This is nettle.info, produced by makeinfo version 4.0 from
nettle.texinfo.

INFO-DIR-SECTION GNU Libraries
START-INFO-DIR-ENTRY
* Nettle: (nettle).           A low-level cryptographics library.
END-INFO-DIR-ENTRY

   Draft manual for the Nettle library. This manual corresponds to
version 1.5.

   Copyright 2001 Niels Möller

   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.


File: nettle.info,  Node: Top,  Next: Introduction,  Prev: (dir),  Up: (dir)

Nettle
******

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

   This manual corresponds to version 1.5 of the library.

* Menu:

* Introduction::                What is Nettle?
* Copyright::                   Your rights.
* Conventions::
* Example::
* Reference::                   All Nettle functions and features.
* Nettle soup::                 For the serious nettle hacker.
* Installation::                How to install Nettle.
* Index::


File: nettle.info,  Node: Introduction,  Next: Copyright,  Prev: Top,  Up: Top

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 _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. For this first version, the only
application using Nettle is LSH, and it uses 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.


File: nettle.info,  Node: Copyright,  Next: Conventions,  Prev: Introduction,  Up: Top

Copyright
*********

   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.

   A list of the supported algorithms, their origins and licenses:

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

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

_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.

_CAST128_
     The implementation of the CAST128 cipher is written by Steve Reid.
     Released into the public domain.

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

_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.

_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 Nettle by Niels Möller. Released under the GPL.

_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.

_TWOFISH_
     The implementation of the TWOFISH cipher is written by Ruud de
     Rooij.  Released under the LGPL.


File: nettle.info,  Node: Conventions,  Next: Example,  Prev: Copyright,  Up: Top

Conventions
***********

   For each supported algorithm, there is an include file that defines a
_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 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.

   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 `foo', the struct tag for the
context struct is `foo_ctx', constants and functions uses prefixes like
`FOO_BLOCK_SIZE' (a constant) and `foo_set_key' (a function).

   In all functions, strings are represented with an explicit length, of
type `unsigned', and a pointer of type `uint8_t *' or `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, but they _must not_
overlap in any other way.


File: nettle.info,  Node: Example,  Next: Reference,  Prev: Conventions,  Up: Top

Example
*******

   A simple example program that reads a file from standard in and
writes its SHA1 checksum on standard output should give the flavor of
Nettle.

     /* FIXME: This code is untested. */
     #include <stdio.h>
     #include <stdlib.h>
     
     #include <nettle/sha.h>
     
     #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;
     }


File: nettle.info,  Node: Reference,  Next: Nettle soup,  Prev: Example,  Up: Top

Reference
*********

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

* Menu:

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


File: nettle.info,  Node: Hash functions,  Next: Cipher functions,  Prev: Reference,  Up: Reference

Hash functions
==============

   A cryptographic "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
`H' should have the following properties:

_One-way_
     Given a hash value `H(x)' it is hard to find a string `x' that
     hashes to that value.

_Collision-resistant_
     It is hard to find two different strings, `x' and `y', such that
     `H(x)' = `H(y)'.

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

MD5
---

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

 - Context struct: struct md5_ctx

 - Constant: MD5_DIGEST_SIZE
     The size of an MD5 digest, i.e. 16.

 - Constant: MD5_DATA_SIZE
     The internal block size of MD5. Useful for some special
     constructions, in particular HMAC-MD5.

 - Function: void md5_init (struct md5_ctx *CTX)
     Initialize the MD5 state.

 - Function: void md5_update (struct md5_ctx *CTX, unsigned LENGTH,
          const uint8_t *DATA)
     Hash some more data.

 - Function: void md5_digest (struct md5_ctx *CTX, unsigned LENGTH,
          uint8_t *DIGEST)
     Performs final processing and extracts the message digest, writing
     it to DIGEST. LENGTH may be smaller than `MD5_DIGEST_SIZE', in
     which case only the first LENGTH octets of the digest are written.

     This function also resets the context in the same way as
     `md5_init'.

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

   To start over, you can call `md5_init' at any time.

SHA1
----

   SHA1 is a hash function specified by "NIST" (The U.S. National
Institute for Standards and Technology). It outputs hash values of 160
bits, or 20 octets. Nettle defines SHA1 in `<nettle/sha.h>'.

   The functions are analogous to the MD5 ones.

 - Context struct: struct sha1_ctx

 - Constant: SHA1_DIGEST_SIZE
     The size of an SHA1 digest, i.e. 20.

 - Constant: SHA1_DATA_SIZE
     The internal block size of SHA1. Useful for some special
     constructions, in particular HMAC-SHA1.

 - Function: void sha1_init (struct sha1_ctx *CTX)
     Initialize the SHA1 state.

 - Function: void sha1_update (struct sha1_ctx *CTX, unsigned LENGTH,
          const uint8_t *DATA)
     Hash some more data.

 - Function: void sha1_digest (struct sha1_ctx *CTX, unsigned LENGTH,
          uint8_t *DIGEST)
     Performs final processing and extracts the message digest, writing
     it to DIGEST. LENGTH may be smaller than `SHA1_DIGEST_SIZE', in
     which case only the first LENGTH octets of the digest are written.

     This function also resets the context in the same way as
     `sha1_init'.

SHA256
------

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

   The functions are analogous to the MD5 ones.

