key (PRK) to an arbitrary size according to HKDF.
The HMAC must have been initialized, with its key being the
PRK from the Extract operation. This function will call the
@var{update} and @var{digest} functions passing the @var{mac_ctx}
context parameter as an argument in order to compute digest of size
@var{digest_size}.  Inputs are the info @var{info} of length
@var{info_length}, and the desired derived output length @var{length}.
The output buffer is @var{dst} which must have room for at least @var{length} octets.
@end deftypefun


@subsection @acronym{PBKDF2}
@cindex Password Based Key Derivation Function
@cindex PKCS #5
@cindex KDF
@cindex PBKDF
The most well known PBKDF is the @code{PKCS #5 PBKDF2} described in
@cite{RFC 2898} which uses a pseudo-random function such as
@acronym{HMAC-SHA1}.

Nettle's @acronym{PBKDF2} functions are defined in
@file{<nettle/pbkdf2.h>}.  There is an abstract function that operate on
any PRF implemented via the @code{nettle_hash_update_func},
@code{nettle_hash_digest_func} interfaces.  There is also helper macros
and concrete functions PBKDF2-HMAC-SHA1, PBKDF2-HMAC-SHA256, PBKDF2-HMAC-SHA384
and PBKDF2-HMAC-SHA512.  First, the abstract function:

@deftypefun void pbkdf2 (void *mac_ctx, nettle_hash_update_func *update, nettle_hash_digest_func *digest, size_t digest_size, unsigned iterations, size_t salt_length, const uint8_t *salt, size_t length, uint8_t *dst)
Derive symmetric key from a password according to PKCS #5 PBKDF2.  The
PRF is assumed to have been initialized and this function will call the
@var{update} and @var{digest} functions passing the @var{mac_ctx}
context parameter as an argument in order to compute digest of size
@var{digest_size}.  Inputs are the salt @var{salt} of length
@var{salt_length}, the iteration counter @var{iterations} (> 0), and the
desired derived output length @var{length}.  The output buffer is
@var{dst} which must have room for at least @var{length} octets.
@end deftypefun

Like for CBC and HMAC, there is a macro to help use the function
correctly.

@deffn Macro PBKDF2 (@var{ctx}, @var{update}, @var{digest}, @var{digest_size}, @var{iterations}, @var{salt_length}, @var{salt}, @var{length}, @var{dst})
@var{ctx} is a pointer to a context struct passed to the @var{update}
and @var{digest} functions (of the types @code{nettle_hash_update_func}
and @code{nettle_hash_digest_func} respectively) to implement the
underlying PRF with digest size of @var{digest_size}.  Inputs are the
salt @var{salt} of length @var{salt_length}, the iteration counter
@var{iterations} (> 0), and the desired derived output length
@var{length}.  The output buffer is @var{dst} which must have room for
at least @var{length} octets.
@end deffn

@subsection Concrete @acronym{PBKDF2} functions
Now we come to the specialized @acronym{PBKDF2} functions, which are
easier to use than the general @acronym{PBKDF2} function.

@subsubsection @acronym{PBKDF2-HMAC-SHA1}

@deftypefun void pbkdf2_hmac_sha1 (size_t @var{key_length}, const uint8_t *@var{key}, unsigned @var{iterations}, size_t @var{salt_length}, const uint8_t *@var{salt}, size_t @var{length}, uint8_t *@var{dst})
PBKDF2 with HMAC-SHA1.  Derive @var{length} bytes of key into buffer
@var{dst} using the password @var{key} of length @var{key_length} and
salt @var{salt} of length @var{salt_length}, with iteration counter
@var{iterations} (> 0).  The output buffer is @var{dst} which must have
room for at least @var{length} octets.
@end deftypefun

@subsubsection @acronym{PBKDF2-HMAC-SHA256}

@deftypefun void pbkdf2_hmac_sha256 (size_t @var{key_length}, const uint8_t *@var{key}, unsigned @var{iterations}, size_t @var{salt_length}, const uint8_t *@var{salt}, size_t @var{length}, uint8_t *@var{dst})
PBKDF2 with HMAC-SHA256.  Derive @var{length} bytes of key into buffer
@var{dst} using the password @var{key} of length @var{key_length} and
salt @var{salt} of length @var{salt_length}, with iteration counter
@var{iterations} (> 0).  The output buffer is @var{dst} which must have
room for at least @var{length} octets.
@end deftypefun

@subsubsection @acronym{PBKDF2-HMAC-SHA384}

@deftypefun void pbkdf2_hmac_sha384 (size_t @var{key_length}, const uint8_t *@var{key}, unsigned @var{iterations}, size_t @var{salt_length}, const uint8_t *@var{salt}, size_t @var{length}, uint8_t *@var{dst})
PBKDF2 with HMAC-SHA384.  Derive @var{length} bytes of key into buffer
@var{dst} using the password @var{key} of length @var{key_length} and
salt @var{salt} of length @var{salt_length}, with iteration counter
@var{iterations} (> 0).  The output buffer is @var{dst} which must have
room for at least @var{length} octets.
@end deftypefun

@subsubsection @acronym{PBKDF2-HMAC-SHA512}

@deftypefun void pbkdf2_hmac_sha512 (size_t @var{key_length}, const uint8_t *@var{key}, unsigned @var{iterations}, size_t @var{salt_length}, const uint8_t *@var{salt}, size_t @var{length}, uint8_t *@var{dst})
PBKDF2 with HMAC-SHA512.  Derive @var{length} bytes of key into buffer
@var{dst} using the password @var{key} of length @var{key_length} and
salt @var{salt} of length @var{salt_length}, with iteration counter
@var{iterations} (> 0).  The output buffer is @var{dst} which must have
room for at least @var{length} octets.
@end deftypefun


@subsection @acronym{BALLOON}
@cindex Balloon password-hashing algorithm
Balloon is a memory-hard password-hashing algorithm.  An in-depth description
of the algorithm and its properties can be found in an online research paper:
Boneh, D., Corrigan-Gibbs, H., Schechter, S. (2017, May 12). Balloon Hashing:
A Memory-Hard Function Providing Provable Protection Against Sequential Attacks.
Retrieved Sep 1, 2022, from @url{https://eprint.iacr.org/2016/027.pdf}

Nettle's definition of the @acronym{BALLOON} algorithm can be found in
@file{<nettle/balloon.h>}.  There is a general @acronym{BALLOON} function where
the user can specify desired hash algorithm that will be used by the function.
There are also concrete, more user-friendly functions that use common hash algorithms
like SHA1, SHA256, SHA384 and SHA512.  There is also a utility function which helps to
determine the size of the working buffer that must be provided as one of the inputs.

Each @acronym{BALLOON} function takes as an input a password and a salt of arbitrary
lengths, a time and a space parameters, and a scratch buffer.  The space parameter
@var{s_cost} determines how many blocks of working space the algorithm will require
during its computation.  It is common to set @var{s_cost} to a high value in order
to increase the cost of hardware accelerators built by the adversary.  The time
parameter @var{t_cost} determines the number of rounds of computation that the algorithm
will perform. This can be used to further increase the cost of computation without raising
the memory requirement.  Scratch buffer @var{scratch} is a user allocated working space
required by the algorithm.  To determine the required size of the scratch buffer use the
utility function @code{balloon_itch}.  Output of @acronym{BALLOON} algorithm will be
written into the output buffer @var{dst} that has to be at least @var{digest_size} bytes
long.  Note that it is safe to use the same buffer for both @var{scratch} and @var{dst}.
Next follows the description of the general @acronym{BALLOON} function.

@deftypefun void balloon (void *@var{hash_ctx}, nettle_hash_update_func *@var{update}, nettle_hash_digest_func *@var{digest}, size_t @var{digest_size}, size_t @var{s_cost}, size_t @var{t_cost}, size_t @var{passwd_length}, const uint8_t *@var{passwd}, size_t @var{salt_length}, const uint8_t *@var{salt}, uint8_t *@var{scratch}, uint8_t *@var{dst})
Compute hash of given password @var{passwd} of length @var{passwd_length} salted
with @var{salt} of length @var{salt_length} and write @var{digest_size} bytes into
the output buffer @var{dst}.  Parameter @var{hash_ctx} is a context for the
underlying hash function, which much be initialized by the caller.  @var{update}
and @var{digest} are the update and digest functions of the chosen hash algorithm.
@var{digest_size} is the digest size of the chosen hash algorithm and determines
the size of the output.
@end deftypefun

@deftypefun size_t balloon_itch (size_t @var{digest_size}, size_t @var{s_cost})
Compute the size of the scratch buffer @var{scratch}.  @var{digest_size} is the
digest size of the chosen hash algorithm.  @var{s_cost} is the space parameter
used by the @code{balloon} function.
@end deftypefun

@subsection Concrete @acronym{BALLOON} functions
Here follows a list of the specialized @acronym{BALLOON} functions, which are
more user-friendly variants of the general function.

@subsubsection @acronym{BALLOON-SHA1}

@deftypefun void balloon_sha1 (size_t @var{s_cost}, size_t @var{t_cost}, size_t @var{passwd_length}, const uint8_t *@var{passwd}, size_t @var{salt_length}, const uint8_t *@var{salt}, uint8_t *@var{scratch}, uint8_t *@var{dst})
@acronym{BALLOON} algorithm using SHA1 as the underlying hash function.
@end deftypefun

@subsubsection @acronym{BALLOON-SHA256}

@deftypefun void balloon_sha256 (size_t @var{s_cost}, size_t @var{t_cost}, size_t @var{passwd_length}, const uint8_t *@var{passwd}, size_t @var{salt_length}, const uint8_t *@var{salt}, uint8_t *@var{scratch}, uint8_t *@var{dst})
@acronym{BALLOON} algorithm using SHA256 as the underlying hash function.
@end deftypefun

@subsubsection @acronym{BALLOON-SHA384}

@deftypefun void balloon_sha384 (size_t @var{s_cost}, size_t @var{t_cost}, size_t @var{passwd_length}, const uint8_t *@var{passwd}, size_t @var{salt_length}, const uint8_t *@var{salt}, uint8_t *@var{scratch}, uint8_t *@var{dst})
@acronym{BALLOON} algorithm using SHA384 as the underlying hash function.
@end deftypefun

@subsubsection @acronym{BALLOON-SHA512}

@deftypefun void balloon_sha512 (size_t @var{s_cost}, size_t @var{t_cost}, size_t @var{passwd_length}, const uint8_t *@var{passwd}, size_t @var{salt_length}, const uint8_t *@var{salt}, uint8_t *@var{scratch}, uint8_t *@var{dst})
@acronym{BALLOON} algorithm using SHA512 as the underlying hash function.
@end deftypefun


@node Public-key algorithms
@section Public-key algorithms

Nettle uses @acronym{GMP}, the GNU bignum library, for all calculations
with large numbers. In order to use the public-key features of Nettle,
you must install @acronym{GMP}, at least version 3.0, before compiling
Nettle, and you need to link your programs with @code{-lhogweed -lnettle
-lgmp}.

The concept of @dfn{Public-key} encryption and digital signatures was
discovered by Whitfield Diffie and Martin E. Hellman and described in a
paper 1976. In traditional, ``symmetric'', cryptography, sender and
receiver share the same keys, and these keys must be distributed in a
secure way. And if there are many users or entities that need to
communicate, each @emph{pair} needs a shared secret key known by nobody
else.

@cindex Public Key Cryptography
@cindex One-way function

Public-key cryptography uses trapdoor one-way functions. A
@dfn{one-way function} is a function @code{F} such that it is easy to
compute the value @code{F(x)} for any @code{x}, but given a value
@code{y}, it is hard to compute a corresponding @code{x} such that
@code{y = F(x)}. Two examples are cryptographic hash functions, and
exponentiation in certain groups.

