This document describes the Nettle low-level cryptographic library. You can use the library directly from your C programs, or write or use an object-oriented wrapper for your favorite language or application.
This manual is for the Nettle library (version 2.7), a low-level cryptographic library.
Originally written 2001 by Niels Möller, updated 2013.
This manual is placed in the public domain. You may freely copy it, in whole or in part, with or without modification. Attribution is appreciated, but not required.
--- The Detailed Node Listing ---
Reference
Cipher modes
Public-key algorithms
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. Examples are the Nettle module for the Pike language, and LSH, which both use an object-oriented abstraction on top of the library.
This manual explains how to use the Nettle library. It also tries to provide some background on the cryptography, and advice on how to best put it to use.
Nettle is distributed under the GNU Lesser General Public License (LGPL), see the file COPYING.LIB for details. A few of the individual files are in the public domain. To find the current status of particular files, you have to read the copyright notices at the top of the files.
This manual is in the public domain. You may freely copy it in whole or in part, e.g., into documentation of programs that build on Nettle. Attribution, as well as contribution of improvements to the text, is of course appreciated, but it is not required.
A list of the supported algorithms, their origins and licenses:
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 decryption, and whether or not key setup can fail. There are also differences between algorithms that don't show in function prototypes, but which the application must nevertheless be aware of. There is no big difference between the functions for stream ciphers and for block ciphers, although they should be used quite differently by the application.
If your application uses more than one algorithm of the same type, you should probably create an interface that is tailor-made for your needs, and then write a few lines of glue code on top of Nettle.
By convention, for an algorithm named 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.
Many of the functions lack return value and can never fail. Those functions which can fail, return one on success and zero on failure.
A simple example program that reads a file from standard input and writes its SHA1 check-sum on standard output should give the flavor of Nettle.
#include <stdio.h>
#include <stdlib.h>
#include <nettle/sha1.h>
#define BUF_SIZE 1000
static void
display_hex(unsigned length, uint8_t *data)
{
unsigned i;
for (i = 0; i<length; i++)
printf("%02x ", data[i]);
printf("\n");
}
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);
sha1_update(&ctx, done, buffer);
if (done < sizeof(buffer))
break;
}
if (ferror(stdin))
return EXIT_FAILURE;
sha1_digest(&ctx, SHA1_DIGEST_SIZE, digest);
display_hex(SHA1_DIGEST_SIZE, digest);
return EXIT_SUCCESS;
}
On a typical Unix system, this program can be compiled and linked with the command line
gcc sha-example.c -o sha-example -lnettle
Nettle actually consists of two libraries, libnettle and libhogweed. The libhogweed library contains those functions of Nettle that uses bignum operations, and depends on the GMP library. With this division, linking works the same for both static and dynamic libraries.
If an application uses only the symmetric crypto algorithms of Nettle
(i.e., block ciphers, hash functions, and the like), it's sufficient to
link with -lnettle. If an application also uses public-key
algorithms, the recommended linker flags are -lhogweed -lnettle
-lgmp. If the involved libraries are installed as dynamic libraries, it
may be sufficient to link with just -lhogweed, and the loader
will resolve the dependencies automatically.
This chapter describes all the Nettle functions, grouped by family.
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:
H(x) it is hard to find a string x
that hashes to that value.
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 ids to documents, and many other things.
The most commonly used hash functions are MD5 and SHA1. Unfortunately, both these fail the collision-resistance requirement; cryptologists have found ways to construct colliding inputs. The recommended hash functions for new applications are SHA2 (with main variants SHA256 and SHA512). At the time of this writing (December 2012), the winner of the NIST SHA3 competition has recently been announced, and the new SHA3 (earlier known as Keccak) and other top SHA3 candidates may also be reasonable alternatives.
The following hash functions have no known weaknesses, and are suitable for new applications. The SHA2 family of hash functions were specified by NIST, intended as a replacement for SHA1.
SHA256 is a member of the SHA2 family. It outputs hash values of 256 bits, or 32 octets. Nettle defines SHA256 in <nettle/sha2.h>.
The internal block size of SHA256. Useful for some special constructions, in particular HMAC-SHA256.
Hash some more data.
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.
Earlier versions of nettle defined SHA256 in the header file <nettle/sha.h>, which is now deprecated, but kept for compatibility.
SHA224 is a variant of SHA256, with a different initial state, and with the output truncated to 224 bits, or 28 octets. Nettle defines SHA224 in <nettle/sha2.h> (and in <nettle/sha.h>, for backwards compatibility).
The internal block size of SHA224. Useful for some special constructions, in particular HMAC-SHA224.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA224_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
sha224_init.
SHA512 is a larger sibling to SHA256, with a very similar structure but with both the output and the internal variables of twice the size. The internal variables are 64 bits rather than 32, making it significantly slower on 32-bit computers. It outputs hash values of 512 bits, or 64 octets. Nettle defines SHA512 in <nettle/sha2.h> (and in <nettle/sha.h>, for backwards compatibility).
