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\input texinfo          @c -*-texinfo-*-

@c %**start of header
@setfilename nettle.info
@settitle The Nettle low-level cryptographic library.
@c %**end of header

8
@footnotestyle end
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@syncodeindex fn cp

@dircategory GNU Libraries
@direntry
* Nettle: (nettle).           A low-level cryptographics library.
@end direntry

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@set UPDATED-FOR 1.5
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@c Latin-1 doesn't work with TeX output.
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@c Also lookout for é characters.

@set AUTHOR Niels Möller
@ifinfo
Draft manual for the Nettle library. This manual corresponds to version
@value{UPDATED-FOR}.

Copyright 2001 @value{AUTHOR}

Permission is granted to make and distribute verbatim
copies of this manual provided the copyright notice and
this permission notice are preserved on all copies.

@ignore
Permission is granted to process this file through TeX
and print the results, provided the printed document
carries a copying permission notice identical to this
one except for the removal of this paragraph (this
paragraph not being relevant to the printed manual).

@end ignore
Permission is granted to copy and distribute modified
versions of this manual under the conditions for
verbatim copying, provided also that the sections
entitled ``Copying'' and ``GNU General Public License''
are included exactly as in the original, and provided
that the entire resulting derived work is distributed
under the terms of a permission notice identical to this
one.

Permission is granted to copy and distribute
translations of this manual into another language,
under the above conditions for modified versions,
except that this permission notice may be stated in a
translation approved by the Free Software Foundation.

@end ifinfo

@titlepage
@sp 10
@c @center @titlefont{Nettle Manual}

@title Nettle Manual
@subtitle For the Nettle Library version @value{UPDATED-FOR}

@author @value{AUTHOR}

@c The following two commands start the copyright page.
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 2001 @value{AUTHOR}

Permission is granted to make and distribute verbatim
copies of this manual provided the copyright notice and
this permission notice are preserved on all copies.

Permission is granted to copy and distribute modified
versions of this manual under the conditions for
verbatim copying, provided also that the sections
entitled ``Copying'' and ``GNU General Public License''
are included exactly as in the original, and provided
that the entire resulting derived work is distributed
under the terms of a permission notice identical to this
one.

Permission is granted to copy and distribute
translations of this manual into another language,
under the above conditions for modified versions,
except that this permission notice may be stated in a
translation approved by the Free Software Foundation.

@end titlepage

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@contents

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@ifnottex
@node     Top, Introduction, (dir), (dir)
@comment  node-name,  next,  previous,  up
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@top Nettle
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This document describes the nettle low-level cryptographic library. You
can use the library directly from your C-programs, or (recommended)
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write or use an object-oriented wrapper for your favorite language or
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application.

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This manual corresponds to version @value{UPDATED-FOR} of the library.
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@menu
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* Introduction::                What is Nettle?
* Copyright::                   Your rights.
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* Conventions::                 
* Example::                     
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* Reference::                   All Nettle functions and features.
* Nettle soup::                 For the serious nettle hacker.
* Installation::                How to install Nettle.
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* Index::                       
@end menu

@end ifnottex

@node Introduction, Copyright, Top, Top
@comment  node-name,  next,  previous,  up
@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.

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And as the requirements of applications differ in subtle and not so
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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
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interfaces on top of Nettle, and share the code, test-cases, benchmarks,
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documentation, etc. For this first version, the only application using
Nettle is LSH, and it uses an object-oriented abstraction on top of the
library. 

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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.

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@node Copyright, Conventions, Introduction, Top
@comment  node-name,  next,  previous,  up
@chapter Copyright

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Nettle is distributed under the GNU General Public License (GPL) (see
the file COPYING for details). However, most of the individual files
are dual licensed under less restrictive licenses like the GNU Lesser
General Public License (LGPL), or are in the public domain. This means
that if you don't use the parts of nettle that are GPL-only, you have
the option to use the Nettle library just as if it were licensed under
the LGPL. To find the current status of particular files, you have to
read the copyright notices at the top of the files.
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A list of the supported algorithms, their origins and licenses:

@table @emph
@item AES
The implementation of the AES cipher (also known as rijndael) is written
by Rafael Sevilla. Released under the LGPL.

@item ARCFOUR
The implementation of the ARCFOUR (also known as RC4) cipher is written
by Niels Möller. Released under the LGPL.

@item BLOWFISH
The implementation of the BLOWFISH cipher is written by Werner Koch,
copyright owned by the Free Software Foundation. Also hacked by Ray
Dassen and Niels Möller. Released under the GPL.