A @dfn{trapdoor one-way function} is a function @code{F} that is
one-way, unless one knows some secret information about @code{F}. If one
knows the secret, it is easy to compute both @code{F} and it's inverse.
If this sounds strange, look at the @acronym{RSA} example below.

Two important uses for one-way functions with trapdoors are public-key
encryption, and digital signatures. The public-key encryption functions
in Nettle are not yet documented; the rest of this chapter is about
digital signatures.

To use a digital signature algorithm, one must first create a
@dfn{key-pair}: A public key and a corresponding private key. The private
key is used to sign messages, while the public key is used for verifying
that that signatures and messages match. Some care must be taken when
distributing the public key; it need not be kept secret, but if a bad
guy is able to replace it (in transit, or in some user's list of known
public keys), bad things may happen.

There are two operations one can do with the keys. The signature
operation takes a message and a private key, and creates a signature for
the message. A signature is some string of bits, usually at most a few
thousand bits or a few hundred octets. Unlike paper-and-ink signatures,
the digital signature depends on the message, so one can't cut it out of
context and glue it to a different message.

The verification operation takes a public key, a message, and a string
that is claimed to be a signature on the message, and returns true or
false. If it returns true, that means that the three input values
matched, and the verifier can be sure that someone went through with the
signature operation on that very message, and that the ``someone'' also
knows the private key corresponding to the public key.

The desired properties of a digital signature algorithm are as follows:
Given the public key and pairs of messages and valid signatures on them,
it should be hard to compute the private key, and it should also be hard
to create a new message and signature that is accepted by the
verification operation.

Besides signing meaningful messages, digital signatures can be used for
authorization. A server can be configured with a public key, such that
any client that connects to the service is given a random nonce message.
If the server gets a reply with a correct signature matching the nonce
message and the configured public key, the client is granted access. So
the configuration of the server can be understood as ``grant access to
whoever knows the private key corresponding to this particular public
key, and to no others''.


@menu
* RSA::                         The RSA public key algorithm.
* DSA::                         The DSA digital signature algorithm.
* Elliptic curves::             Elliptic curves and ECDSA
@end menu

@node RSA
@subsection @acronym{RSA}

The @acronym{RSA} algorithm was the first practical digital signature
algorithm that was constructed. It was described 1978 in a paper by
Ronald Rivest, Adi Shamir and L.M. Adleman, and the technique was also
patented in the @acronym{USA} in 1983. The patent expired on September 20, 2000, and since
that day, @acronym{RSA} can be used freely, even in the @acronym{USA}.

It's remarkably simple to describe the trapdoor function behind
@acronym{RSA}. The ``one-way''-function used is

@example
F(x) = x^e mod n
@end example

I.e. raise x to the @code{e}'th power, while discarding all multiples of
@code{n}. The pair of numbers @code{n} and @code{e} is the public key.
@code{e} can be quite small, even @code{e = 3} has been used, although
slightly larger numbers are recommended. @code{n} should be about 2000
bits or larger.

If @code{n} is large enough, and properly chosen, the inverse of F,
the computation of @code{e}'th roots modulo @code{n}, is very difficult.
But, where's the trapdoor?

Let's first look at how @acronym{RSA} key-pairs are generated. First
@code{n} is chosen as the product of two large prime numbers @code{p}
and @code{q} of roughly the same size (so if @code{n} is 2000 bits,
@code{p} and @code{q} are about 1000 bits each). One also computes the
number @code{phi = (p-1)(q-1)}, in mathematical speak, @code{phi} is the
order of the multiplicative group of integers modulo n.

Next, @code{e} is chosen. It must have no factors in common with @code{phi} (in
particular, it must be odd), but can otherwise be chosen more or less
randomly. @code{e = 65537} is a popular choice, because it makes raising
to the @code{e}'th power particularly efficient, and being prime, it
usually has no factors common with @code{phi}.

Finally, a number @code{d}, @code{d < n} is computed such that @code{e d
mod phi = 1}. It can be shown that such a number exists (this is why
@code{e} and @code{phi} must have no common factors), and that for all x,

@example
(x^e)^d mod n = x^(ed) mod n = (x^d)^e mod n = x
@end example

Using Euclid's algorithm, @code{d} can be computed quite easily from
@code{phi} and @code{e}. But it is still hard to get @code{d} without
knowing @code{phi}, which depends on the factorization of @code{n}.

So @code{d} is the trapdoor, if we know @code{d} and @code{y = F(x)}, we can
recover x as @code{y^d mod n}. @code{d} is also the private half of
the @acronym{RSA} key-pair.

The most common signature operation for @acronym{RSA} is defined in
@cite{PKCS#1}, a specification by RSA Laboratories. The message to be
signed is first hashed using a cryptographic hash function, e.g.
@acronym{MD5} or @acronym{SHA1}. Next, some padding, the @acronym{ASN.1}
``Algorithm Identifier'' for the hash function, and the message digest
itself, are concatenated and converted to a number @code{x}. The
signature is computed from @code{x} and the private key as @code{s = x^d
mod n}@footnote{Actually, the computation is not done like this, it is
done more efficiently using @code{p}, @code{q} and the Chinese remainder
theorem (@acronym{CRT}). But the result is the same.}. The signature, @code{s} is a
number of about the same size of @code{n}, and it usually encoded as a
sequence of octets, most significant octet first.

The verification operation is straight-forward, @code{x} is computed
from the message in the same way as above. Then @code{s^e mod n} is
computed, the operation returns true if and only if the result equals
@code{x}.

The @acronym{RSA} algorithm can also be used for encryption. RSA encryption uses
the public key @code{(n,e)} to compute the ciphertext @code{m^e mod n}.
The @cite{PKCS#1} padding scheme will use at least 8 random and non-zero
octets, using @var{m} of the form @code{[00 02 padding 00 plaintext]}.
It is required that @code{m < n}, and therefor the plaintext must be
smaller than the octet size of the modulo @code{n}, with some margin.

To decrypt the message, one needs the private key to compute @code{m =
c^e mod n} followed by checking and removing the padding.

@subsubsection Nettle's @acronym{RSA} support

Nettle represents @acronym{RSA} keys using two structures that contain
large numbers (of type @code{mpz_t}).

@deftp {Context struct} {rsa_public_key} size n e
@code{size} is the size, in octets, of the modulo, and is used internally.
@code{n} and @code{e} is the public key.
@end deftp

@deftp {Context struct} {rsa_private_key} size d p q a b c
@code{size} is the size, in octets, of the modulo, and is used internally.
@code{d} is the secret exponent, but it is not actually used when
signing. Instead, the factors @code{p} and @code{q}, and the parameters
@code{a}, @code{b} and @code{c} are used. They are computed from @code{p},
@code{q} and @code{e} such that @code{a e mod (p - 1) = 1, b e mod (q -
1) = 1, c q mod p = 1}.
@end deftp

Before use, these structs must be initialized by calling one of

@deftypefun void rsa_public_key_init (struct rsa_public_key *@var{pub})
@deftypefunx void rsa_private_key_init (struct rsa_private_key *@var{key})
Calls @code{mpz_init} on all numbers in the key struct.
@end deftypefun

and when finished with them, the space for the numbers must be
deallocated by calling one of

@deftypefun void rsa_public_key_clear (struct rsa_public_key *@var{pub})
@deftypefunx void rsa_private_key_clear (struct rsa_private_key *@var{key})
Calls @code{mpz_clear} on all numbers in the key struct.
@end deftypefun

In general, Nettle's @acronym{RSA} functions deviates from Nettle's ``no
memory allocation''-policy. Space for all the numbers, both in the key structs
above, and temporaries, are allocated dynamically. For information on how
to customize allocation, see
@xref{Custom Allocation,,GMP Allocation,gmp, GMP Manual}.

When you have assigned values to the attributes of a key, you must call

@deftypefun int rsa_public_key_prepare (struct rsa_public_key *@var{pub})
@deftypefunx int rsa_private_key_prepare (struct rsa_private_key *@var{key})
Computes the octet size of the key (stored in the @code{size} attribute,
and may also do other basic sanity checks. Returns one if successful, or
zero if the key can't be used, for instance if the modulo is smaller
than the minimum size needed for @acronym{RSA} operations specified by PKCS#1.
@end deftypefun

For each operation using the private key, there are two variants, e.g.,
@code{rsa_sha256_sign} and @code{rsa_sha256_sign_tr}. The former
function is older, and it should be avoided, because it provides no
defenses against side-channel attacks. The latter function use
randomized @acronym{RSA} blinding, which defends against timing attacks
using chosen-ciphertext, and it also checks the correctness of the
private key computation using the public key, which defends against
software or hardware errors which could leak the private key.

Before signing or verifying a message, you first hash it with the
appropriate hash function. You pass the hash function's context struct
to the @acronym{RSA} signature function, and it will extract the message
digest and do the rest of the work. There are also alternative functions
that take the hash digest as argument.

There is currently no support for using SHA224 or SHA384 with
@acronym{RSA} signatures, since there's no gain in either computation
time nor message size compared to using SHA256 and SHA512, respectively.

Creating an @acronym{RSA} signature is done with one of the following
functions:

@deftypefun int rsa_md5_sign_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, struct md5_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha1_sign_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, struct sha1_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha256_sign_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, struct sha256_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha512_sign_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, struct sha512_ctx *@var{hash}, mpz_t @var{signature})
The signature is stored in @var{signature} (which must have been
@code{mpz_init}'ed earlier). The hash context is reset so that it can be
used for new messages. The @var{random_ctx} and @var{random} pointers
are used to generate the @acronym{RSA} blinding. Returns one on success,
or zero on failure. Signing fails if an error in the computation was
detected, or if the key is too small for the given hash size, e.g., it's
not possible to create a signature using SHA512 and a 512-bit
@acronym{RSA} key.
@end deftypefun

@deftypefun int rsa_md5_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha1_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha256_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha512_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, const uint8_t *@var{digest}, mpz_t @var{signature})
Creates a signature from the given hash digest. @var{digest} should
point to a digest of size @code{MD5_DIGEST_SIZE},
@code{SHA1_DIGEST_SIZE}, @code{SHA256_DIGEST_SIZE}, or
@code{SHA512_DIGEST_SIZE}respectively. The signature is stored in
@var{signature} (which must have been @code{mpz_init}:ed earlier).
Returns one on success, or zero on failure.
@end deftypefun

@deftypefun int rsa_pkcs1_sign_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{length}, const uint8_t *@var{digest_info}, mpz_t @var{signature})
Similar to the above @code{_sign_digest_tr} functions, but the input is not the
plain hash digest, but a PKCS#1 ``DigestInfo'', an ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
@end deftypefun

@deftypefun int rsa_md5_sign (const struct rsa_private_key *@var{key}, struct md5_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha1_sign (const struct rsa_private_key *@var{key}, struct sha1_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha256_sign (const struct rsa_private_key *@var{key}, struct sha256_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx int rsa_sha512_sign (const struct rsa_private_key *@var{key}, struct sha512_ctx *@var{hash}, mpz_t @var{signature})
The signature is stored in @var{signature} (which must have been
@code{mpz_init}'ed earlier). The hash context is reset so that it can be
used for new messages. Returns one on success, or zero on failure.
Signing fails if the key is too small for the given hash size, e.g.,
it's not possible to create a signature using SHA512 and a 512-bit
@acronym{RSA} key.
@end deftypefun