 - Context struct: struct sha256_ctx

 - Constant: SHA256_DIGEST_SIZE
     The size of an SHA256 digest, i.e. 20.

 - Constant: SHA256_DATA_SIZE
     The internal block size of SHA256. Useful for some special
     constructions, in particular HMAC-SHA256.

 - Function: void sha256_init (struct sha256_ctx *CTX)
     Initialize the SHA256 state.

 - Function: void sha256_update (struct sha256_ctx *CTX, unsigned
          LENGTH, const uint8_t *DATA)
     Hash some more data.

 - Function: void sha256_digest (struct sha256_ctx *CTX, unsigned
          LENGTH, uint8_t *DIGEST)
     Performs final processing and extracts the message digest, writing
     it to DIGEST. LENGTH may be smaller than `SHA256_DIGEST_SIZE', in
     which case only the first LENGTH octets of the digest are written.

     This function also resets the context in the same way as
     `sha256_init'.

`struct nettle_hash'
--------------------

   Nettle includes a struct including information about the supported
hash functions. It is defined in `<nettle/nettle-meta.h>', and is used
by Nettle's implementation of HMAC *note Keyed hash functions::.

 - Meta struct: `struct nettle_hash' name context_size digest_size
          block_size init update digest
     The last three attributes are function pointers, of types
     `nettle_hash_init_func', `nettle_hash_update_func', and
     `nettle_hash_digest_func'. The first argument to these functions is
     `void *' pointer so a context struct, which is of size
     `context_size'.

 - Constant Struct: struct nettle_cipher nettle_md5
 - Constant Struct: struct nettle_cipher nettle_sha1
 - Constant Struct: struct nettle_cipher nettle_sha256
     These are all the hash functions that Nettle implements.


File: nettle.info,  Node: Cipher functions,  Next: Cipher Block Chaining,  Prev: Hash functions,  Up: Reference

Cipher functions
================

   A "cipher" is a function that takes a message or "plaintext" and a
secret "key" and transforms it to a "ciphertext". Given only the
ciphertext, but not the key, it should be hard to find the clear-text.
Given matching pairs of plaintext and ciphertext, it should 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
"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 "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, "CBC" (Cipher Block Chaining) being one of the most
popular. *Note Cipher Block Chaining::, for information on how to apply
CBC 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 N octets, you key the generator, generate 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.

   *Caution:* The first rule for this kind of cipher is the same as for
a One Time Pad: _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 clear-text
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 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 _always_ use an authentication mechanism in
addition to encrypting the messages. Popular choices are Message
Authentication Codes like HMAC-SHA1 *note Keyed hash functions::, or
digital signatures like 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, 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 `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.

   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 "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.

AES
---

   AES is a quite new 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 variable 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 `<nettle/aes.h>'.

 - Context struct: struct aes_ctx

 - Constant: AES_BLOCK_SIZE
     The AES block-size, 16

 - Constant: AES_MIN_KEY_SIZE

 - Constant: AES_MAX_KEY_SIZE

 - Constant: AES_KEY_SIZE
     Default AES key size, 32

 - Function: void aes_set_key (struct aes_ctx *CTX, unsigned LENGTH,
          const uint8_t *KEY)
     Initialize the cipher. The same function is used for both
     encryption and decryption.

 - Function: void aes_encrypt (struct aes_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void aes_decrypt (struct aes_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Analogous to `aes_encrypt'

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", ..... 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

     /* A more robust key setup function for ARCFOUR */
     void
     arcfour_set_key_hashed(struct arcfour_ctx *ctx,
                            unsigned length, const uint8_t *key)
     {
       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);
     }

   Nettle defines ARCFOUR in `<nettle/arcfour.h>'.

 - Context struct: struct arcfour_ctx

 - Constant: ARCFOUR_MIN_KEY_SIZE
     Minimum key size, 1

 - Constant: ARCFOUR_MAX_KEY_SIZE
     Maximum key size, 256

 - Constant: ARCFOUR_KEY_SIZE
     Default ARCFOUR key size, 16

 - Function: void arcfour_set_key (struct arcfour_ctx *CTX, unsigned
          LENGTH, const uint8_t *KEY)
     Initialize the cipher. The same function is used for both
     encryption and decryption.

 - Function: void arcfour_crypt (struct arcfour_ctx *CTX, unsigned
          LENGTH, const uint8_t *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 `arcfour_crypt' only once with all the data.

CAST128
-------

   CAST-128 is a block cipher, specified in `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 `<nettle/cast128.h>'.

 - Context struct: struct cast128_ctx

 - Constant: CAST128_BLOCK_SIZE
     The CAST128 block-size, 8

 - Constant: CAST128_MIN_KEY_SIZE
     Minimum CAST128 key size, 5

 - Constant: CAST128_MAX_KEY_SIZE
     Maximum CAST128 key size, 16

 - Constant: CAST128_KEY_SIZE
     Default CAST128 key size, 16

 - Function: void cast128_set_key (struct cast128_ctx *CTX, unsigned
          LENGTH, const uint8_t *KEY)
     Initialize the cipher. The same function is used for both
     encryption and decryption.

 - Function: void cast128_encrypt (struct cast128_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void cast128_decrypt (struct cast128_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Analogous to `cast128_encrypt'

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
`<nettle/blowfish.h>'.