The internal block size of SHA512. Useful for some special constructions, in particular HMAC-SHA512.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA512_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
sha512_init.
SHA384 is a variant of SHA512, with a different initial state, and with the output truncated to 384 bits, or 48 octets. Nettle defines SHA384 in <nettle/sha2.h> (and in <nettle/sha.h>, for backwards compatibility).
The internal block size of SHA384. Useful for some special constructions, in particular HMAC-SHA384.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA384_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
sha384_init.
The SHA3 hash functions were specified by NIST in response to weaknesses in SHA1, and doubts about SHA2 hash functions which structurally are very similar to SHA1. The standard is a result of a competition, where the winner, also known as Keccak, was designed by Guido Bertoni, Joan Daemen, Michaël Peeters and Gilles Van Assche. It is structurally very different from all widely used earlier hash functions. Like SHA2, there are several variants, with output sizes of 224, 256, 384 and 512 bits (28, 32, 48 and 64 octets, respectively).
Nettle defines SHA3-224 in <nettle/sha3.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA3_224_DIGEST_SIZE, in which case only the first length octets of the digest are written.This function also resets the context.
This is SHA3 with 256-bit output size, and possibly the most useful of the SHA3 hash functions.
Nettle defines SHA3-256 in <nettle/sha3.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA3_256_DIGEST_SIZE, in which case only the first length octets of the digest are written.This function also resets the context.
This is SHA3 with 384-bit output size.
Nettle defines SHA3-384 in <nettle/sha3.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA3_384_DIGEST_SIZE, in which case only the first length octets of the digest are written.This function also resets the context.
This is SHA3 with 512-bit output size.
Nettle defines SHA3-512 in <nettle/sha3.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
SHA3_512_DIGEST_SIZE, in which case only the first length octets of the digest are written.This function also resets the context.
The hash functions in this section all have some known weaknesses, and should be avoided for new applications. These hash functions are mainly useful for compatibility with old applications and protocols. Some are still considered safe as building blocks for particular constructions, e.g., there seems to be no known attacks against HMAC-SHA1 or even HMAC-MD5. In some important cases, use of a “legacy” hash function does not in itself make the application insecure; if a known weakness is relevant depends on how the hash function is used, and on the threat model.
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>.
The internal block size of MD5. Useful for some special constructions, in particular HMAC-MD5.
Hash some more data.
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.
MD2 is another hash function of Ronald Rivest's, described in RFC 1319. It outputs message digests of 128 bits, or 16 octets. Nettle defines MD2 in <nettle/md2.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
MD2_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
md2_init.
MD4 is a predecessor of MD5, described in RFC 1320. Like MD5, it is constructed by Ronald Rivest. It outputs message digests of 128 bits, or 16 octets. Nettle defines MD4 in <nettle/md4.h>. Use of MD4 is not recommended, but it is sometimes needed for compatibility with existing applications and protocols.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
MD4_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
md4_init.
RIPEMD160 is a hash function designed by Hans Dobbertin, Antoon Bosselaers, and Bart Preneel, as a strengthened version of RIPEMD (which, like MD4 and MD5, fails the collision-resistance requirement). It produces message digests of 160 bits, or 20 octets. Nettle defined RIPEMD160 in nettle/ripemd160.h.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
RIPEMD160_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
ripemd160_init.
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/sha1.h> (and in <nettle/sha.h>, for backwards compatibility).
The internal block size of SHA1. Useful for some special constructions, in particular HMAC-SHA1.
Hash some more data.
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.
The GOST94 or GOST R 34.11-94 hash algorithm is a Soviet-era algorithm used in Russian government standards (see RFC 4357). It outputs message digests of 256 bits, or 32 octets. Nettle defines GOSTHASH94 in <nettle/gosthash94.h>.
Hash some more data.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than
GOSTHASH94_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
gosthash94_init.
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 (see Keyed hash functions).
struct nettle_hash name context_size digest_size block_size init update digestThe last three attributes are function pointers, of types
nettle_hash_init_func,nettle_hash_update_func, andnettle_hash_digest_func. The first argument to these functions isvoid *pointer to a context struct, which is of sizecontext_size.
These are all the hash functions that Nettle implements.
Nettle also exports a list of all these hashes.
This list can be used to dynamically enumerate or search the supported algorithms. NULL-terminated.
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 plaintext. 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) and CTR (Counter mode) being two of of the most popular. See See Cipher modes, for information on how to apply CBC and CTR with Nettle.