@deftypefun int rsa_md5_sign_digest (const struct rsa_private_key *@var{key}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha1_sign_digest (const struct rsa_private_key *@var{key}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha256_sign_digest (const struct rsa_private_key *@var{key}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_sha512_sign_digest (const struct rsa_private_key *@var{key}, const uint8_t *@var{digest}, mpz_t @var{signature})
Creates a signature from the given hash digest; otherwise analoguous to
the above signing functions. @var{digest} should point to a digest of
size @code{MD5_DIGEST_SIZE}, @code{SHA1_DIGEST_SIZE},
@code{SHA256_DIGEST_SIZE}, or @code{SHA512_DIGEST_SIZE}, respectively.
The signature is stored in @var{signature} (which must have been
@code{mpz_init}:ed earlier). Returns one on success, or zero on failure.
@end deftypefun

@deftypefun int rsa_pkcs1_sign (const struct rsa_private_key *@var{key}, size_t @var{length}, const uint8_t *@var{digest_info}, mpz_t @var{s})
Similar to the above _sign_digest functions, but the input is not the
plain hash digest, but a PKCS#1 ``DigestInfo'', an ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
@end deftypefun

Verifying an RSA signature is done with one of the following functions:

@deftypefun int rsa_md5_verify (const struct rsa_public_key *@var{key}, struct md5_ctx *@var{hash}, const mpz_t @var{signature})
@deftypefunx int rsa_sha1_verify (const struct rsa_public_key *@var{key}, struct sha1_ctx *@var{hash}, const mpz_t @var{signature})
@deftypefunx int rsa_sha256_verify (const struct rsa_public_key *@var{key}, struct sha256_ctx *@var{hash}, const mpz_t @var{signature})
@deftypefunx int rsa_sha512_verify (const struct rsa_public_key *@var{key}, struct sha512_ctx *@var{hash}, const mpz_t @var{signature})
Returns 1 if the signature is valid, or 0 if it isn't. In either case,
the hash context is reset so that it can be used for new messages.
@end deftypefun

@deftypefun int rsa_md5_verify_digest (const struct rsa_public_key *@var{key}, const uint8_t *@var{digest}, const mpz_t @var{signature})
@deftypefunx int rsa_sha1_verify_digest (const struct rsa_public_key *@var{key}, const uint8_t *@var{digest}, const mpz_t @var{signature})
@deftypefunx int rsa_sha256_verify_digest (const struct rsa_public_key *@var{key}, const uint8_t *@var{digest}, const mpz_t @var{signature})
@deftypefunx int rsa_sha512_verify_digest (const struct rsa_public_key *@var{key}, const uint8_t *@var{digest}, const mpz_t @var{signature})
Returns 1 if the signature is valid, or 0 if it isn't. @var{digest}
should point to a digest of size @code{MD5_DIGEST_SIZE},
@code{SHA1_DIGEST_SIZE}, @code{SHA256_DIGEST_SIZE}, or
@code{SHA512_DIGEST_SIZE} respectively.
@end deftypefun

@deftypefun int rsa_pkcs1_verify (const struct rsa_public_key *@var{key}, size_t @var{length}, const uint8_t *@var{digest_info}, const mpz_t @var{signature})
Similar to the above _verify_digest functions, but the input is not the
plain hash digest, but a PKCS#1 ``DigestInfo'', and ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
@end deftypefun

While the above functions for the RSA signature operations use the
@cite{PKCS#1} padding scheme, Nettle also provides the variants based on
the PSS padding scheme, specified in @cite{RFC 8017}.  These variants
take advantage of a randomly choosen salt value, which could enhance the
security by causing output to be different for equivalent inputs.
However, assuming the same security level as inverting the @acronym{RSA}
algorithm, a longer salt value does not always mean a better security
@url{https://www.iacr.org/archive/eurocrypt2002/23320268/coron.pdf}.
The typical choices of the length are between 0 and the digest size of
the underlying hash function.

Creating an RSA signature with the PSS padding scheme is done with one
of the following functions:

@deftypefun int rsa_pss_sha256_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{salt_length}, const uint8_t *@var{salt}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_pss_sha384_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{salt_length}, const uint8_t *@var{salt}, const uint8_t *@var{digest}, mpz_t @var{signature})
@deftypefunx int rsa_pss_sha512_sign_digest_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{salt_length}, const uint8_t *@var{salt}, const uint8_t *@var{digest}, mpz_t @var{signature})
Creates a signature using the PSS padding scheme. @var{salt} should
point to a salt string of size @var{salt_length}. @var{digest} should
point to a digest of size @code{SHA256_DIGEST_SIZE},
@code{SHA384_DIGEST_SIZE}, or @code{SHA512_DIGEST_SIZE}respectively. The
signature is stored in @var{signature} (which must have been
@code{mpz_init}:ed earlier).
Returns one on success, or zero on failure.
@end deftypefun

Verifying an RSA signature with the PSS padding scheme is done with one
of the following functions:

@deftypefun int rsa_pss_sha256_verify_digest (const struct rsa_public_key *@var{key}, size_t @var{salt_length}, const uint8_t *@var{digest}, const mpz_t @var{signature})
@deftypefunx int rsa_pss_sha384_verify_digest (const struct rsa_public_key *@var{key}, size_t @var{salt_length}, const uint8_t *@var{digest}, const mpz_t @var{signature})
@deftypefunx int rsa_pss_sha512_verify_digest (const struct rsa_public_key *@var{key}, size_t @var{salt_length}, const uint8_t *@var{digest}, const mpz_t @var{signature})
Returns 1 if the signature is valid, or 0 if it isn't. @var{digest}
should point to a digest of size @code{SHA256_DIGEST_SIZE},
@code{SHA384_DIGEST_SIZE}, or @code{SHA512_DIGEST_SIZE} respectively.
@end deftypefun

The following function is used to encrypt a clear text message using RSA.
@deftypefun int rsa_encrypt (const struct rsa_public_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{length}, const uint8_t *@var{cleartext}, mpz_t @var{ciphertext})
Returns 1 on success, 0 on failure. If the message is too long then this
will lead to a failure.
@end deftypefun
The following function is used to decrypt a cipher text message using RSA.
@deftypefun int rsa_decrypt (const struct rsa_private_key *@var{key}, size_t *@var{length}, uint8_t *@var{cleartext}, const mpz_t @var{ciphertext})
Returns 1 on success, 0 on failure. Causes of failure include decryption
failing or the resulting message being to large. The message buffer
pointed to by @var{cleartext} must be of size *@var{length}. After
decryption, *@var{length} will be updated with the size of the
message.
@end deftypefun
There is also a timing resistant version of decryption that utilizes
randomized RSA blinding.
@deftypefun int rsa_decrypt_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t *@var{length}, uint8_t *@var{message}, const mpz_t @var{ciphertext})
Returns 1 on success, 0 on failure.
@end deftypefun

While the above functions for the RSA encryption operations use the
@cite{PKCS#1} padding scheme, Nettle also provides the variants based
on the OAEP padding scheme, specified in @cite{RFC 8017}.  These
variants take advantage of a randomly choosen seed value, which could
enhance the security by causing output to be different for equivalent
inputs.

Encrypting a clear text message using RSA with the OAEP padding scheme
is done with one of the following functions:

@deftypefun int rsa_oaep_sha256_encrypt (const struct rsa_public_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t @var{length}, const uint8_t *@var{message}, uint8_t *@var{ciphertext})
@deftypefunx int rsa_oaep_sha384_encrypt (const struct rsa_public_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t @var{length}, const uint8_t *@var{message}, uint8_t *@var{ciphertext})
@deftypefunx int rsa_oaep_sha512_encrypt (const struct rsa_public_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t @var{length}, const uint8_t *@var{message}, uint8_t *@var{ciphertext})
Returns 1 on success, 0 on failure. The label is optional and if
omitted, @var{label_length} and @var{label} is set to 0 and
@code{NULL} respectively. The maximum size of @var{message} can be
calculated with @code{k - 2 * hLen - 2}, where @code{k} is the key
size in octets obtained with @var{key}->size, and @code{hLen} is the
output size of the underlying hash function (e.g.,
@code{SHA256_DIGEST_SIZE} for @code{rsa_oaep_sha256_encrypt}).
@end deftypefun

Decrypting a cipher text message using RSA with the OAEP padding
scheme is done with one of the following functions:

@deftypefun int rsa_oaep_sha256_decrypt (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t *@var{length}, uint8_t *@var{message}, const uint8_t *@var{ciphertext})
@deftypefunx int rsa_oaep_sha384_decrypt (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t *@var{length}, uint8_t *@var{message}, const uint8_t *@var{ciphertext})
@deftypefunx int rsa_oaep_sha512_decrypt (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{label_length}, const uint8_t *@var{label}, size_t *@var{length}, uint8_t *@var{message}, const uint8_t *@var{ciphertext})
Returns 1 on success, 0 on failure. These function utilize randomized
RSA blinding similarly to @code{rsa_decrypt_tr}. The message buffer
pointed to by @var{cleartext} must be of size *@var{length}. After
decryption, *@var{length} will be updated with the size of the
message.
@end deftypefun


If you need to use the @acronym{RSA} trapdoor, the private key, in a way
that isn't supported by the above functions Nettle also includes a
function that computes @code{x^d mod n} and nothing more, using the
@acronym{CRT} optimization.

@deftypefun int rsa_compute_root_tr (const struct rsa_public_key *@var{pub}, const struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, mpz_t @var{x}, const mpz_t @var{m})
Computes @code{x = m^d}. Returns one on success, or zero if a failure in
the computation was detected.
@end deftypefun

@deftypefun void rsa_compute_root (struct rsa_private_key *@var{key}, mpz_t @var{x}, const mpz_t @var{m})
Computes @code{x = m^d}.
@end deftypefun

At last, how do you create new keys?

@deftypefun int rsa_generate_keypair (struct rsa_public_key *@var{pub}, struct rsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, void *@var{progress_ctx}, nettle_progress_func @var{progress}, unsigned @var{n_size}, unsigned @var{e_size})
There are lots of parameters. @var{pub} and @var{key} is where the
resulting key pair is stored. The structs should be initialized, but you
don't need to call @code{rsa_public_key_prepare} or
@code{rsa_private_key_prepare} after key generation.

@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}.

@var{progress} and @var{progress_ctx} can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. @var{progress} can be NULL, in that case there are no
callbacks.

@var{size_n} is the desired size of the modulo, in bits. If @var{size_e}
is non-zero, it is the desired size of the public exponent and a random
exponent of that size is selected. But if @var{e_size} is zero, it is
assumed that the caller has already chosen a value for @code{e}, and
stored it in @var{pub}.
Returns one on success, and zero on failure. The function can fail for
example if if @var{n_size} is too small, or if @var{e_size} is zero and
@code{pub->e} is an even number.
@end deftypefun

@node DSA
@subsection @acronym{DSA}

The @acronym{DSA} digital signature algorithm is more complex than
@acronym{RSA}. It was specified during the early 1990s, and in 1994 NIST
published @acronym{FIPS} 186 which is the authoritative specification.
Sometimes @acronym{DSA} is referred to using the acronym @acronym{DSS},
for Digital Signature Standard. The most recent revision of the
specification, FIPS186-3, was issued in 2009, and it adds support for
larger hash functions than @acronym{sha1}.

For @acronym{DSA}, the underlying mathematical problem is the
computation of discrete logarithms. The public key consists of a large
prime @code{p}, a small prime @code{q} which is a factor of @code{p-1},
a number @code{g} which generates a subgroup of order @code{q} modulo
@code{p}, and an element @code{y} in that subgroup.

In the original @acronym{DSA}, the size of @code{q} is fixed to 160
bits, to match with the @acronym{SHA1} hash algorithm. The size of
@code{p} is in principle unlimited, but the
standard specifies only nine specific sizes: @code{512 + l*64}, where
@code{l} is between 0 and 8. Thus, the maximum size of @code{p} is 1024
bits, and sizes less than 1024 bits are considered obsolete and not
secure.