@item CAST128
The implementation of the CAST128 cipher is written by Steve Reid.
Released into the public domain.

@item DES
The implementation of the DES cipher is written by Dana L. How, and
released under the LGPL.

@item MD5
The implementation of the MD5 message digest is written by Colin Plumb.
It has been hacked some more by Andrew Kuchling and Niels Möller.
Released into the public domain.

@item SERPENT
The implementation of the SERPENT cipher is written by Ross Anderson,
Eli Biham, and Lars Knudsen, adapted to LSH by Rafael Sevilla, and to
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Nettle by Niels Möller. Released under the GPL.
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@item SHA1
The implementation of the SHA1 message digest is written by Peter
Gutmann, and hacked some more by Andrew Kuchling and Niels Möller.
Released into the public domain.

@item TWOFISH
The implementation of the TWOFISH cipher is written by Ruud de Rooij.
Released under the LGPL.
@end table

@node Conventions, Example, Copyright, Top
@comment  node-name,  next,  previous,  up
@chapter Conventions

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

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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 encryption, 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.
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If your application uses more than one algorithm, 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
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type @code{unsigned}, and a pointer of type @code{uint8_t *} or
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@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 of the same length. Source and
destination may be the same, so that you can process strings in place,
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but they @emph{must not} overlap in any other way.
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@node Example, Reference, Conventions, Top
@comment  node-name,  next,  previous,  up
@chapter Example

A simple example program that reads a file from standard in and writes
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its SHA1 checksum on standard output should give the flavor of Nettle.
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@example
/* FIXME: This code is untested. */
#include <stdio.h>
#include <stdlib.h>

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#include <nettle/sha.h>
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#define BUF_SIZE 1000

static void
display_hex(unsigned length, uint8_t *data)
@{
  static const char digits[16] = "0123456789abcdef";
  unsigned i;

  for (i = 0; i<length; i++)
  @{
    uint8_t byte = data[i];
    printf("%c%c ", digits[(byte / 16) & 0xf], digits[byte & 0xf]);
  @}
@}

int
main(int argc, char **argv)
@{
  struct sha1_ctx ctx;
  uint8_t buffer[BUF_SIZE];
  uint8_t digest[SHA1_DIGEST_SIZE];
  
  sha1_init(&ctx);
  for (;;)
  @{
    int done = fread(buffer, 1, sizeof(buffer), stdin);
    if (done <= 0)
      break;
    sha1_update(&ctx, done, buf);
  @}
  if (ferror(stdin))
    return EXIT_FAILURE;

  sha1_digest(&ctx, SHA1_DIGEST_SIZE, digest);

  display_hex(SHA1_DIGEST_SIZE, digest);
  return EXIT_SUCCESS;  
@}
@end example

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@node Reference, Nettle soup, Example, Top
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@comment  node-name,  next,  previous,  up
@chapter Reference

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

@menu
* Hash functions::              
* Cipher functions::            
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* Cipher Block Chaining::       
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* Keyed hash functions::        
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* Public-key algorithms::       
* Randomness::                  
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* Miscellaneous functions::     
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* Compatibility functions::     
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@end menu

@node Hash functions, Cipher functions, Reference, Reference
@comment  node-name,  next,  previous,  up
@section Hash functions

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

@item 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,
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message authentication codes, pseudo random generators, association of
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unique id:s to documents, and many other things.

@subsection @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_DATA_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}, unsigned @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void md5_digest (struct md5_ctx *@var{ctx}, unsigned @var{length}, uint8_t *@var{digest})
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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.
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This function also resets the context in the same way as
@code{md5_init}.
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@end deftypefun

The normal way to use MD5 is to call the functions in order: First
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@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.
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To start over, you can call @code{md5_init} at any time.

@subsection @acronym{SHA1}

SHA1 is a hash function specified by @dfn{NIST} (The U.S. National Institute
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for Standards and Technology). It outputs hash values of 160 bits, or 20
octets. Nettle defines SHA1 in @file{<nettle/sha.h>}.
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The functions are analogous to the MD5 ones.

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

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

@defvr Constant SHA1_DATA_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}, unsigned @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

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@deftypefun void sha1_digest (struct sha1_ctx *@var{ctx}, unsigned @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}.
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@end deftypefun

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@subsection @acronym{SHA256}

SHA256 is another hash function specified by @dfn{NIST}, intended as a
replacement for @acronym{SHA1}, generating larger digests. It outputs
hash values of 256 bits, or 32 octets. Nettle defines SHA256 in
@file{<nettle/sha.h>}.