 - Context struct: struct blowfish_ctx

 - Constant: BLOWFISH_BLOCK_SIZE
     The BLOWFISH block-size, 8

 - Constant: BLOWFISH_MIN_KEY_SIZE
     Minimum BLOWFISH key size, 8

 - Constant: BLOWFISH_MAX_KEY_SIZE
     Maximum BLOWFISH key size, 56

 - Constant: BLOWFISH_KEY_SIZE
     Default BLOWFISH key size, 16

 - Function: int blowfish_set_key (struct blowfish_ctx *CTX, unsigned
          LENGTH, const uint8_t *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 `blowfish_encrypt' or `blowfish_decrypt' with a
     weak key will crash with an assert violation.

 - Function: void blowfish_encrypt (struct blowfish_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void blowfish_decrypt (struct blowfish_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Analogous to `blowfish_encrypt'

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 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
parallel. One shouldn't be using plain DES at all today, if one uses
DES at all one should be using DES3 or "triple DES", see below.

   DES also has some weak keys. Nettle defines DES in `<nettle/des.h>'.

 - Context struct: struct des_ctx

 - Constant: DES_BLOCK_SIZE
     The DES block-size, 8

 - Constant: DES_KEY_SIZE
     DES key size, 8

 - Function: int des_set_key (struct des_ctx *CTX, const uint8_t *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 `des_encrypt' or `des_decrypt'
     with a bad key will crash with an assert violation.

 - Function: void des_encrypt (struct des_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void des_decrypt (struct des_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Analogous to `des_encrypt'

 - Function: void des_fix_parity (unsigned LENGTH, uint8_t *DST, const
          uint8_t *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. DST and SRC
     may be equal.

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 _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,
`<nettle/des.h>'.

 - Context struct: struct des3_ctx

 - Constant: DES3_BLOCK_SIZE
     The DES3 block-size is the same as DES_BLOCK_SIZE, 8

 - Constant: DES3_KEY_SIZE
     DES key size, 24

 - Function: int des3_set_key (struct des3_ctx *CTX, const uint8_t *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 `des_encrypt' or `des_decrypt'
     with a bad key will crash with an assert violation.

   For random-looking strings, you can use `des_fix_parity' to adjust
the parity bits before calling `des3_set_key'.

 - Function: void des3_encrypt (struct des3_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void des3_decrypt (struct des3_ctx *CTX, unsigned LENGTH,
          const uint8_t *DST, uint8_t *SRC)
     Analogous to `des_encrypt'

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 `<nettle/serpent.h>'.

 - Context struct: struct serpent_ctx

 - Constant: SERPENT_BLOCK_SIZE
     The SERPENT block-size, 16

 - Constant: SERPENT_MIN_KEY_SIZE
     Minimum SERPENT key size, 16

 - Constant: SERPENT_MAX_KEY_SIZE
     Maximum SERPENT key size, 32

 - Constant: SERPENT_KEY_SIZE
     Default SERPENT key size, 32

 - Function: void serpent_set_key (struct serpent_ctx *CTX, unsigned
          LENGTH, const uint8_t *KEY)
     Initialize the cipher. The same function is used for both
     encryption and decryption.

 - Function: void serpent_encrypt (struct serpent_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void serpent_decrypt (struct serpent_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Analogous to `serpent_encrypt'

TWOFISH
-------

   Another AES finalist, this one designed by Bruce Schneier and others.
Nettle defines it in `<nettle/twofish.h>'.

 - Context struct: struct twofish_ctx

 - Constant: TWOFISH_BLOCK_SIZE
     The TWOFISH block-size, 16

 - Constant: TWOFISH_MIN_KEY_SIZE
     Minimum TWOFISH key size, 16

 - Constant: TWOFISH_MAX_KEY_SIZE
     Maximum TWOFISH key size, 32

 - Constant: TWOFISH_KEY_SIZE
     Default TWOFISH key size, 32

 - Function: void twofish_set_key (struct twofish_ctx *CTX, unsigned
          LENGTH, const uint8_t *KEY)
     Initialize the cipher. The same function is used for both
     encryption and decryption.

 - Function: void twofish_encrypt (struct twofish_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Encryption function. LENGTH must be an integral multiple of the
     block size. If it is more than one block, the data is processed in
     ECB mode. `src' and `dst' may be equal, but they must not overlap
     in any other way.

 - Function: void twofish_decrypt (struct twofish_ctx *CTX, unsigned
          LENGTH, const uint8_t *DST, uint8_t *SRC)
     Analogous to `twofish_encrypt'

`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
`<nettle/nettle-meta.h>'.

 - Meta struct: `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
     `nettle_set_key_func' and `nettle_crypt_func'. The first argument
     to these functions is a `void *' pointer to a context struct,
     which is of size `context_size'.

 - Constant Struct: struct nettle_cipher nettle_aes128
 - Constant Struct: struct nettle_cipher nettle_aes192
 - Constant Struct: struct nettle_cipher nettle_aes256
 - Constant Struct: struct nettle_cipher nettle_arcfour128
 - Constant Struct: struct nettle_cipher nettle_cast128
 - Constant Struct: struct nettle_cipher nettle_serpent128
 - Constant Struct: struct nettle_cipher nettle_serpent192
 - Constant Struct: struct nettle_cipher nettle_serpent256
 - Constant Struct: struct nettle_cipher nettle_twofish128
 - Constant Struct: struct nettle_cipher nettle_twofish192
 - Constant Struct: struct nettle_cipher nettle_twofish256
     Nettle includes such structs for all the _regular_ ciphers, i.e.
     ones without weak keys or other oddity.