The subgroup requirement means that if you compute 

@example
g^t mod p
@end example

for all possible integers @code{t}, you will get precisely @code{q}
distinct values.

The private key is a secret exponent @code{x}, such that

@example
g^x = y mod p
@end example

In mathematical speak, @code{x} is the @dfn{discrete logarithm} of
@code{y} mod @code{p}, with respect to the generator @code{g}. The size
of @code{x} will also be about the same size as @code{q}. The security of the
@acronym{DSA} algorithm relies on the difficulty of the discrete
logarithm problem. Current algorithms to compute discrete logarithms in
this setting, and hence crack @acronym{DSA}, are of two types. The first
type works directly in the (multiplicative) group of integers mod
@code{p}. The best known algorithm of this type is the Number Field
Sieve, and it's complexity is similar to the complexity of factoring
numbers of the same size as @code{p}. The other type works in the
smaller @code{q}-sized subgroup generated by @code{g}, which has a more
difficult group structure. One good algorithm is Pollard-rho, which has
complexity @code{sqrt(q)}.

The important point is that security depends on the size of @emph{both}
@code{p} and @code{q}, and they should be chosen so that the difficulty
of both discrete logarithm methods are comparable. Today, the security
margin of the original @acronym{DSA} may be uncomfortably small. Using a
@code{p} of 1024 bits implies that cracking using the number field sieve
is expected to take about the same time as factoring a 1024-bit
@acronym{RSA} modulo, and using a @code{q} of size 160 bits implies
that cracking using Pollard-rho will take roughly @code{2^80} group
operations. With the size of @code{q} fixed, tied to the @acronym{SHA1}
digest size, it may be tempting to increase the size of @code{p} to,
say, 4096 bits. This will provide excellent resistance against attacks
like the number field sieve which works in the large group. But it will
do very little to defend against Pollard-rho attacking the small
subgroup; the attacker is slowed down at most by a single factor of 10
due to the more expensive group operation. And the attacker will surely
choose the latter attack.

The signature generation algorithm is randomized; in order to create a
@acronym{DSA} signature, you need a good source for random numbers
(@pxref{Randomness}). Let us describe the common case of a 160-bit
@code{q}.

To create a signature, one starts with the hash digest of the message,
@code{h}, which is a 160 bit number, and a random number @code{k,
0<k<q}, also 160 bits. Next, one computes 

@example
r = (g^k mod p) mod q
s = k^-1 (h + x r) mod q
@end example

The signature is the pair @code{(r, s)}, two 160 bit numbers. Note the
two different mod operations when computing @code{r}, and the use of the
secret exponent @code{x}.

To verify a signature, one first checks that @code{0 < r,s < q}, and
then one computes backwards,

@example
w = s^-1 mod q
v = (g^(w h) y^(w r) mod p) mod q
@end example

The signature is valid if @code{v = r}. This works out because @code{w =
s^-1 mod q = k (h + x r)^-1 mod q}, so that

@example
g^(w h) y^(w r) = g^(w h) (g^x)^(w r) = g^(w (h + x r)) = g^k 
@end example

When reducing mod @code{q} this yields @code{r}. Note that when
verifying a signature, we don't know either @code{k} or @code{x}: those
numbers are secret.

If you can choose between @acronym{RSA} and @acronym{DSA}, which one is
best? Both are believed to be secure. @acronym{DSA} gained popularity in
the late 1990s, as a patent free alternative to @acronym{RSA}. Now that
the @acronym{RSA} patents have expired, there's no compelling reason to
want to use @acronym{DSA}. Today, the original @acronym{DSA} key size
does not provide a large security margin, and it should probably be
phased out together with @acronym{RSA} keys of 1024 bits. Using the
revised @acronym{DSA} algorithm with a larger hash function, in
particular, @acronym{SHA256}, a 256-bit @code{q}, and @code{p} of size
2048 bits or more, should provide for a more comfortable security
margin, but these variants are not yet in wide use.

@acronym{DSA} signatures are smaller than @acronym{RSA} signatures,
which is important for some specialized applications.

From a practical point of view, @acronym{DSA}'s need for a good
randomness source is a serious disadvantage. If you ever use the same
@code{k} (and @code{r}) for two different message, you leak your private
key.

@subsubsection Nettle's @acronym{DSA} support

Like for @acronym{RSA}, Nettle represents @acronym{DSA} keys using two
structures, containing values of type @code{mpz_t}. For information on
how to customize allocation, see @xref{Custom Allocation,,GMP
Allocation,gmp, GMP Manual}. Nettle's @acronym{DSA} interface is defined
in @file{<nettle/dsa.h>}.

A @acronym{DSA} group is represented using the following struct.

@deftp {Context struct} {dsa_params} p q g
Parameters of the @acronym{DSA} group.
@end deftp

@deftypefun void dsa_params_init (struct dsa_params *@var{params})
Calls @code{mpz_init} on all numbers in the struct.
@end deftypefun

@deftypefun void dsa_params_clear (struct dsa_params *@var{params}params)
Calls @code{mpz_clear} on all numbers in the struct.
@end deftypefun

@deftypefun int dsa_generate_params (struct dsa_params *@var{params}, void *@var{random_ctx}, nettle_random_func *@var{random}, void *@var{progress_ctx}, nettle_progress_func *@var{progress}, unsigned @var{p_bits}, unsigned @var{q_bits})
Generates parameters of a new group. The @var{params} struct should be
initialized before you call this function.

@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}.

@var{progress} and @var{progress_ctx} can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. @var{progress} can be NULL, in that case there are no
callbacks.

@var{p_bits} and @var{q_bits} are the desired sizes of @code{p} and
@code{q}. To generate keys that conform to the original @acronym{DSA}
standard, you must use @code{q_bits = 160} and select @var{p_bits} of
the form @code{p_bits = 512 + l*64}, for @code{0 <= l <= 8}, where the
smaller sizes are no longer recommended, so you should most likely stick
to @code{p_bits = 1024}. Non-standard sizes are possible, in particular
@code{p_bits} larger than 1024, although @acronym{DSA} implementations
can not in general be expected to support such keys. Also note that
using very large @var{p_bits}, with @var{q_bits} fixed at 160, doesn't
make much sense, because the security is also limited by the size of the
smaller prime. To generate @acronym{DSA} keys for use with
@acronym{SHA256}, use @code{q_bits = 256} and, e.g., @code{p_bits =
2048}.

Returns one on success, and zero on failure. The function will fail if
@var{q_bits} is too small, or too close to @var{p_bits}.
@end deftypefun

Signatures are represented using the structure below.

@deftp {Context struct} {dsa_signature} r s
The @var{r} and @var{s} fields are both of type @code{mpz_t}.
@end deftp

@deftypefun void dsa_signature_init (struct dsa_signature *@var{signature})
@deftypefunx void dsa_signature_clear (struct dsa_signature *@var{signature})
You must call @code{dsa_signature_init} before creating or using a
signature, and call @code{dsa_signature_clear} when you are finished
with it.
@end deftypefun

Keys are represented as bignums, of type @code{mpz_t}. A public key
represents a group element, and is of the same size as @code{p}, while a
private key is an exponent, of the same size as @code{q}.

@deftypefun int dsa_sign (const struct dsa_params *@var{params}, const mpz_t @var{x}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{digest_size}, const uint8_t *@var{digest}, struct dsa_signature *@var{signature})
Creates a signature from the given hash digest, using the private key
@var{x}. @var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}. Returns one on success, or zero on failure. Signing
can fail only if the key is invalid, so that inversion modulo @code{q}
fails.
@end deftypefun

@deftypefun int dsa_verify (const struct dsa_params *@var{params}, const mpz_t @var{y}, size_t @var{digest_size}, const uint8_t *@var{digest}, const struct dsa_signature *@var{signature})
Verifies a signature, using the public key y. Returns 1 if the signature
is valid, otherwise 0.
@end deftypefun

To generate a keypair, first generate a @acronym{DSA} group using
@code{dsa_generate_params}. A keypair in this group is then created
using

@deftypefun void dsa_generate_keypair (const struct dsa_params *@var{params}, mpz_t @var{pub}, mpz_t @var{key}, void *@var{random_ctx}, nettle_random_func *@var{random})
Generates a new keypair, using the group @var{params}. The public key is
stored in @var{pub}, and the private key in @var{key}. Both variables
must be initialized using @code{mpz_init} before this call.

@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}.
@end deftypefun

@subsubsection Old, deprecated, @acronym{DSA} interface

Versions before nettle-3.0 used a different interface for @acronym{DSA}
signatures, where the group parameters and the public key was packed
together as @code{struct dsa_public_key}. Most of this interface is kept
for backwards compatibility, and declared in @file{nettle/dsa-compat.h}.
Below is the old documentation. The old and new interface use distinct
names and don't confict, with one exception: The key generation
function. The @file{nettle/dsa-compat.h} redefines
@code{dsa_generate_keypair} as an alias for
@code{dsa_compat_generate_keypair}, compatible with the old interface
and documented below.

The old @acronym{DSA} functions are very similar to the corresponding
@acronym{RSA} functions, but there are a few differences pointed out
below. For a start, there are no functions corresponding to
@code{rsa_public_key_prepare} and @code{rsa_private_key_prepare}.

@deftp {Context struct} {dsa_public_key} p q g y
The public parameters described above.
@end deftp

@deftp {Context struct} {dsa_private_key} x
The private key @code{x}.
@end deftp

Before use, these structs must be initialized by calling one of

@deftypefun void dsa_public_key_init (struct dsa_public_key *@var{pub})
@deftypefunx void dsa_private_key_init (struct dsa_private_key *@var{key})
Calls @code{mpz_init} on all numbers in the key struct.
@end deftypefun

When finished with them, the space for the numbers must be
deallocated by calling one of

@deftypefun void dsa_public_key_clear (struct dsa_public_key *@var{pub})
@deftypefunx void dsa_private_key_clear (struct dsa_private_key *@var{key})
Calls @code{mpz_clear} on all numbers in the key struct.
@end deftypefun

Signatures are represented using @code{struct dsa_signature}, described
earlier.

For signing, you need to provide both the public and the private key
(unlike @acronym{RSA}, where the private key struct includes all
information needed for signing), and a source for random numbers.
Signatures can use the @acronym{SHA1} or the @acronym{SHA256} hash
function, although the implementation of @acronym{DSA} with
@acronym{SHA256} should be considered somewhat experimental due to lack
of official test vectors and interoperability testing.

@deftypefun int dsa_sha1_sign (const struct dsa_public_key *@var{pub}, const struct dsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, struct sha1_ctx *@var{hash}, struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha1_sign_digest (const struct dsa_public_key *@var{pub}, const struct dsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, const uint8_t *@var{digest}, struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha256_sign (const struct dsa_public_key *@var{pub}, const struct dsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, struct sha256_ctx *@var{hash}, struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha256_sign_digest (const struct dsa_public_key *@var{pub}, const struct dsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, const uint8_t *@var{digest}, struct dsa_signature *@var{signature})
Creates a signature from the given hash context or digest.
@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}. Returns one on success, or zero on failure.
Signing fails if the key size and the hash size don't match.
@end deftypefun

Verifying signatures is a little easier, since no randomness generator is
needed. The functions are

@deftypefun int dsa_sha1_verify (const struct dsa_public_key *@var{key}, struct sha1_ctx *@var{hash}, const struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha1_verify_digest (const struct dsa_public_key *@var{key}, const uint8_t *@var{digest}, const struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha256_verify (const struct dsa_public_key *@var{key}, struct sha256_ctx *@var{hash}, const struct dsa_signature *@var{signature})
@deftypefunx int dsa_sha256_verify_digest (const struct dsa_public_key *@var{key}, const uint8_t *@var{digest}, const struct dsa_signature *@var{signature})
Verifies a signature. Returns 1 if the signature is valid, otherwise 0.
@end deftypefun

Key generation uses mostly the same parameters as the corresponding
@acronym{RSA} function.