The functions are analogous to the MD5 ones.

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

@defvr Constant SHA256_DIGEST_SIZE
The size of an SHA256 digest, i.e. 20.
@end defvr

@defvr Constant SHA256_DATA_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}, unsigned @var{length}, const uint8_t *@var{data})
Hash some more data.
@end deftypefun

@deftypefun void sha256_digest (struct sha256_ctx *@var{ctx}, unsigned @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.
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This function also resets the context in the same way as
@code{sha256_init}.
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@end deftypefun

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@subsection @code{struct 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 so a context struct, which is of size
@code{context_size}. 
@end deftp

@deftypevr {Constant Struct} {struct nettle_cipher} nettle_md5
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_sha1
@deftypevrx {Constant Struct} {struct nettle_cipher} nettle_sha256

These are all the hash functions that Nettle implements.
@end deftypevr

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@node Cipher functions, Cipher Block Chaining, Hash functions, Reference
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@comment  node-name,  next,  previous,  up
@section Cipher functions

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
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clear-text. Given matching pairs of plaintext and ciphertext, it should
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be hard to find the key.

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 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) being one
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of the most popular. @xref{Cipher Block Chaining}, for information on
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how to apply @acronym{CBC} with Nettle.
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A stream cipher can be used for messages of arbitrary length; a typical
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stream cipher is a keyed pseudo-random generator. To encrypt a plaintext
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message of @var{n} octets, you key the generator, generate @var{n}
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octets of pseudo-random data, and XOR it with the plaintext. To decrypt,
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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
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receive an encrypted message. You apply the key, and get a clear-text
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message that makes sense to you. Can you then be sure that it really was
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your friend that wrote the message you're reading? The answer is no. For
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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
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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.
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It is recommended to @emph{always} use an authentication mechanism in
addition to encrypting the messages. Popular choices are Message
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Authentication Codes like @acronym{HMAC-SHA1} @pxref{Keyed hash
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functions}, or digital signatures like @acronym{RSA}.
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Some ciphers have so called "weak keys", keys that results in
undesirable structure after the key setup processing, and should be
avoided. In Nettle, the presence of weak keys for a cipher mean that the
key setup function can fail, so you have to check its return value. In
addition, the context struct has a field @code{status}, that is set to a
non-zero value if key setup fails. When possible, avoid algorithm that
have weak keys. There are several good ciphers that don't have any weak
keys.

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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 called @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.

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@subsection AES
AES is a quite new block cipher, specified by NIST as a replacement for
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the older DES standard. The standard is the result of a competition
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between cipher designers. The winning design, also known as RIJNDAEL,
was constructed by Joan Daemen and Vincent Rijnmen.
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Like all the AES candidates, the winning design uses a block size of 128
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bits, or 16 octets, and variable key-size, 128, 192 and 256 bits (16, 24
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and 32 octets) being the allowed key sizes. It does not have any weak
keys. Nettle defines AES in @file{<nettle/aes.h>}.
 
@deftp {Context struct} {struct aes_ctx}
@end deftp

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

@defvr Constant AES_MIN_KEY_SIZE
@end defvr

@defvr Constant AES_MAX_KEY_SIZE
@end defvr

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

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

@deftypefun void aes_encrypt (struct aes_ctx *@var{ctx}, unsigned @var{length}, const uint8_t *@var{dst}, 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 aes_decrypt (struct aes_ctx *@var{ctx}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{aes_encrypt}
@end deftypefun

@subsection ARCFOUR
ARCFOUR is a stream cipher, also known under the trade marked name RC4,
and it is one of the fastest ciphers around. A 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. For example

@example
/* A more robust key setup function for ARCFOUR */
void
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arcfour_set_key_hashed(struct arcfour_ctx *ctx,
                       unsigned length, const uint8_t *key)
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@{
  struct sha1_ctx hash;
  uint8_t digest[SHA1_DIGEST_SIZE];

  sha1_init(&hash);
  sha1_update(&hash, length, key);
  sha1_digest(&hash, SHA1_DIGEST_SIZE, digest);

  arcfour_set_key(ctx, SHA1_DIGEST_SIZE, digest);
@}
@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}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{key})
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

@subsection CAST128

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CAST-128 is a block cipher, specified in @cite{RFC 2144}. It uses a 64
bit (8 octets) block size, and a variable key size of up to 128 bits.
Nettle defines cast128 in @file{<nettle/cast128.h>}.