A stream cipher can be used for messages of arbitrary length. A typical stream cipher is a keyed pseudo-random generator. To encrypt a plaintext message of 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 plaintext message that makes sense to you. Can you then be sure that it really was your friend that wrote the message you're reading? The answer is no. For example, if you were using a block cipher in ECB mode, an attacker may pick up the message on its way, and reorder, delete or repeat some of the blocks. Even if the attacker can't decrypt the message, he can change it so that you are not reading the same message as your friend wrote. If you are using a block cipher in 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 (see 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, most key setup functions have no return value, but for ciphers with weak keys, the return value indicates whether or not the given key is weak. For good keys, key setup returns 1, and for weak keys, it returns 0. When possible, avoid algorithms that have weak keys. There are several good ciphers that don't have any weak keys.
To encrypt a message, you first initialize a cipher context for encryption or decryption with a particular key. You then use the context to process plaintext or ciphertext messages. The initialization is known as 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 is a block cipher, specified by NIST as a replacement for the older DES standard. The standard is the result of a competition between cipher designers. The winning design, also known as RIJNDAEL, was constructed by Joan Daemen and Vincent Rijnmen.
Like all the AES candidates, the winning design uses a block size of 128 bits, or 16 octets, and 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>.
Initialize the cipher, for encryption or decryption, respectively.
Given a context src initialized for encryption, initializes the context struct dst for decryption, using the same key. If the same context struct is passed for both
srcanddst, it is converted in place. Callingaes_set_encrypt_keyandaes_invert_keyis more efficient than callingaes_set_encrypt_keyandaes_set_decrypt_key. This function is mainly useful for applications which needs to both encrypt and decrypt using the same key.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
aes_encrypt
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. Furthermore, the initial bytes of the generated key stream leak information about the key; for this reason, it is recommended to discard the first 512 bytes of the key stream.
/* A more robust key setup function for ARCFOUR */
void
arcfour_set_key_hashed(struct arcfour_ctx *ctx,
unsigned length, const uint8_t *key)
{
struct sha256_ctx hash;
uint8_t digest[SHA256_DIGEST_SIZE];
uint8_t buffer[0x200];
sha256_init(&hash);
sha256_update(&hash, length, key);
sha256_digest(&hash, SHA256_DIGEST_SIZE, digest);
arcfour_set_key(ctx, SHA256_DIGEST_SIZE, digest);
arcfour_crypt(ctx, sizeof(buffer), buffer, buffer);
}
Nettle defines ARCFOUR in <nettle/arcfour.h>.
Initialize the cipher. The same function is used for both encryption and decryption.
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_cryptonly once with all the data.
ARCTWO (also known as the trade marked name RC2) is a block cipher
specified in RFC 2268. Nettle also include a variation of the ARCTWO
set key operation that lack one step, to be compatible with the
reverse engineered RC2 cipher description, as described in a Usenet
post to sci.crypt by Peter Gutmann.
ARCTWO uses a block size of 64 bits, and variable key-size ranging
from 1 to 128 octets. Besides the key, ARCTWO also has a second
parameter to key setup, the number of effective key bits, ekb.
This parameter can be used to artificially reduce the key size. In
practice, ekb is usually set equal to the input key size.
Nettle defines ARCTWO in <nettle/arctwo.h>.
We do not recommend the use of ARCTWO; the Nettle implementation is provided primarily for interoperability with existing applications and standards.
Initialize the cipher. The same function is used for both encryption and decryption. The first function is the most general one, which lets you provide both the variable size key, and the desired effective key size (in bits). The maximum value for ekb is 1024, and for convenience,
ekb = 0has the same effect asekb = 1024.
arctwo_set_key(ctx, length, key)is equivalent toarctwo_set_key_ekb(ctx, length, key, 8*length), andarctwo_set_key_gutmann(ctx, length, key)is equivalent toarctwo_set_key_ekb(ctx, length, key, 1024)
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
arctwo_encrypt
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>.
Initialize the cipher. The same function is used for both encryption and decryption. Checks for weak keys, returning 1 for good keys and 0 for weak keys. Applications that don't care about weak keys can ignore the return value.
blowfish_encryptorblowfish_decryptwith a weak key will crash with an assert violation.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
blowfish_encrypt
Camellia is a block cipher developed by Mitsubishi and Nippon Telegraph and Telephone Corporation, described in RFC3713, and recommended by some Japanese and European authorities as an alternative to AES. The algorithm is patented. The implementation in Nettle is derived from the implementation released by NTT under the GNU LGPL (v2.1 or later), and relies on the implicit patent license of the LGPL. There is also a statement of royalty-free licensing for Camellia at http://www.ntt.co.jp/news/news01e/0104/010417.html, but this statement has some limitations which seem problematic for free software.
Camellia uses a the same block size and key sizes as AES: The block size is 128 bits (16 octets), and the supported key sizes are 128, 192, and 256 bits. Nettle defines Camellia in <nettle/camellia.h>.
Initialize the cipher, for encryption or decryption, respectively.