@deftypefun int dsa_compat_generate_keypair (struct dsa_public_key *@var{pub}, struct dsa_private_key *@var{key}, void *@var{random_ctx}, nettle_random_func @var{random}, void *@var{progress_ctx}, nettle_progress_func @var{progress}, unsigned @var{p_bits}, unsigned @var{q_bits})
@var{pub} and @var{key} is where the resulting key pair is stored. The
structs should be initialized before you call this function. 

@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}.

@var{progress} and @var{progress_ctx} can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. @var{progress} can be NULL, in that case there are no
callbacks.

@var{p_bits} and @var{q_bits} are the desired sizes of @code{p} and
@code{q}. See @code{dsa_generate_keypair} for details.
@end deftypefun

@node Elliptic curves
@subsection Elliptic curves

For cryptographic purposes, an elliptic curve is a mathematical group of
points, and computing logarithms in this group is computationally
difficult problem. Nettle uses additive notation for elliptic curve
groups. If @math{P} and @math{Q} are two points, and @math{k} is an
integer, the point sum, @math{P + Q}, and the multiple @math{k P} can be
computed efficiently, but given only two points @math{P} and @math{Q},
finding an integer @math{k} such that @math{Q = k P} is the elliptic
curve discrete logarithm problem.

Nettle supports standard curves which are all of the form @math{y^2 =
x^3 - 3 x + b @pmod{p}}, i.e., the points have coordinates @math{(x,y)},
both considered as integers modulo a specified prime @math{p}. Curves
are represented as a @code{struct ecc_curve}. It also supports
curve25519, which uses a different form of curve. Supported curves are
declared in @file{<nettle/ecc-curve.h>}, e.g., call
@code{nettle_get_secp_256r1} for a standardized curve using the 256-bit
prime @math{p = 2^{256} - 2^{224} + 2^{192} + 2^{96} - 1}. The contents
of these structs is not visible to nettle users. The ``bitsize of the
curve'' is used as a shorthand for the bitsize of the curve's prime
@math{p}, e.g., 256 bits for the SECP 256R1 curve.

@menu
* Side-channel silence::
* ECDSA::
* GOSTDSA::
* Curve 25519 and Curve 448::
@end menu

@node Side-channel silence
@subsubsection Side-channel silence
@cindex Side-channel attack

Nettle's implementation of the elliptic curve operations is intended to
be side-channel silent. The side-channel attacks considered are:

@itemize
@item Timing attacks
If the timing of operations depends on secret values, an attacker
interacting with your system can measure the response time, and infer
information about your secrets, e.g., a private signature key.

@item Attacks using memory caches
Assume you have some secret data on a multi-user system, and that this
data is properly protected so that other users get no direct access to
it. If you have a process operating on the secret data, and this process
does memory accesses depending on the data, e.g, an internal lookup
table in some cryptographic algorithm, an attacker running a separate
process on the same system may use behavior of internal CPU caches to
get information about your secrets. This type of attack can even cross
virtual machine boundaries.
@end itemize

Nettle's ECC implementation is designed to be @dfn{side-channel silent},
and not leak any information to these attacks. Timing and memory
accesses depend only on the size of the input data and its location in
memory, not on the actual data bits. This implies a performance penalty
in several of the building blocks.

@node ECDSA
@subsubsection ECDSA

ECDSA is a variant of the DSA digital signature scheme (@pxref{DSA}),
which works over an elliptic curve group rather than over a (subgroup
of) integers modulo @math{p}. Like DSA, creating a signature requires a unique
random nonce (repeating the nonce with two different messages reveals
the private key, and any leak or bias in the generation of the nonce
also leaks information about the key).

Unlike DSA, signatures are in general not tied to any particular hash
function or even hash size. Any hash function can be used, and the hash
value is truncated or padded as needed to get a size matching the curve
being used. It is recommended to use a strong cryptographic hash
function with digest size close to the bit size of the curve, e.g.,
SHA256 is a reasonable choice when using ECDSA signature over the curve
secp256r1. A protocol or application using ECDSA has to specify which
curve and which hash function to use, or provide some mechanism for
negotiating.

Nettle defines ECDSA in @file{<nettle/ecdsa.h>}. We first need
to define the data types used to represent public and private keys.

@deftp {struct} {struct ecc_point}
Represents a point on an elliptic curve. In particular, it is used to
represent an ECDSA public key.
@end deftp

@deftypefun void ecc_point_init (struct ecc_point *@var{p}, const struct ecc_curve *@var{ecc})
Initializes @var{p} to represent points on the given curve @var{ecc}.
Allocates storage for the coordinates, using the same allocation
functions as GMP.
@end deftypefun

@deftypefun void ecc_point_clear (struct ecc_point *@var{p})
Deallocate storage allocated by previous ecc_point_init.
@end deftypefun

@deftypefun int ecc_point_set (struct ecc_point *@var{p}, const mpz_t @var{x}, const mpz_t @var{y})
Check that the given coordinates represent a point on the curve. If so,
the coordinates are copied and converted to internal representation, and
the function returns 1. Otherwise, it returns 0. Currently, the
infinity point (or zero point, with additive notation) is not allowed.
@end deftypefun

@deftypefun void ecc_point_get (const struct ecc_point *@var{p}, mpz_t @var{x}, mpz_t @var{y})
Extracts the coordinate of the point @var{p}. The output parameters
@var{x} or @var{y} may be NULL if the caller doesn't want that
coordinate.
@end deftypefun

@deftp {struct} {struct ecc_scalar}
Represents an integer in the range @math{0 < x < group order}, where the
``group order'' refers to the order of an ECC group. In particular, it
is used to represent an ECDSA private key.
@end deftp

@deftypefun void ecc_scalar_init (struct ecc_scalar *@var{s}, const struct ecc_curve *@var{ecc})
Initializes @var{s} to represent a scalar suitable for the given curve
@var{ecc}. Allocates storage using the same allocation functions as GMP.
@end deftypefun

@deftypefun void ecc_scalar_clear (struct ecc_scalar *@var{s})
Deallocate the storage allocated by previous ecc_scalar_init.
@end deftypefun

@deftypefun int ecc_scalar_set (struct ecc_scalar *@var{s}, const mpz_t @var{z})
Check that @var{z} is in the correct range. If so, copies the value to
@var{s} and returns 1, otherwise returns 0.
@end deftypefun

@deftypefun void ecc_scalar_get (const struct ecc_scalar *@var{s}, mpz_t @var{z})
Extracts the scalar, in GMP @code{mpz_t} representation.
@end deftypefun

To create and verify ECDSA signatures, the following functions are used.

@deftypefun void ecdsa_sign (const struct ecc_scalar *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{digest_length}, const uint8_t *@var{digest}, struct dsa_signature *@var{signature})
Uses the private key @var{key} to create a signature of @var{digest}.
@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. The signature is stored in
@var{signature}, in the same way as for plain DSA.
@end deftypefun

@deftypefun int ecdsa_verify (const struct ecc_point *@var{pub}, size_t @var{length}, const uint8_t *@var{digest}, const struct dsa_signature *@var{signature})
Uses the public key @var{pub} to verify that @var{signature} is a valid
signature for the message digest @var{digest} (of @var{length} octets).
Returns 1 if the signature is valid, otherwise 0.
@end deftypefun

Finally, generating a new ECDSA key pair:

@deftypefun void ecdsa_generate_keypair (struct ecc_point *@var{pub}, struct ecc_scalar *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random})
@var{pub} and @var{key} is where the resulting key pair is stored. The
structs should be initialized, for the desired ECC curve, before you call this function.

@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. For advice, see
@xref{Randomness}.
@end deftypefun

@node GOSTDSA
@subsubsection GOSTDSA
@cindex GOST DSA

GOSTDSA (GOST R 34.10-2001, GOST R 34.10-2012) is a variant of the DSA
(@pxref{DSA}) and ECDSA (@pxref{ECDSA}) digital signature schemes, which works
over an elliptic curve group. Original documents are written in Russian.
English translations are provided in @cite{RFC 5832} and @cite{RFC 7091}.
While technically nothing stops one from using GOSTDSA over any curve, it
is defined only over several 256 and 512-bit curves.  Like DSA and ECDSA,
creating a signature requires a unique random nonce (repeating the nonce
with two different messages reveals the private key, and any leak or bias
in the generation of the nonce also leaks information about the key).

GOST R 34.10-2001 was defined to use GOST R 34.11-94 hash function
(GOSTHASH94 and GOSTHASH94CP, @cite{RFC 5831}).  GOST R 34.10-2012 is
defined to use GOST R 34.11-2012 hash function (Streebog, @cite{RFC
6986}) of corresponding size (256 or 512) depending on curve size.

Nettle defines GOSTDSA in @file{<nettle/gostdsa.h>}. GOSTDSA reuses ECDSA
data types (@code{struct ecc_point}, @code{struct ecc_scalar}) to
represent public and private keys.  Also to generate a new GOSTDSA key
pair one has to use @code{ecdsa_generate_keypair()} function.

To create and verify GOSTDSA signatures, the following functions are used.

@deftypefun void gostdsa_sign (const struct ecc_scalar *@var{key}, void *@var{random_ctx}, nettle_random_func *@var{random}, size_t @var{digest_length}, const uint8_t *@var{digest}, struct dsa_signature *@var{signature})
Uses the private key @var{key} to create a signature of @var{digest}.
@var{random_ctx} and @var{random} is a randomness generator.
@code{random(random_ctx, length, dst)} should generate @code{length}
random octets and store them at @code{dst}. The signature is stored in
@var{signature}, in the same was as for plain DSA.
@end deftypefun

@deftypefun int gostdsa_verify (const struct ecc_point *@var{pub}, size_t @var{length}, const uint8_t *@var{digest}, const struct dsa_signature *@var{signature})
Uses the public key @var{pub} to verify that @var{signature} is a valid
signature for the message digest @var{digest} (of @var{length} octets).
Returns 1 if the signature is valid, otherwise 0.
@end deftypefun

For historical reason several curve IDs (OIDs) may correspond to a single
curve/generator combination. Following list defines correspondence
between nettle's view on curves and actual identifiers defined in @cite{RFC
4357} and @cite{RFC 7836}.

@deftypefun {const struct ecc_curve} nettle_get_gost_gc256b (void)
Returns curve corresponding to following identifiers:
@itemize
@item id-GostR3410-2001-CryptoPro-A-ParamSet (@cite{RFC 4357})
@item id-GostR3410-2001-CryptoPro-XchA-ParamSet (@cite{RFC 4357})
@item id-tc26-gost-3410-12-256-paramSetB
@end itemize
@end deftypefun

@deftypefun {const struct ecc_curve} nettle_get_gost_gc512a (void)
Returns curve corresponding to following identifiers:
@itemize
@item id-tc26-gost-3410-12-512-paramSetA (@cite{RFC 7836})
@end itemize
@end deftypefun

For GOST key pairs key derivation/key agreement function (VKO) is defined in
@cite{RFC 4357} and @cite{RFC 7836}.  Basically shared key is equal to
hash(cofactor * ukm * priv * pub). Nettle library provides a function that does
multiplication. Caller should do hashing on his own (it will be either
GOST R 34.11-94 (@pxref{GOSTHASH94CP}) or GOST R 34.11-2012, Streebog, which nor part of the library yet).