File: nettle.info,  Node: Cipher Block Chaining,  Next: Keyed hash functions,  Prev: Cipher functions,  Up: Reference

Cipher Block Chaining
=====================

   When using CBC mode, clear-text blocks are not encrypted
independently of each other, like in Electronic Cook Book mode. Instead,
when encrypting a block in CBC mode, the previous ciphertext block is
XOR:ed with the clear-text before it is fed to the block cipher.  When
encrypting the first block, a random block called an "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 `E_k' is the encryption function of a block-cipher,
and `IV' is the initialization vector, then `n' clear-text blocks
`M_1',... `M_n' are transformed into `n' ciphertext blocks `C_1',...
`C_n' as follows:

     C_1 = E_k(IV  XOR M_1)
     C_2 = E_k(C_1 XOR M_2)
     
     ...
     
     C_n = E_k(C_(n-1) XOR M_n)

   Nettle includes a few utility functions for applying a block cipher
in Cipher Block Chaining (CBC) mode. The functions uses `void *' to
pass cipher contexts around.

 - Function: void cbc_encrypt (void *CTX, void (*F)(), unsigned
          BLOCK_SIZE, uint8_t *IV, unsigned LENGTH, uint8_t *DST, const
          uint8_t *SRC)
 - Function: void cbc_decrypt (void *CTX, void (*F)(), unsigned
          BLOCK_SIZE, uint8_t *IV, unsigned LENGTH, uint8_t *DST, const
          uint8_t *SRC)
     Applies the encryption or decryption function F in CBC mode. The
     function F is really typed as

     `void f (void *CTX, unsigned LENGTH, uint8_t DST, const uint8_t
     *SRC)',

     and the `cbc_encrypt' and `cbc_decrypt' functions pass their
     argument CTX on to F.

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

 - Macro: CBC_CTX (CONTEXT_TYPE, BLOCK_SIZE)
     Expands into
          {
             context_type ctx;
             uint8_t iv[block_size];
          }

   It can be used to define a CBC context struct, either directly,

     struct CBC_CTX(struct aes_ctx, AES_BLOCK_SIZE) ctx;

   or to give it a struct tag,

     struct aes_cbc_ctx CBC_CTX (struct aes_ctx, AES_BLOCK_SIZE);

 - Macro: CBC_SET_IV (CTX, IV)
     First argument is a pointer to a context struct as defined by
     `CBC_CTX', and the second is a pointer to an Initialization Vector
     (IV) that is copied into that context.

 - Macro: CBC_ENCRYPT (CTX, F, LENGTH, DST, SRC)
 - Macro: CBC_DECRYPT (CTX, F, LENGTH, DST, SRC)
     A simpler way to invoke `cbc_encrypt' and `cbc_decrypt'. The first
     argument is a pointer to a context struct as defined by `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.

   These macros use some tricks to make the compiler display a warning
if the types of F and CTX don't match, e.g. if you try to use an
`struct aes_ctx' context with the `des_encrypt' function.


File: nettle.info,  Node: Keyed hash functions,  Next: Public-key algorithms,  Prev: Cipher Block Chaining,  Up: Reference

Keyed Hash Functions
====================

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

   Keyed hash functions are useful primarily for message authentication,
when the Alice and Bob shares a secret: The sender, Alice, computes the
MAC and attaches it to the message. The receiver, Bob, also computes
the 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 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 _same_ key is used on
both sides, and anyone knowing the key can create a correct MAC for any
message. If Bob believes that only he and Alice knows the key, and he
knows that he didn't attach a MAC to a particular message, he knows it
must be Alice who did it. However, the third party can't distinguish
between MAC created by Alice and one created by Bob.

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

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 HMAC, described in `RFC 2104'.

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

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

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

 - Function: void hmac_set_key (void *OUTER, void *INNER, void *STATE,
          const struct nettle_hash *H, unsigned LENGTH, const uint8_t
          *KEY)
     Initializes the three context structs from the key. The OUTER and
     INNER contexts corresponds to the sub-keys `k_o' and `k_i'. STATE
     is used for hashing the message, and is initialized as a copy of
     the INNER context.

 - Function: void hmac_update(void *STATE, const struct nettle_hash *H,
          unsigned LENGTH, const uint8_t *DATA)
     This function is called zero or more times to process the message.
     Actually, `hmac_update(state, H, length, data)' is equivalent to
     `H->update(state, length, data)', so if you wish you can use the
     ordinary update function of the underlying hash function instead.

 - Function: void hmac_digest (const void *OUTER, const void *INNER,
          void *STATE, const struct nettle_hash *H, unsigned LENGTH,
          uint8_t *DIGEST)
     Extracts the MAC of the message, writing it to DIGEST.  OUTER and
     INNER are not modified. LENGTH is usually equal to
     `H->digest_size', but if you provide a smaller value, only the
     first LENGTH octets of the MAC are written.

     This function also resets the STATE context so that you can start
     over processing a new message (with the same key).

   Like for CBC, there are some macros to help use these functions
correctly.