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

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

@defvr Constant CAST128_MIN_KEY_SIZE
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Minimum CAST128 key size, 5
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@end defvr

@defvr Constant CAST128_MAX_KEY_SIZE
Maximum CAST128 key size, 16
@end defvr

@defvr Constant CAST128_KEY_SIZE
Default CAST128 key size, 16
@end defvr

@deftypefun void cast128_set_key (struct cast128_ctx *@var{ctx}, unsigned @var{length}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{cast128_encrypt}
@end deftypefun

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@subsection BLOWFISH

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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
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The BLOWFISH block-size, 8
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@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}, unsigned @var{length}, const uint8_t *@var{key})
Initialize the cipher. The same function is used for both encryption and
decryption. Returns 1 on success, and 0 if the key was weak. Calling
@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}, unsigned @var{length}, const uint8_t *@var{dst}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{blowfish_encrypt}
@end deftypefun

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@subsection DES
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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 is 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
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parallel. One shouldn't be using plain DES at all today, if one uses
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DES at all one should be using DES3 or "triple DES", see below.
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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
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The DES block-size, 8
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@end defvr

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

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@deftypefun int des_set_key (struct des_ctx *@var{ctx}, const uint8_t *@var{key})
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Initialize the cipher. The same function is used for both encryption and
decryption. Returns 1 on success, and 0 if the key was weak or had bad
parity. Calling @code{des_encrypt} or @code{des_decrypt} with a bad key
will crash with an assert violation.
@end deftypefun

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

@subsection DES3
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
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functions. Nettle includes an implementation of three-key "ede"
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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
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The DES3 block-size is the same as DES_BLOCK_SIZE, 8
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@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. Returns 1 on success, and 0 if the key was weak or had bad
parity. Calling @code{des_encrypt} or @code{des_decrypt} with a bad key
will crash with an assert violation.
@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}, unsigned @var{length}, const uint8_t *@var{dst}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{des_encrypt}
@end deftypefun

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@subsection SERPENT
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SERPENT is one of the AES finalists, designed by Ross Anderson, Eli
Biham and Lars Knudsen. Thus, the interface and properties are similar
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to AES'. One peculiarity is that it is quite pointless to use it with
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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
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The SERPENT block-size, 16
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@end defvr

@defvr Constant SERPENT_MIN_KEY_SIZE
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Minimum SERPENT key size, 16
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@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}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{dst}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{serpent_encrypt}
@end deftypefun

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@subsection TWOFISH
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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
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The TWOFISH block-size, 16
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@end defvr

@defvr Constant TWOFISH_MIN_KEY_SIZE
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Minimum TWOFISH key size, 16
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@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}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{dst}, 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}, unsigned @var{length}, const uint8_t *@var{dst}, uint8_t *@var{src})
Analogous to @code{twofish_encrypt}
@end deftypefun

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@c @node nettle_cipher, Cipher Block Chaining, Cipher functions, Reference
@c @comment  node-name,  next,  previous,  up
@subsection @code{struct nettle_cipher}

Nettle includes a struct including information about some of the more
regular cipher functions. It should be considered a little experimental,
but 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_crypt_func}. The first
argument to these functions is a @code{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_arcfour128
@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.
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ones without weak keys or other oddity.
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@end deftypevr

@node Cipher Block Chaining, Keyed hash functions, Cipher functions, Reference
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@comment  node-name,  next,  previous,  up
@section Cipher Block Chaining

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When using @acronym{CBC} mode, clear-text blocks are not encrypted
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independently of each other, like in Electronic Cook Book mode. Instead,
when encrypting a block in @acronym{CBC} mode, the previous ciphertext
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block is XOR:ed with the clear-text before it is fed to the block cipher.
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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.
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In symbols, if @code{E_k} is the encryption function of a block-cipher,
and @code{IV} is the initialization vector, then @code{n} clear-text blocks
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@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

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Nettle includes a few utility functions for applying a block cipher in
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Cipher Block Chaining (@acronym{CBC}) mode. The functions uses @code{void *} to
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pass cipher contexts around.