@deftypefun void gostdsa_vko (const struct ecc_scalar *@var{priv}, const struct ecc_point *@var{pub}, size_t @var{ukm_length}, const uint8_t *@var{ukm}, uint8_t *@var{out})
Uses private key @var{priv}, public ket @var{pub} and shared key material
@var{ukm} to generate shared secret, written to buffer @var{out}. The buffer
should be of the size equal to 2 private key lengths: 64 bytes for 256 bit
curves and 128 bytes for 512 bit ones. UKM is a shared key material, usually
transferred in cleartext. It does not have to be secret.
@end deftypefun

@node Curve 25519 and Curve 448
@subsubsection Curve25519 and Curve448
@cindex Curve 25519
@cindex Curve 448

@c FIXME: Make 2^255 pretty in all output formats. Use @sup?
@c There are other places too (2^32, 2^130).

Curve25519 is an elliptic curve of Montgomery type, @math{y^2 = x^3 +
486662 x^2 + x @pmod{p}}, with @math{p = 2^255 - 19}. Montgomery curves
have the advantage of simple and efficient point addition based on the
x-coordinate only. This particular curve was proposed by D. J. Bernstein
in 2006, for fast Diffie-Hellman key exchange, and is also described in
@cite{RFC 7748}. The group generator is defined by @math{x = 9} (there
are actually two points with @math{x = 9}, differing by the sign of the
y-coordinate, but that doesn't matter for the curve25519 operations
which work with the x-coordinate only).

The curve25519 functions are defined as operations on octet strings,
representing 255-bit scalars or x-coordinates, in little-endian byte
order. The most significant input bit, i.e, the most significant bit of
the last octet, is always ignored.

For scalars, in addition, the least significant three bits are ignored,
and treated as zero, and the second most significant bit is ignored too,
and treated as one. Then the scalar input string always represents 8
times a number in the range @math{2^251 <= s < 2^252}.

Of all the possible input strings, only about half correspond to
x-coordinates of points on curve25519, i.e., a value @math{x} for which
the the curve equation can be solved for @math{y}. The other half
correspond to points on a related ``twist curve''. The function
@code{curve25519_mul} uses a Montgomery ladder for the scalar
multiplication, as suggested in the curve25519 literature, and required
by @cite{RFC 7748}. The output is therefore well defined for
@emph{all} possible inputs, no matter if the input string represents a
valid point on the curve or not.

Note that the curve25519 implementation in earlier versions of Nettle
deviates slightly from @cite{RFC 7748}, in that bit 255 of the @math{x}
coordinate of the point input to curve25519_mul was not ignored. The
@file{nette/curve25519.h} defines a preprocessor symbol
@code{NETTLE_CURVE25519_RFC7748} to indicate conformance with the
standard.

Nettle defines Curve 25519 in @file{<nettle/curve25519.h>}.

@defvr Constant NETTLE_CURVE25519_RFC7748
Defined to 1 in Nettle versions conforming to RFC 7748. Undefined in
earlier versions.
@end defvr

@defvr Constant CURVE25519_SIZE
The size of the strings representing curve25519 points and scalars, 32.
@end defvr

@deftypefun void curve25519_mul_g (uint8_t *@var{q}, const uint8_t *@var{n})
Computes @math{Q = N G}, where @math{G} is the group generator and
@math{N} is an integer. The input argument @var{n} and the output
argument @var{q} use a little-endian representation of the scalar and
the x-coordinate, respectively. They are both of size
@code{CURVE25519_SIZE}.

This function is intended to be compatible with the function
@code{crypto_scalar_mult_base} in the NaCl library.
@end deftypefun

@deftypefun void curve25519_mul (uint8_t *@var{q}, const uint8_t *@var{n}, const uint8_t *@var{p})
Computes @math{Q = N P}, where @math{P} is an input point and @math{N}
is an integer. The input arguments @var{n} and @var{p} and the output
argument @var{q} use a little-endian representation of the scalar and
the x-coordinates, respectively. They are all of size
@code{CURVE25519_SIZE}.

This function is intended to be compatible with the function
@code{crypto_scalar_mult} in the NaCl library.
@end deftypefun

Similarly, Nettle also implements Curve448, an elliptic curve of
Montgomery type, @math{y^2 = x^3 + 156326 x^2 + x @pmod{p}}, with
@math{p = 2^448 - 2^224 - 1}.  This particular curve was proposed by
Mike Hamburg in 2015, for fast Diffie-Hellman key exchange, and is also
described in @cite{RFC 7748}.

Nettle defines Curve 448 in @file{<nettle/curve448.h>}.

@defvr Constant CURVE448_SIZE
The octet length of the strings representing curve448 points and scalars, 56.
@end defvr

@deftypefun void curve448_mul_g (uint8_t *@var{q}, const uint8_t *@var{n})
Computes @math{Q = N G}, where @math{G} is the group generator and
@math{N} is an integer. The input argument @var{n} and the output
argument @var{q} use a little-endian representation of the scalar and
the x-coordinate, respectively. They are both of size
@code{CURVE448_SIZE}.

This function is intended to be compatible with the function
@code{crypto_scalar_mult_base} in the NaCl library.
@end deftypefun

@deftypefun void curve448_mul (uint8_t *@var{q}, const uint8_t *@var{n}, const uint8_t *@var{p})
Computes @math{Q = N P}, where @math{P} is an input point and @math{N}
is an integer. The input arguments @var{n} and @var{p} and the output
argument @var{q} use a little-endian representation of the scalar and
the x-coordinates, respectively. They are all of size
@code{CURVE448_SIZE}.

This function is intended to be compatible with the function
@code{crypto_scalar_mult} in the NaCl library.
@end deftypefun

@subsubsection EdDSA
@cindex eddsa

EdDSA is a signature scheme proposed by D. J. Bernstein et al. in 2011.
It is defined using a ``Twisted Edwards curve'', of the form @math{-x^2
+ y^2 = 1 + d x^2 y^2}. The specific signature scheme Ed25519 uses a
curve which is equivalent to curve25519: The two groups used differ only
by a simple change of coordinates, so that the discrete logarithm
problem is of equal difficulty in both groups.

Unlike other signature schemes in Nettle, the input to the EdDSA sign
and verify functions is the possibly large message itself, not a hash
digest. EdDSA is a variant of Schnorr signatures, where the message is
hashed together with other data during the signature process, providing
resilience to hash-collisions: A successful attack finding collisions in
the hash function does not automatically translate into an attack to
forge signatures. EdDSA also avoids the use of a randomness source by
generating the needed signature nonce from a hash of the private key and
the message, which means that the message is actually hashed twice when
creating a signature. If signing huge messages, it is possible to hash
the message first and pass the short message digest as input to the sign
and verify functions, however, the resilience to hash collision is then
lost.

@defvr Constant ED25519_KEY_SIZE
The size of a private or public Ed25519 key, 32 octets.
@end defvr

@defvr Constant ED25519_SIGNATURE_SIZE
The size of an Ed25519 signature, 64 octets.
@end defvr

@deftypefun void ed25519_sha512_public_key (uint8_t *@var{pub}, const uint8_t *@var{priv})
Computes the public key corresponding to the given private key. Both
input and output are of size @code{ED25519_KEY_SIZE}.
@end deftypefun

@deftypefun void ed25519_sha512_sign (const uint8_t *@var{pub}, const uint8_t *@var{priv}, size_t @var{length}, const uint8_t *@var{msg}, uint8_t *@var{signature})
Signs a message using the provided key pair.
@end deftypefun

@deftypefun int ed25519_sha512_verify (const uint8_t *@var{pub}, size_t @var{length}, const uint8_t *@var{msg}, const uint8_t *@var{signature})
Verifies a message using the provided public key. Returns 1 if the
signature is valid, otherwise 0.
@end deftypefun

Nettle also provides Ed448, an EdDSA signature scheme based on an
Edwards curve equivalent to curve448.

@defvr Constant ED448_KEY_SIZE
The size of a private or public Ed448 key, 57 octets.
@end defvr

@defvr Constant ED448_SIGNATURE_SIZE
The size of an Ed448 signature, 114 octets.
@end defvr

@deftypefun void ed448_shake256_public_key (uint8_t *@var{pub}, const uint8_t *@var{priv})
Computes the public key corresponding to the given private key. Both
input and output are of size @code{ED448_KEY_SIZE}.
@end deftypefun

@deftypefun void ed448_shake256_sign (const uint8_t *@var{pub}, const uint8_t *@var{priv}, size_t @var{length}, const uint8_t *@var{msg}, uint8_t *@var{signature})
Signs a message using the provided key pair.
@end deftypefun

@deftypefun int ed448_shake256_verify (const uint8_t *@var{pub}, size_t @var{length}, const uint8_t *@var{msg}, const uint8_t *@var{signature})
Verifies a message using the provided public key. Returns 1 if the
signature is valid, otherwise 0.
@end deftypefun

@node Randomness
@section Randomness

@cindex Randomness

A crucial ingredient in many cryptographic contexts is randomness: Let
@code{p} be a random prime, choose a random initialization vector
@code{iv}, a random key @code{k} and a random exponent @code{e}, etc. In
the theories, it is assumed that you have plenty of randomness around.
If this assumption is not true in practice, systems that are otherwise
perfectly secure, can be broken. Randomness has often turned out to be
the weakest link in the chain.

In non-cryptographic applications, such as games as well as scientific
simulation, a good randomness generator usually means a generator that
has good statistical properties, and is seeded by some simple function
of things like the current time, process id, and host name.

However, such a generator is inadequate for cryptography, for at least
two reasons:


@itemize

@item
It's too easy for an attacker to guess the initial seed. Even if it will
take some 2^32 tries before he guesses right, that's far too easy. For
example, if the process id is 16 bits, the resolution of ``current time''
is one second, and the attacker knows what day the generator was seeded,
there are only about 2^32 possibilities to try if all possible values
for the process id and time-of-day are tried.

@item
The generator output reveals too much. By observing only a small segment
of the generator's output, its internal state can be recovered, and from
there, all previous output and all future output can be computed by the
attacker. 
@end itemize

A randomness generator that is used for cryptographic purposes must have
better properties. Let's first look at the seeding, as the issues here
are mostly independent of the rest of the generator. The initial state
of the generator (its seed) must be unguessable by the attacker. So
what's unguessable? It depends on what the attacker already knows. The
concept used in information theory to reason about such things is called
``entropy'', or ``conditional entropy'' (not to be confused with the
thermodynamic concept with the same name). A reasonable requirement is
that the seed contains a conditional entropy of at least some 80-100
bits. This property can be explained as follows: Allow the attacker to
ask @code{n} yes-no-questions, of his own choice, about the seed. If
the attacker, using this question-and-answer session, as well as any
other information he knows about the seeding process, still can't guess
the seed correctly, then the conditional entropy is more than @code{n}
bits.

@cindex Entropy
@cindex Conditional entropy

Let's look at an example. Say information about timing of received
network packets is used in the seeding process. If there is some random
network traffic going on, this will contribute some bits of entropy or
``unguessability'' to the seed. However, if the attacker can listen in to
the local network, or if all but a small number of the packets were
transmitted by machines that the attacker can monitor, this additional
information makes the seed easier for the attacker to figure out. Even
if the information is exactly the same, the conditional entropy, or
unguessability, is smaller for an attacker that knows some of it already
before the hypothetical question-and-answer session.

Seeding of good generators is usually based on several sources. The key
point here is that the amount of unguessability that each source
contributes, depends on who the attacker is. Some sources that have been
used are:

@table @asis
@item High resolution timing of i/o activities
Such as completed blocks from spinning hard disks, network packets, etc.
Getting access to such information is quite system dependent, and not
all systems include suitable hardware. If available, it's one of the
better randomness source one can find in a digital, mostly predictable,
computer.