 - Macro: HMAC_CTX (TYPE)
     Expands into
          {
             type outer;
             type inner;
             type state;
          }

   It can be used to define a HMAC context struct, either directly,

     struct HMAC_CTX(struct md5_ctx) ctx;

   or to give it a struct tag,

     struct hmac_md5_ctx HMAC_CTX (struct md5_ctx);

 - Macro: HMAC_SET_KEY (CTX, H, LENGTH, KEY)
     CTX is a pointer to a context struct as defined by `HMAC_CTX', H
     is a pointer to a `const struct nettle_hash' describing the
     underlying hash function (so it must match the type of the
     components of CTX). The last two arguments specify the secret key.

 - Macro: HMAC_DIGEST (CTX, H, LENGTH, DIGEST)
     CTX is a pointer to a context struct as defined by `HMAC_CTX', H
     is a pointer to a `const struct nettle_hash' describing the
     underlying hash function. The last two arguments specify where the
     digest is written.

   Note that there is no `HMAC_UPDATE' macro; simply call hmac_update
function directly, or the update function of the underlying hash
function.

Concrete HMAC functions
-----------------------

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

HMAC-MD5
........

 - Context struct: struct hmac_md5_ctx

 - Function: void hmac_md5_set_key (struct hmac_md5_ctx *CTX, unsigned
          KEY_LENGTH, const uint8_t *KEY)
     Initializes the context with the key.

 - Function: void hmac_md5_update (struct hmac_md5_ctx *CTX, unsigned
          LENGTH, const uint8_t *DATA)
     Process some more data.

 - Function: void hmac_md5_digest (struct hmac_md5_ctx *CTX, unsigned
          LENGTH, uint8_t *DIGEST)
     Extracts the MAC, writing it to DIGEST. LENGTH may be smaller than
     `MD5_DIGEST_SIZE', in which case only the first LENGTH octets of
     the MAC are written.

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

HMAC-SHA1
.........

 - Context struct: struct hmac_sha1_ctx

 - Function: void hmac_sha1_set_key (struct hmac_sha1_ctx *CTX,
          unsigned KEY_LENGTH, const uint8_t *KEY)
     Initializes the context with the key.

 - Function: void hmac_sha1_update (struct hmac_sha1_ctx *CTX, unsigned
          LENGTH, const uint8_t *DATA)
     Process some more data.

 - Function: void hmac_sha1_digest (struct hmac_sha1_ctx *CTX, unsigned
          LENGTH, uint8_t *DIGEST)
     Extracts the MAC, writing it to DIGEST. LENGTH may be smaller than
     `SHA1_DIGEST_SIZE', in which case only the first LENGTH octets of
     the MAC are written.

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

HMAC-SHA256
...........

 - Context struct: struct hmac_sha256_ctx

 - Function: void hmac_sha256_set_key (struct hmac_sha256_ctx *CTX,
          unsigned KEY_LENGTH, const uint8_t *KEY)
     Initializes the context with the key.

 - Function: void hmac_sha256_update (struct hmac_sha256_ctx *CTX,
          unsigned LENGTH, const uint8_t *DATA)
     Process some more data.

 - Function: void hmac_sha256_digest (struct hmac_sha256_ctx *CTX,
          unsigned LENGTH, uint8_t *DIGEST)
     Extracts the MAC, writing it to DIGEST. LENGTH may be smaller than
     `SHA256_DIGEST_SIZE', in which case only the first LENGTH octets
     of the MAC are written.

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


File: nettle.info,  Node: Public-key algorithms,  Next: Randomness,  Prev: Keyed hash functions,  Up: Reference

Public-key algorithms
=====================

   Nettle uses GMP, the GNU bignum library, for all calculations with
large numbers. In order to use the public-key features of Nettle, you
must install GMP, at least version 3.0, before compiling Nettle, and
you need to link your programs with `-lgmp'.

   The concept of "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 _pair_ needs a shared secret key known by nobody else.

   Public-key cryptography uses trapdoor one-way functions. A "one-way
function" is a function `F' such that it is easy to compute the value
`F(x)' for any `x', but given a value `y', it is hard to compute a
corresponding `x' such that `y = F(x)'. Two examples are cryptographic
hash functions, and exponentiation in certain groups.

   A "trapdoor one-way function" is a function `F' that is one-way,
unless one knows some secret information about `F'. If one knows the
secret, it is easy to compute both `F' and it's inverse.  If this
sounds strange, look at the 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
"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".

RSA
---

   The 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, RSA can
be used freely.

   It's remarkably simple to describe the trapdoor function behind RSA.
The "one-way"-function used is

     F(x) = x^e mod n

   I.e. raise x to the `e':th power, while discarding all multiples of
`n'. The pair of numbers `n' and `e' is the public key.  `e' can be
quite small, even `e = 3' has been used, although slightly larger
numbers are recommended. `n' should be about 1000 bits or larger.

   If `n' is large enough, and properly chosen, the inverse of F, the
computation of `e':th roots modulo `n', is very difficult.  But,
where's the trapdoor?

   Let's first look at how RSA key-pairs are generated. First `n' is
chosen as the product of two large prime numbers `p' and `q' of roughly
the same size (so if `n' is 1000 bits, `p' and `q' are about 500 bits
each). One also computes the number `phi = (p-1)(q-1)', in mathematical
speak, phi is the order of the multiplicative group of integers modulo
n.

   Next, `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. `e = 65537' is a popular choice, because it makes raising to
the `e':th power particularly efficient, and being prime, it usually
has no factors common with `phi'.