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

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Applies the encryption or decryption function @var{f} in @acronym{CBC}
mode. The function @var{f} is really typed as
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@code{void f (void *@var{ctx}, unsigned @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
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There are also some macros to help use these functions correctly.
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@deffn Macro CBC_CTX (@var{context_type}, @var{block_size})
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Expands into
@example
@{
   context_type ctx;
   uint8_t iv[block_size];
@}
@end example
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@end deffn

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

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@deffn Macro CBC_SET_IV (@var{ctx}, @var{iv})
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First argument is a pointer to a context struct as defined by @code{CBC_CTX},
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and the second is a pointer to an Initialization Vector (IV) that is
copied into that context.
@end deffn
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@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})
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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.
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@end deffn
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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.
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@node Keyed hash functions, Public-key algorithms, Cipher Block Chaining, Reference
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@comment  node-name,  next,  previous,  up
@section Keyed Hash Functions

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 the 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 it's 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 @acronym{MAC} created by Alice and one created by
Bob.

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

@subsection @acronym{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
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follows: From a given key @code{k}, two distinct sub-keys @code{k_i} and
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@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-SHA1}, and @acronym{HMAC-SHA256}. First, the abstract
functions:

@deftypefun void hmac_set_key (void *@var{outer}, void *@var{inner}, void *@var{state}, const struct nettle_hash *@var{H}, unsigned @var{length}, const uint8_t *@var{key})
Initializes the three context structs from the key. The @var{outer} and
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@var{inner} contexts corresponds to the sub-keys @code{k_o} and
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@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}, unsigned @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}, unsigned @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 into
@example
@{
   type outer;
   type inner;
   type state;
@}
@end example
@end deffn

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It can be used to define a @acronym{HMAC} context struct, either
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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 hmac_update
function directly, or the update function of the underlying hash function.

@subsection Concrete @acronym{HMAC} functions
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}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_md5_digest (struct hmac_md5_ctx *@var{ctx}, unsigned @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-SHA1}

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

@deftypefun void hmac_sha1_set_key (struct hmac_sha1_ctx *@var{ctx}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sha1_digest (struct hmac_sha1_ctx *@var{ctx}, unsigned @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}, unsigned @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}, unsigned @var{length}, const uint8_t *@var{data})
Process some more data.
@end deftypefun

@deftypefun void hmac_sha256_digest (struct hmac_sha256_ctx *@var{ctx}, unsigned @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

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@node Public-key algorithms, Randomness, Keyed hash functions, Reference
@comment  node-name,  next,  previous,  up
@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{-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.

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
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@code{y = F(x)}. Two examples are cryptographic hash functions, and
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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. Of these, I won't say more about
public-key encryption, as that isn't yet supported by Nettle. So the
rest of this chapter is about digital signatures.

To use a digital signature algorithm, one must first create a
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@dfn{key-pair}: A public key and a corresponding private key. The private
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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".

@subsection @acronym{RSA}

The @acronym{RSA} 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
1983. The patent expired on September 20, 2000, and since that day,
@acronym{RSA} can be used freely.

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It's remarkably simple to describe the trapdoor function behind
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@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.
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@code{e} can be quite small, even @code{e = 3} has been used, although
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slightly larger numbers are recommended. @code{n} should be about 1000
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?

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Let's first look at how @acronym{RSA} key-pairs are generated. First
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@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 1000 bits,
@code{p} and @code{q} are about 500 bits each). One also computes the
number @code{phi = (p-1)(q-1)}, in mathematical speak, 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 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
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the @acronym{RSA} key-pair.
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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
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mod n}@footnote{Actually, the computation is not done like this, it is
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done more efficiently using @code{p}, @code{q} and the Chinese remainder
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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}.

@subsection 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{d} 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_init_public_key (struct rsa_public_key *@var{pub})
@deftypefunx void rsa_init_private_key (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_clear_public_key (struct rsa_public_key *@var{pub})
@deftypefunx void rsa_clear_private_key (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
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above, and temporaries, are allocated dynamically. For information on how
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to customize allocation, see
@xref{Custom Allocation,,GMP Allocation,gmp, GMP Manual}.
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When you have assigned values to the attributes of a key, you must call
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@deftypefun int rsa_prepare_public_key (struct rsa_public_key *@var{pub})
@deftypefunx int rsa_prepare_private_key (struct rsa_private_key *@var{key})
Computes the octet size of the key (stored in the @code{size} attribute,
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and may also do other basic sanity checks. Returns one if successful, or
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zero if the key can't be used, for instance if the modulo is smaller
than the minimum size specified by PKCS#1.
@end deftypefun

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 rsa function, and it will extract the message digest and do the
rest of the work.