@item User activity
Timing and contents of user interaction events is another popular source
that is available for interactive programs (even if I suspect that it is
sometimes used in order to make the user feel good, not because the
quality of the input is needed or used properly). Obviously, not
available when a machine is unattended. Also beware of networks: User
interaction that happens across a long serial cable, @acronym{TELNET}
session, or even @acronym{SSH} session may be visible to an attacker, in
full or partially.

@item Audio input
Any room, or even a microphone input that's left unconnected, is a
source of some random background noise, which can be fed into the
seeding process.

@item Specialized hardware
Hardware devices with the sole purpose of generating random data have
been designed. They range from radioactive samples with an attached
Geiger counter, to amplification of the inherent noise in electronic
components such as diodes and resistors, to low-frequency sampling of
chaotic systems. Hashing successive images of a Lava lamp is a
spectacular example of the latter type.

@item Secret information
Secret information, such as user passwords or keys, or private files
stored on disk, can provide some unguessability. A problem is that if
the information is revealed at a later time, the unguessability
vanishes. Another problem is that this kind of information tends to be
fairly constant, so if you rely on it and seed your generator regularly,
you risk constructing almost similar seeds or even constructing the same
seed more than once.
@end table

For all practical sources, it's difficult but important to provide a
reliable lower bound on the amount of unguessability that it provides.
Two important points are to make sure that the attacker can't observe
your sources (so if you like the Lava lamp idea, remember that you have
to get your own lamp, and not put it by a window or anywhere else where
strangers can see it), and that hardware failures are detected. What if
the bulb in the Lava lamp, which you keep locked into a cupboard
following the above advice, breaks after a few months?

So let's assume that we have been able to find an unguessable seed,
which contains at least 80 bits of conditional entropy, relative to all
attackers that we care about (typically, we must at the very least
assume that no attacker has root privileges on our machine).

How do we generate output from this seed, and how much can we get? Some
generators (notably the Linux @file{/dev/random} generator) tries to
estimate available entropy and restrict the amount of output. The goal
is that if you read 128 bits from @file{/dev/random}, you should get 128
``truly random'' bits. This is a property that is useful in some
specialized circumstances, for instance when generating key material for
a one time pad, or when working with unconditional blinding, but in most
cases, it doesn't matter much. For most application, there's no limit on
the amount of useful ``random'' data that we can generate from a small
seed; what matters is that the seed is unguessable and that the
generator has good cryptographic properties.

At the heart of all generators lies its internal state. Future output
is determined by the internal state alone. Let's call it the generator's
key. The key is initialized from the unguessable seed. Important
properties of a generator are:

@table @dfn

@item Key-hiding
An attacker observing the output should not be able to recover the
generator's key.

@item Independence of outputs
Observing some of the output should not help the attacker to guess
previous or future output.

@item Forward secrecy
Even if an attacker compromises the generator's key, he should not be
able to guess the generator output @emph{before} the key compromise.

@item Recovery from key compromise
If an attacker compromises the generator's key, he can compute
@emph{all} future output. This is inevitable if the generator is seeded
only once, at startup. However, the generator can provide a reseeding
mechanism, to achieve recovery from key compromise. More precisely: If
the attacker compromises the key at a particular time @code{t_1}, there
is another later time @code{t_2}, such that if the attacker observes all
output generated between @code{t_1} and @code{t_2}, he still can't guess
what output is generated after @code{t_2}.

@end table

Nettle includes one randomness generator that is believed to have all
the above properties, and two simpler ones.

@acronym{ChaCha} (@pxref{ChaCha}), like any stream cipher, can be used
as a randomness generator. Its output should be of reasonable
quality. There's no single natural way to reseed it, but if you need
reseeding, you should be using Yarrow instead.  Historically ARCFOUR
(@pxref{Arcfour}) has been used as a randomness generator, however it is
known to be distinguishable from random data and the output leaks
information about the key.

The ``lagged Fibonacci'' generator in @file{<nettle/knuth-lfib.h>} is a
fast generator with good statistical properties, but is @strong{not} for
cryptographic use, and therefore not documented here. It is included
mostly because the Nettle test suite needs to generate some test data
from a small seed.

The recommended generator to use is Yarrow, described below.

@subsection Yarrow

Yarrow is a family of pseudo-randomness generators, designed for
cryptographic use, by John Kelsey, Bruce Schneier and Niels Ferguson.
Yarrow-160 is described in a paper at
@url{https://www.schneier.com/academic/yarrow/}, and it uses @acronym{SHA1}
and triple-DES, and has a 160-bit internal state. Nettle implements
Yarrow-256, which is similar, but uses @acronym{SHA256} and
@acronym{AES} to get an internal state of 256 bits.

Yarrow was an almost finished project, the paper mentioned above is the
closest thing to a specification for it, but some smaller details are
left out. There is no official reference implementation or test cases.
This section includes an overview of Yarrow, but for the details of
Yarrow-256, as implemented by Nettle, you have to consult the source
code. Maybe a complete specification can be written later.

Yarrow can use many sources (at least two are needed for proper
reseeding), and two randomness ``pools'', referred to as the ``slow pool'' and
the ``fast pool''. Input from the sources is fed alternatingly into the
two pools. When one of the sources has contributed 100 bits of entropy
to the fast pool, a ``fast reseed'' happens and the fast pool is mixed
into the internal state. When at least two of the sources have
contributed at least 160 bits each to the slow pool, a ``slow reseed''
takes place. The contents of both pools are mixed into the internal
state. These procedures should ensure that the generator will eventually
recover after a key compromise.

The output is generated by using @acronym{AES} to encrypt a counter,
using the generator's current key. After each request for output,
another 256 bits are generated which replace the key. This ensures
forward secrecy.

Yarrow can also use a @dfn{seed file} to save state across restarts.
Yarrow is seeded by either feeding it the contents of the previous seed
file, or feeding it input from its sources until a slow reseed happens.

Nettle defines Yarrow-256 in @file{<nettle/yarrow.h>}. 

@deftp {Context struct} {struct yarrow256_ctx}
@end deftp

@deftp {Context struct} {struct yarrow_source}
Information about a single source.
@end deftp

@defvr Constant YARROW256_SEED_FILE_SIZE
Recommended size of the Yarrow-256 seed file.
@end defvr

@deftypefun void yarrow256_init (struct yarrow256_ctx *@var{ctx}, unsigned @var{nsources}, struct yarrow_source *@var{sources})
Initializes the yarrow context, and its @var{nsources} sources. It's
possible to call it with @var{nsources}=0 and @var{sources}=NULL, if
you don't need the update features.
@end deftypefun

@deftypefun void yarrow256_seed (struct yarrow256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{seed_file})
Seeds Yarrow-256 from a previous seed file. @var{length} should be at least
@code{YARROW256_SEED_FILE_SIZE}, but it can be larger.

The generator will trust you that the @var{seed_file} data really is
unguessable. After calling this function, you @emph{must} overwrite the old
seed file with newly generated data from @code{yarrow256_random}. If it's
possible for several processes to read the seed file at about the same
time, access must be coordinated using some locking mechanism.
@end deftypefun

@deftypefun int yarrow256_update (struct yarrow256_ctx *@var{ctx}, unsigned @var{source}, unsigned @var{entropy}, size_t @var{length}, const uint8_t *@var{data})
Updates the generator with data from source @var{SOURCE} (an index that
must be smaller than the number of sources). @var{entropy} is your
estimated lower bound for the entropy in the data, measured in bits.
Calling update with zero @var{entropy} is always safe, no matter if the
data is random or not.

Returns 1 if a reseed happened, in which case an application using a
seed file may want to generate new seed data with
@code{yarrow256_random} and overwrite the seed file. Otherwise, the
function returns 0.
@end deftypefun

@deftypefun void yarrow256_random (struct yarrow256_ctx *@var{ctx}, size_t @var{length}, uint8_t *@var{dst})
Generates @var{length} octets of output. The generator must be seeded
before you call this function.

If you don't need forward secrecy, e.g. if you need non-secret
randomness for initialization vectors or padding, you can gain some
efficiency by buffering, calling this function for reasonably large
blocks of data, say 100-1000 octets at a time.
@end deftypefun

@deftypefun int yarrow256_is_seeded (struct yarrow256_ctx *@var{ctx})
Returns 1 if the generator is seeded and ready to generate output,
otherwise 0.
@end deftypefun

@deftypefun unsigned yarrow256_needed_sources (struct yarrow256_ctx *@var{ctx})
Returns the number of sources that must reach the threshold before a
slow reseed will happen. Useful primarily when the generator is unseeded.
@end deftypefun

@deftypefun void yarrow256_fast_reseed (struct yarrow256_ctx *@var{ctx})
@deftypefunx void yarrow256_slow_reseed (struct yarrow256_ctx *@var{ctx})
Causes a fast or slow reseed to take place immediately, regardless of the
current entropy estimates of the two pools. Use with care.
@end deftypefun

Nettle includes an entropy estimator for one kind of input source: User
keyboard input.

@deftp {Context struct} {struct yarrow_key_event_ctx}
Information about recent key events.
@end deftp

@deftypefun void yarrow_key_event_init (struct yarrow_key_event_ctx *@var{ctx})
Initializes the context.
@end deftypefun

@deftypefun unsigned yarrow_key_event_estimate (struct yarrow_key_event_ctx *@var{ctx}, unsigned @var{key}, unsigned @var{time})
@var{key} is the id of the key (ASCII value, hardware key code, X
keysym, @dots{}, it doesn't matter), and @var{time} is the timestamp of
the event. The time must be given in units matching the resolution by
which you read the clock. If you read the clock with microsecond
precision, @var{time} should be provided in units of microseconds. But
if you use @code{gettimeofday} on a typical Unix system where the clock
ticks 10 or so microseconds at a time, @var{time} should be given in
units of 10 microseconds.

Returns an entropy estimate, in bits, suitable for calling
@code{yarrow256_update}. Usually, 0, 1 or 2 bits.
@end deftypefun

@subsection DRBG-CTR

The Deterministic Random Bit Generator (DRBG) family is a complex family
of deterministic randomness generators published by NIST in SP 800-90A.

We support what we believe is the reasonable parts of the CTR_DRBG
algorithm for AES256.  Re-seeding, personalization strings, derivation
functions and support for non-AES256 is not implemented.
Personalization strings can be implemented by the caller, if desired,
with xor.  If you need re-seeding or entropy derivation, we suggest that
you use Yarrow instead.

The security bounds of DRBG-CTR are not intuitive, see ``Security Bounds
for the NIST Codebook-based Deterministic Random Bit Generator'' by
Matthew J. Campagna, from @url{https://eprint.iacr.org/2006/379.pdf}.

Our suggested use-case for DRBG-CTR is to deterministically generate
known values from a seed when comparing against expected values for some
other algorithm.

Nettle defines DRBG-CTR in @file{<nettle/drbg-ctr.h>}.

@deftp {Context struct} {struct drbg_ctr_aes256_ctx}
@end deftp

@defvr Constant DRBG_CTR_AES256_SEED_SIZE
The size of the seeding material.
@end defvr

@deftypefun void drbg_ctr_aes256_init (struct drbg_ctr_aes256_ctx *@var{ctx}, uint8_t *@var{seed_material})
Initialize the DRBG-CTR-AES256 context using
@code{DRBG_CTR_AES256_SEED_SIZE} bytes of @var{seed_material}.
@end deftypefun

@deftypefun void drbg_ctr_aes256_random (struct drbg_ctr_aes256_ctx *@var{ctx}, size_t n, uint8_t *@var{dst})
Generates @var{n} octets of output into @var{dst}.  The generator must
be initialized before you call this function.
@end deftypefun

@node ASCII encoding
@section ASCII encoding

Encryption will transform your data from text into binary format, and that
may be a problem if, for example, you want to send the data as if it was
plain text in an email, or store it along with descriptive text in a
file. You may then use an encoding from binary to text: each binary byte
is translated into a number of bytes of plain text.