   Finally, a number `d', `d < n' is computed such that `e d mod phi =
1'. It can be shown that such a number exists (this is why `e' and
`phi' must have no common factors), and that for all x,

     (x^e)^d mod n = x^(ed) mod n = (x^d)^e mod n = x

   Using Euclid's algorithm, `d' can be computed quite easily from
`phi' and `e'. But it is still hard to get `d' without knowing `phi',
which depends on the factorization of `n'.

   So `d' is the trapdoor, if we know `d' and `y = F(x)', we can
recover x as `y^d mod n'. `d' is also the private half of the RSA
key-pair.

   The most common signature operation for RSA is defined in `PKCS#1',
a specification by RSA Laboratories. The message to be signed is first
hashed using a cryptographic hash function, e.g.  MD5 or SHA1. Next,
some padding, the ASN.1 "Algorithm Identifier" for the hash function,
and the message digest itself, are concatenated and converted to a
number `x'. The signature is computed from `x' and the private key as
`s = x^d mod n'(1). The signature, `s' is a number of about the same
size of `n', and it usually encoded as a sequence of octets, most
significant octet first.

   The verification operation is straight-forward, `x' is computed from
the message in the same way as above. Then `s^e mod n' is computed, the
operation returns true if and only if the result equals `x'.

Nettle's RSA support
--------------------

   Nettle represents RSA keys using two structures that contain large
numbers (of type `mpz_t').

 - Context struct: rsa_public_key size n e
     `size' is the size, in octets, of the modulo, and is used
     internally.  `n' and `e' is the public key.

 - Context struct: rsa_private_key size d p q a b c
     `size' is the size, in octets, of the modulo, and is used
     internally.  `d' is the secret exponent, but it is not actually
     used when signing. Instead, the factors `p' and `q', and the
     parameters `a', `b' and `c' are used. They are computed from `p',
     `q' and `d' such that `a e mod (p - 1) = 1, b e mod (q - 1) = 1, c
     q mod p= 1'.

   Before use, these structs must be initialized by calling one of

 - Function: void rsa_init_public_key (struct rsa_public_key *PUB)
 - Function: void rsa_init_private_key (struct rsa_private_key *KEY)
     Calls `mpz_init' on all numbers in the key struct.

   and when finished with them, the space for the numbers must be
deallocated by calling one of

 - Function: void rsa_clear_public_key (struct rsa_public_key *PUB)
 - Function: void rsa_clear_private_key (struct rsa_private_key *KEY)
     Calls `mpz_clear' on all numbers in the key struct.

   In general, Nettle's 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 *Note GMP Allocation: (gmp)Custom
Allocation.

   When you have assigned values to the attributes of a key, you must
call

 - Function: int rsa_prepare_public_key (struct rsa_public_key *PUB)
 - Function: int rsa_prepare_private_key (struct rsa_private_key *KEY)
     Computes the octet size of the key (stored in the `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 specified by PKCS#1.

   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:

 - Function: void rsa_md5_sign (struct rsa_private_key *KEY, struct
          md5_ctx *HASH, mpz_t SIGNATURE)
 - Function: void rsa_sha1_sign (struct rsa_private_key *KEY, struct
          sha1_ctx *HASH, mpz_t SIGNATURE)
     The signature is stored in SIGNATURE (which must have been
     `mpz_init':ed earlier). The hash context is reset so that it can be
     used for new messages.

 - Function: int rsa_md5_verify (struct rsa_public_key *KEY, struct
          md5_ctx *HASH, const mpz_t SIGNATURE)
 - Function: int rsa_sha1_verify (struct rsa_public_key *KEY, struct
          sha1_ctx *HASH, const mpz_t 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.

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

 - Function: void rsa_compute_root (struct rsa_private_key *KEY, mpz_t
          X, const mpz_t M)
     Computes `x = m^d', efficiently.

   At last, how do you create new keys?

 - Function: int rsa_generate_keypair (struct rsa_public_key *PUB,
          struct rsa_private_key *KEY, void *RANDOM_CTX,
          nettle_random_func RANDOM, void *PROGRESS_CTX,
          nettle_progress_func PROGRESS, unsigned N_SIZE, unsigned
          E_SIZE);
     There are lots of parameters. PUB and KEY is where the resulting
     key pair is stored. The structs should be initialized, but you
     don't need to call `rsa_prepare_public_key' or
     `rsa_prepare_private_key' after key generation.

     RANDOM_CTX and RANDOM is a randomness generator.
     `random(random_ctx, length, dst)' should generate `length' random
     octets and store them at `dst'. For advice, see *Note Randomness::.

     PROGRESS and PROGRESS_CTX can be used to get callbacks during the
     key generation process, in order to uphold an illusion of
     progress. PROGRESS can be NULL, in that case there are no
     callbacks.

     SIZE_N is the desired size of the modulo, in bits. If 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 E_SIZE is zero,
     it is assumed that the caller has already chosen a value for `e',
     and stored it in PUB.

     Returns 1 on success, and 0 on failure. The function can fail for
     example if if N_SIZE is too small, or if E_SIZE is zero and
     `pub->e' is an even number.

   ---------- Footnotes ----------

   (1) Actually, the computation is not done like this, it is done more
efficiently using `p', `q' and the Chinese remainder theorem (CRT). But
the result is the same.