Creation and verification of signatures is done with the following functions:

@deftypefun void rsa_md5_sign (struct rsa_private_key *@var{key}, struct md5_ctx *@var{hash}, mpz_t @var{signature})
@deftypefunx void rsa_sha1_sign (struct rsa_private_key *@var{key}, struct sha1_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.
@end deftypefun

@deftypefun int rsa_md5_verify (struct rsa_public_key *@var{key}, struct md5_ctx *@var{hash}, const mpz_t @var{signature})
@deftypefunx int rsa_sha1_verify (struct rsa_public_key *@var{key}, struct sha1_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

If you need to use the @acronym{RSA} trapdoor, the private key, in a way
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that isn't supported by the above functions Nettle also includes a
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function that computes @code{x^d mod n} and nothing more, using the
@acronym{CRT} optimization.

@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}, efficiently.
@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_prepare_public_key} or
@code{rsa_prepare_private_key} 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 1 on success, and 0 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 Randomness, Miscellaneous functions, Public-key algorithms, Reference
@comment  node-name,  next,  previous,  up
@section Randomness

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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
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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.
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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
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Nettle includes one randomness generator that is believed to have all
the above properties, and two simpler ones.

@acronym{ARCFOUR}, like any stream cipher, can be used as a randomness
generator. Its output should be of reasonable quality, if the seed is
hashed properly before it is used with @code{arcfour_set_key}. There's
no single natural way to reseed it, but if you need reseeding, you
should be using Yarrow instead.

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{http://www.counterpane.com/yarrow.html}, 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 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 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
The 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.
@end deftypefun

@deftypefun void yarrow256_seed (struct yarrow256_ctx *@var{ctx}, unsigned @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 the contents of @code{@var{ctx}->seed_file}. If it's
possible for several processes to read the seed file at about the same
time, access must be coordinated, for example using lock files.
@end deftypefun

@deftypefun int yarrow256_update (struct yarrow256_ctx *@var{ctx}, unsigned @var{source}, unsigned @var{entropy}, unsigned @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 the seed file can be
overwritten with the contents of @code{@var{ctx}->seed_file}. Otherwise,
the function returns 0.
@end deftypefun

@deftypefun void yarrow256_random (struct yarrow256_ctx *@var{ctx}, unsigned @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_force_reseed (struct yarrow256_ctx *@var{ctx})
Causes a 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

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@node Miscellaneous functions, Compatibility functions, Randomness, Reference
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@comment  node-name,  next,  previous,  up
@section Miscellaneous functions

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@deftypefun {uint8_t *} memxor (uint8_t *@var{dst}, const uint8_t *@var{src}, size_t @var{n})
XOR:s 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

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@code{memxor} is declared in @file{<nettle/memxor.h>}.

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@node Compatibility functions,  , Miscellaneous functions, Reference
@comment  node-name,  next,  previous,  up
@section Compatibility functions

For convenience, Nettle includes alternative interfaces to some
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algorithms, for compatibility with some other popular crypto toolkits.
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These are not fully documented here; refer to the source or to the
documentation for the original implementation.

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MD5 is defined in [RFC 1321], which includes a reference implementation.
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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}.

Eric Young's "libdes" (also part of OpenSSL) is a quite popular DES
implementation. Nettle includes a subset if it's interface in
@file{<nettle/des-compat.h>}. This file defines the typedefs
@code{des_key_schedule} and @code{des_cblock}, two constants
@code{DES_ENCRYPT} and @code{DES_DECRYPT}, and declares one global
variable @code{des_check_key}, and the functions @code{des_cbc_cksum}
@code{des_cbc_encrypt}, @code{des_ecb2_encrypt},
@code{des_ecb3_encrypt}, @code{des_ecb_encrypt},
@code{des_ede2_cbc_encrypt}, @code{des_ede3_cbc_encrypt},
@code{des_is_weak_key}, @code{des_key_sched}, @code{des_ncbc_encrypt}
@code{des_set_key}, and @code{des_set_odd_parity}.

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@node Nettle soup, Installation, Reference, Top
@comment  node-name,  next,  previous,  up
@chapter Traditional Nettle Soup
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For the serious nettle hacker, here is a recipe for nettle-soup. 4 servings
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@itemize @w{}
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@item
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1 liter fresh nettles (urtica dioica)
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@item
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2 tablespoons butter
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@item
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3 tablespoons flour
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@item
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1 liter bouillon (meat or vegetable)
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@item
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