A base-N encoding of data is one representation of data that only uses N
different symbols (instead of the 256 possible values of a byte).

The base64 encoding will always use alphanumeric (upper and lower case)
characters and the '+', '/' and '=' symbols to represent the data. Four
output characters are generated for each three bytes of input. In case
the length of the input is not a multiple of three, padding characters
are added at the end. There's also a ``URL safe'' variant, which is
useful for encoding binary data into URLs and filenames. See @cite{RFC
4648}.

The base16 encoding, also known as ``hexadecimal'', uses the decimal
digits and the letters from A to F. Two hexadecimal digits are generated
for each input byte.

Nettle supports both base64 and base16 encoding and decoding.

Encoding and decoding uses a context struct to maintain its state (with
the exception of base16 encoding, which doesn't need any). To encode or
decode the data, first initialize the context, then call the update
function as many times as necessary, and complete the operation by
calling the final function.

The following functions can be used to perform base64 encoding and decoding.
They are defined in @file{<nettle/base64.h>}.

@deftp {Context struct} {struct base64_encode_ctx}
@end deftp

@deftypefun {void} base64_encode_init (struct base64_encode_ctx *@var{ctx})
@deftypefunx {void} base64url_encode_init (struct base64_encode_ctx *@var{ctx})
Initializes a base64 context. This is necessary before starting an
encoding session. @code{base64_encode_init} selects the standard base64
alphabet, while @code{base64url_encode_init} selects the URL safe
alphabet.
@end deftypefun


@deftypefun {size_t} base64_encode_single (struct base64_encode_ctx *@var{ctx}, uint8_t *@var{dst}, uint8_t @var{src})
Encodes a single byte. Returns amount of output (always 1 or 2).
@end deftypefun

@deffn Macro BASE64_ENCODE_LENGTH (@var{length})
The maximum number of output bytes when passing @var{length} input bytes
to @code{base64_encode_update}.
@end deffn

@deftypefun {size_t} base64_encode_update (struct base64_encode_ctx *@var{ctx}, uint8_t *@var{dst}, size_t @var{length}, const uint8_t *@var{src})
After @var{ctx} is initialized, this function may be called to encode @var{length}
bytes from @var{src}. The result will be placed in @var{dst}, and the return value
will be the number of bytes generated. Note that @var{dst} must be at least of size
BASE64_ENCODE_LENGTH(@var{length}).
@end deftypefun

@defvr Constant BASE64_ENCODE_FINAL_LENGTH
The maximum amount of output from @code{base64_encode_final}.
@end defvr

@deftypefun {size_t} base64_encode_final (struct base64_encode_ctx *@var{ctx}, uint8_t *@var{dst})
After calling base64_encode_update one or more times, this function
should be called to generate the final output bytes, including any
needed paddding. The return value is the number of output bytes
generated.
@end deftypefun

@deftp {Context struct} {struct base64_decode_ctx}
@end deftp

@deftypefun {void} base64_decode_init (struct base64_decode_ctx *@var{ctx})
@deftypefunx {void} base64url_decode_init (struct base64_decode_ctx *@var{ctx})
Initializes a base64 decoding context. This is necessary before starting
a decoding session. @code{base64_decode_init} selects the standard
base64 alphabet, while @code{base64url_decode_init} selects the URL safe
alphabet.
@end deftypefun

@deftypefun {int} base64_decode_single (struct base64_decode_ctx *@var{ctx}, uint8_t *@var{dst}, uint8_t @var{src})
Decodes a single byte (@var{src}) and stores the result in @var{dst}.
Returns amount of output (0 or 1), or -1 on errors.
@end deftypefun

@deffn Macro BASE64_DECODE_LENGTH (@var{length})
The maximum number of output bytes when passing @var{length} input bytes
to @code{base64_decode_update}.
@end deffn

@deftypefun {void} base64_decode_update (struct base64_decode_ctx *@var{ctx}, size_t *@var{dst_length}, uint8_t *@var{dst}, size_t @var{src_length}, const uint8_t *@var{src})
After @var{ctx} is initialized, this function may be called to decode
@var{src_length} bytes from @var{src}. @var{dst} should point to an area
of size at least BASE64_DECODE_LENGTH(@var{src_length}). The amount of data
generated is returned in *@var{dst_length}. Returns 1 on success
and 0 on error.
@end deftypefun

@deftypefun {int} base64_decode_final (struct base64_decode_ctx *@var{ctx})
Check that final padding is correct. Returns 1 on success, and 0 on
error.
@end deftypefun

Similarly to the base64 functions, the following functions perform base16 encoding,
and are defined in @file{<nettle/base16.h>}. Note that there is no encoding context
necessary for doing base16 encoding.

@deftypefun {void} base16_encode_single (uint8_t *@var{dst}, uint8_t @var{src})
Encodes a single byte. Always stores two digits in @var{dst}[0] and @var{dst}[1].
@end deftypefun

@deffn Macro BASE16_ENCODE_LENGTH (@var{length})
The number of output bytes when passing @var{length} input bytes to
@code{base16_encode_update}.
@end deffn

@deftypefun {void} base16_encode_update (uint8_t *@var{dst}, size_t @var{length}, const uint8_t *@var{src})
Always stores BASE16_ENCODE_LENGTH(@var{length}) digits in @var{dst}.
@end deftypefun

@deftp {Context struct} {struct base16_decode_ctx}
@end deftp

@deftypefun {void} base16_decode_init (struct base16_decode_ctx *@var{ctx})
Initializes a base16 decoding context. This is necessary before starting a decoding
session.
@end deftypefun

@deftypefun {int} base16_decode_single (struct base16_decode_ctx *@var{ctx}, uint8_t *@var{dst}, uint8_t @var{src})
Decodes a single byte from @var{src} into @var{dst}. Returns amount of output (0 or 1), or -1 on errors.
@end deftypefun

@deffn Macro BASE16_DECODE_LENGTH (@var{length})
The maximum number of output bytes when passing @var{length} input bytes
to @code{base16_decode_update}.
@end deffn

@deftypefun {int} base16_decode_update (struct base16_decode_ctx *@var{ctx}, size_t *@var{dst_length}, uint8_t *@var{dst}, size_t @var{src_length}, const uint8_t *@var{src})
After @var{ctx} is initialized, this function may be called to decode
@var{src_length} bytes from @var{src}. @var{dst} should point to an area
of size at least BASE16_DECODE_LENGTH(@var{src_length}). The amount of data
generated is returned in *@var{dst_length}. Returns 1 on success
and 0 on error.
@end deftypefun

@deftypefun {int} base16_decode_final (struct base16_decode_ctx *@var{ctx})
Checks that the end of data is correct (i.e., an even number of
hexadecimal digits have been seen). Returns 1 on success, and 0 on
error.
@end deftypefun

@node Miscellaneous functions
@section Miscellaneous functions

@deftypefun {void *} memxor (void *@var{dst}, const void *@var{src}, size_t @var{n})
XORs the source area on top of the destination area. The interface
doesn't follow the Nettle conventions, because it is intended to be
similar to the ANSI-C @code{memcpy} function.
@end deftypefun

@deftypefun {void *} memxor3 (void *@var{dst}, const void *@var{a}, const void *@var{b}, size_t @var{n})
Like @code{memxor}, but takes two source areas and separate
destination area.
@end deftypefun

@deftypefun int memeql_sec (const void *@var{a}, const void *@var{b}, size_t @var{n})
Side-channel silent comparison of the @var{n} bytes at @var{a} and
@var{b}. I.e., instructions executed and memory accesses are identical
no matter where the areas differ, @pxref{Side-channel silence}. Return
non-zero if the areas are equal, and zero if they differ.
@end deftypefun

These functions are declared in @file{<nettle/memops.h>}. For
compatibility with earlier versions of Nettle, @code{memxor} and
@code{memxor3} are also declared in @file{<nettle/memxor.h>}.

@node Compatibility functions
@section Compatibility functions

For convenience, Nettle includes alternative interfaces to some
algorithms, for compatibility with some other popular crypto toolkits.
These are not fully documented here; refer to the source or to the
documentation for the original implementation.

MD5 is defined in [RFC 1321], which includes a reference implementation.
Nettle defines a compatible interface to MD5 in
@file{<nettle/md5-compat.h>}. This file defines the typedef
@code{MD5_CTX}, and declares the functions @code{MD5Init}, @code{MD5Update} and
@code{MD5Final}.

@node Nettle soup
@chapter Traditional Nettle Soup
For the serious nettle hacker, here is a recipe for nettle soup. 4 servings.

@itemize @w{}
@item
1 liter fresh nettles (urtica dioica)
@item
2 tablespoons butter
@item
3 tablespoons flour
@item
1 liter stock (meat or vegetable)
@item
1/2 teaspoon salt
@item
a tad white pepper
@item
some cream or milk
@end itemize

Gather 1 liter fresh nettles. Use gloves! Small, tender shoots are
preferable but the tops of larger nettles can also be used.

Rinse the nettles very well. Boil them for 10 minutes in lightly salted
water. Strain the nettles and save the water. Hack the nettles. Melt the
butter and mix in the flour. Dilute with stock and the nettle-water you
saved earlier. Add the hacked nettles. If you wish you can add some milk
or cream at this stage. Bring to a boil and let boil for a few minutes.
Season with salt and pepper.

Serve with boiled egg-halves.

@c And the original Swedish version.
@ignore

Recept på nässelsoppa
4 portioner

1 l färska nässlor
2 msk smör
3 msk vetemjöl
1 l kött- eller grönsaksbuljong
1/2 tsk salt
1-2 krm peppar
(lite grädde eller mjölk)

Plocka 1 liter färska nässlor. Använd handskar! Helst små och späda
skott, men topparna av större nässlor går också bra.

Skölj nässlorna väl. Förväll dem ca 10 minuter i lätt saltat vatten.
Häll av och spara spadet. Hacka nässlorna. Smält smöret, rör i mjöl och
späd med buljong och nässelspad. Lägg i de hackade nässlorna. Om så
önskas, häll i en skvätt mjölk eller grädde. Koka några minuter, och
smaksätt med salt och peppar.

Servera med kokta ägghalvor.
@end ignore

@node Installation
@chapter Installation

Nettle uses @command{autoconf}. To build it, unpack the source and run

@example
./configure
make
make check
make install
@end example

@noindent
to install it under the default prefix, @file{/usr/local}. Using GNU
make is strongly recommended. By default, both static and shared
libraries are built and installed.

To get a list of configure options, use @code{./configure --help}. Some
of the more interesting are:

@table @option
@item --enable-fat
Include multiple versions of certain functions in the library, and
select the ones to use at run-time, depending on available processor
features. Supported for ARM and x86_64.

@item --enable-mini-gmp
Use the smaller and slower ``mini-gmp'' implementation of the bignum
functions needed for public-key cryptography, instead of the real GNU
GMP library. This option is intended primarily for smaller embedded
systems. Note that builds using mini-gmp are @strong{not} binary compatible
with regular builds of Nettle, and more likely to leak side-channel
information.

@item --disable-shared
Omit building the shared libraries.

@item --disable-dependency-tracking
Disable the automatic dependency tracking. You will likely need this
option to be able to build with BSD make.

@end table

@node Index
@unnumbered Function and Concept Index

@printindex cp

@bye

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