File: nettle.info,  Node: Randomness,  Next: Miscellaneous functions,  Prev: Public-key algorithms,  Up: Reference

Randomness
==========

   A crucial ingredient in many cryptographic contexts is randomness:
Let `p' be a random prime, choose a random initialization vector `iv',
a random key `k' and a random exponent `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:

   * 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.

   * 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.

   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 `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 `n' bits.

   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:

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.

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, TELNET session, or even SSH session may be
     visible to an attacker, in full or partially.

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.

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.

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.

   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 `/dev/random' generator) tries to
estimate available entropy and restrict the amount of output. The goal
is that if you read 128 bits from `/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:

"Key-hiding"
     An attacker observing the output should not be able to recover the
     generator's key.

"Independence of outputs"
     Observing some of the output should not help the attacker to guess
     previous or future output.

"Forward secrecy"
     Even if an attacker compromises the generator's key, he should not
     be able to guess the generator output _before_ the key compromise.

"Recovery from key compromise"
     If an attacker compromises the generator's key, he can compute
     _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 `t_1', there is another later time `t_2', such that if the
     attacker observes all output generated between `t_1' and `t_2', he
     still can't guess what output is generated after `t_2'.

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

   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 `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 `<nettle/knuth-lfib.h>' is a
fast generator with good statistical properties, but is *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.

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
<http://www.counterpane.com/yarrow.html>, and it uses SHA1 and
triple-DES, and has a 160-bit internal state. Nettle implements
Yarrow-256, which is similar, but uses SHA256 and 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 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 "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 `<nettle/yarrow.h>'.

 - Context struct: struct yarrow256_ctx

 - Context struct: struct yarrow_source
     Information about a single source.

 - Constant: YARROW256_SEED_FILE_SIZE
     The size of the Yarrow-256 seed file.

 - Function: void yarrow256_init (struct yarrow256_ctx *CTX, unsigned
          NSOURCES, struct yarrow_source *SOURCES)
     Initializes the yarrow context, and its NSOURCES sources.

 - Function: void yarrow256_seed (struct yarrow256_ctx *CTX, unsigned
          LENGTH, uint8_t *SEED_FILE)
     Seeds Yarrow-256 from a previous seed file. LENGTH should be at
     least `YARROW256_SEED_FILE_SIZE', but it can be larger.

     The generator will trust you that the SEED_FILE data really is
     unguessable. After calling this function, you _must_ overwrite the
     old seed file with the contents of `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.

 - Function: int yarrow256_update (struct yarrow256_ctx *CTX, unsigned
          SOURCE, unsigned ENTROPY, unsigned LENGTH, const uint8_t
          *DATA)
     Updates the generator with data from source SOURCE (an index that
     must be smaller than the number of sources). ENTROPY is your
     estimated lower bound for the entropy in the data, measured in
     bits.  Calling update with zero 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 `CTX->seed_file'. Otherwise, the
     function returns 0.

 - Function: void yarrow256_random (struct yarrow256_ctx *CTX, unsigned
          LENGTH, uint8_t *DST)
     Generates 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.

 - Function: int yarrow256_is_seeded (struct yarrow256_ctx *CTX)
     Returns 1 if the generator is seeded and ready to generate output,
     otherwise 0.

 - Function: unsigned yarrow256_needed_sources (struct yarrow256_ctx
          *CTX)
     Returns the number of sources that must reach the threshold before
     a slow reseed will happen. Useful primarily when the generator is
     unseeded.

 - Function: void yarrow256_force_reseed (struct yarrow256_ctx *CTX)
     Causes a slow reseed to take place immediately, regardless of the
     current entropy estimates of the two pools. Use with care.

   Nettle includes an entropy estimator for one kind of input source:
User keyboard input.

 - Context struct: struct yarrow_key_event_ctx
     Information about recent key events.

 - Function: void yarrow_key_event_init (struct yarrow_key_event_ctx
          *CTX)
     Initializes the context.

 - Function: unsigned yarrow_key_event_estimate(struct
          yarrow_key_event_ctx *CTX, unsigned KEY, unsigned TIME)
     KEY is the id of the key (ASCII value, hardware key-code, X
     keysym, ... it doesn't matter), and 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, TIME should be provided in units of microseconds. But
     if you use `gettimeofday' on a typical Unix system where the clock
     ticks 10 or so microseconds at a time, TIME should be given in
     units of 10 microseconds.

     Returns an entropy estimate, in bits, suitable for calling
     `yarrow256_update'. Usually, 0, 1 or 2 bits.


File: nettle.info,  Node: Miscellaneous functions,  Next: Compatibility functions,  Prev: Randomness,  Up: Reference

Miscellaneous functions
=======================

 - Function: uint8_t * memxor (uint8_t *DST, const uint8_t *SRC, size_t
          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 `memcpy' function.

   `memxor' is declared in `<nettle/memxor.h>'.


File: nettle.info,  Node: Compatibility functions,  Prev: Miscellaneous functions,  Up: Reference

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
`<nettle/md5-compat.h>'. This file defines the typedef `MD5_CTX', and
declares the functions `MD5Init', `MD5Update' and `MD5Final'.

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


File: nettle.info,  Node: Nettle soup,  Next: Installation,  Prev: Reference,  Up: Top

Traditional Nettle Soup
***********************

   For the serious nettle hacker, here is a recipe for nettle-soup. 4
servings

     1 liter fresh nettles (urtica dioica)

     2 tablespoons butter

     3 tablespoons flour

     1 liter bouillon (meat or vegetable)

     1/2 teaspoon salt

     a tad white pepper

     some cream or milk

   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 bouillon and the
nettle-water you save 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.


File: nettle.info,  Node: Installation,  Next: Index,  Prev: Nettle soup,  Up: Top

Installation
************

   Nettle uses `autoconf' and `automake'. To build it, unpack the
source and run

     ./configure
     make
     make check
     make install

to install in the default location, `/usr/local'. The library is
installed in `/use/local/lib/libnettle.a' and the include files are
installed in `/use/local/include/nettle/'.

   Only static libraries are installed.


File: nettle.info,  Node: Index,  Prev: Installation,  Up: Top

Function and Concept Index
**************************

* Menu:

* aes_decrypt:                           Cipher functions.
* aes_encrypt:                           Cipher functions.
* aes_set_key:                           Cipher functions.
* arcfour_crypt:                         Cipher functions.
* arcfour_set_key:                       Cipher functions.
* blowfish_decrypt:                      Cipher functions.
* blowfish_encrypt:                      Cipher functions.
* blowfish_set_key:                      Cipher functions.
* cast128_decrypt:                       Cipher functions.
* cast128_encrypt:                       Cipher functions.
* cast128_set_key:                       Cipher functions.
* CBC_CTX:                               Cipher Block Chaining.
* cbc_decrypt:                           Cipher Block Chaining.
* CBC_DECRYPT:                           Cipher Block Chaining.
* cbc_encrypt:                           Cipher Block Chaining.
* CBC_ENCRYPT:                           Cipher Block Chaining.
* CBC_SET_IV:                            Cipher Block Chaining.
* des3_decrypt:                          Cipher functions.
* des3_encrypt:                          Cipher functions.
* des3_set_key:                          Cipher functions.
* des_decrypt:                           Cipher functions.
* des_encrypt:                           Cipher functions.
* des_fix_parity:                        Cipher functions.
* des_set_key:                           Cipher functions.
* HMAC_CTX:                              Keyed hash functions.
* hmac_digest:                           Keyed hash functions.
* HMAC_DIGEST:                           Keyed hash functions.
* hmac_md5_digest:                       Keyed hash functions.
* hmac_md5_set_key:                      Keyed hash functions.
* hmac_md5_update:                       Keyed hash functions.
* HMAC_SET_KEY:                          Keyed hash functions.
* hmac_set_key:                          Keyed hash functions.
* hmac_sha1_digest:                      Keyed hash functions.
* hmac_sha1_set_key:                     Keyed hash functions.
* hmac_sha1_update:                      Keyed hash functions.
* hmac_sha256_digest:                    Keyed hash functions.
* hmac_sha256_set_key:                   Keyed hash functions.
* hmac_sha256_update:                    Keyed hash functions.
* hmac_update:                           Keyed hash functions.
* md5_digest:                            Hash functions.
* md5_init:                              Hash functions.
* md5_update:                            Hash functions.
* memxor:                                Miscellaneous functions.
* rsa_clear_private_key:                 Public-key algorithms.
* rsa_clear_public_key:                  Public-key algorithms.
* rsa_compute_root:                      Public-key algorithms.
* rsa_generate_keypair:                  Public-key algorithms.
* rsa_init_private_key:                  Public-key algorithms.
* rsa_init_public_key:                   Public-key algorithms.
* rsa_md5_sign:                          Public-key algorithms.
* rsa_md5_verify:                        Public-key algorithms.
* rsa_prepare_private_key:               Public-key algorithms.
* rsa_prepare_public_key:                Public-key algorithms.
* rsa_sha1_sign:                         Public-key algorithms.
* rsa_sha1_verify:                       Public-key algorithms.
* serpent_decrypt:                       Cipher functions.
* serpent_encrypt:                       Cipher functions.
* serpent_set_key:                       Cipher functions.
* sha1_digest:                           Hash functions.
* sha1_init:                             Hash functions.
* sha1_update:                           Hash functions.
* sha256_digest:                         Hash functions.
* sha256_init:                           Hash functions.
* sha256_update:                         Hash functions.
* twofish_decrypt:                       Cipher functions.
* twofish_encrypt:                       Cipher functions.
* twofish_set_key:                       Cipher functions.
* yarrow256_force_reseed:                Randomness.
* yarrow256_init:                        Randomness.
* yarrow256_is_seeded:                   Randomness.
* yarrow256_needed_sources:              Randomness.
* yarrow256_random:                      Randomness.
* yarrow256_seed:                        Randomness.
* yarrow256_update:                      Randomness.
* yarrow_key_event_estimate:             Randomness.
* yarrow_key_event_init:                 Randomness.



Tag Table:
Node: Top1130
Node: Introduction1837
Node: Copyright3402
Node: Conventions5556
Node: Example7361
Node: Reference8659
Node: Hash functions9035
Node: Cipher functions14461
Node: Cipher Block Chaining33231
Node: Keyed hash functions36346
Node: Public-key algorithms44017
Ref: Public-key algorithms-Footnote-155658
Node: Randomness55827
Node: Miscellaneous functions70646
Node: Compatibility functions71142
Node: Nettle soup72383
Node: Installation73379
Node: Index73854

End Tag Table