Given a context src initialized for encryption, initializes the context struct dst for decryption, using the same key. If the same context struct is passed for both
srcanddst, it is converted in place. Callingcamellia_set_encrypt_keyandcamellia_invert_keyis more efficient than callingcamellia_set_encrypt_keyandcamellia_set_decrypt_key. This function is mainly useful for applications which needs to both encrypt and decrypt using the same key.
The same function is used for both encryption and decryption. length must be an integral multiple of the block size. If it is more than one block, the data is processed in ECB mode.
srcanddstmay be equal, but they must not overlap in any other way.
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>.
Initialize the cipher. The same function is used for both encryption and decryption.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
cast128_encrypt
DES is the old Data Encryption Standard, specified by NIST. It uses a block size of 64 bits (8 octets), and a key size of 56 bits. However, the key bits are distributed over 8 octets, where the least significant bit of each octet may be used for parity. A common way to use DES is to generate 8 random octets in some way, then set the least significant bit of each octet to get odd parity, and initialize DES with the resulting key.
The key size of DES is so small that keys can be found by brute force, using specialized hardware or lots of ordinary work stations in parallel. One shouldn't be using plain DES at all today, if one uses DES at all one should be using “triple DES”, see DES3 below.
DES also has some weak keys. Nettle defines DES in <nettle/des.h>.
Initialize the cipher. The same function is used for both encryption and decryption. Parity bits are ignored. Checks for weak keys, returning 1 for good keys and 0 for weak keys. Applications that don't care about weak keys can ignore the return value.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
des_encrypt
Checks that the given key has correct, odd, parity. Returns 1 for correct parity, and 0 for bad parity.
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.
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>.
Initialize the cipher. The same function is used for both encryption and decryption. Parity bits are ignored. Checks for weak keys, returning 1 if all three keys are good keys, and 0 if one or more key is weak. Applications that don't care about weak keys can ignore the return value.
For random-looking strings, you can use des_fix_parity to adjust
the parity bits before calling des3_set_key.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
des_encrypt
Salsa20 is a fairly recent stream cipher designed by D. J. Bernstein. It is built on the observation that a cryptographic hash function can be used for encryption: Form the hash input from the secret key and a counter, xor the hash output and the first block of the plaintext, then increment the counter to process the next block (similar to CTR mode, see see CTR). Bernstein defined an encryption algorithm, Snuffle, in this way to ridicule United States export restrictions which treated hash functions as nice and harmless, but ciphers as dangerous munitions.
Salsa20 uses the same idea, but with a new specialized hash function to mix key, block counter, and a couple of constants. It's also designed for speed; on x86_64, it is currently the fastest cipher offered by nettle. It uses a block size of 512 bits (64 octets) and there are two specified key sizes, 128 and 256 bits (16 and 32 octets).
Caution: The hash function used in Salsa20 is not directly applicable for use as a general hash function. It's not collision resistant if arbitrary inputs are allowed, and furthermore, the input and output is of fixed size.
When using Salsa20 to process a message, one specifies both a key and a nonce, the latter playing a similar rôle to the initialization vector (IV) used with CBC or CTR mode. For this reason, Nettle uses the term IV to refer to the Salsa20 nonce. One can use the same key for several messages, provided one uses a unique random iv for each message. The iv is 64 bits (8 octets). The block counter is initialized to zero for each message, and is also 64 bits (8 octets). Nettle defines Salsa20 in <nettle/salsa20.h>.
The two supported key sizes, 16 and 32 octets.
Initialize the cipher. The same function is used for both encryption and decryption. Before using the cipher, you must also call
salsa20_set_iv, see below.
Sets the IV. It is always of size
SALSA20_IV_SIZE, 8 octets. This function also initializes the block counter, setting it to zero.
Encrypts or decrypts the data of a message, using salsa20. When a message is encrypted using a sequence of calls to
salsa20_crypt, all but the last call must use a length that is a multiple ofSALSA20_BLOCK_SIZE.
The full salsa20 cipher uses 20 rounds of mixing. Variants of Salsa20
with fewer rounds are possible, and the 12-round variant is specified by
eSTREAM, see http://www.ecrypt.eu.org/stream/finallist.html.
Nettle calls this variant salsa20r12. It uses the same context
struct and key setup as the full salsa20 cipher, but a separate function
for encryption and decryption.
Encrypts or decrypts the data of a message, using salsa20 reduced to 12 rounds.
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>.
Initialize the cipher. The same function is used for both encryption and decryption.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
serpent_encrypt
Another AES finalist, this one designed by Bruce Schneier and others. Nettle defines it in <nettle/twofish.h>.
Initialize the cipher. The same function is used for both encryption and decryption.
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.
srcanddstmay be equal, but they must not overlap in any other way.
Analogous to
twofish_encrypt
struct nettle_cipherNettle 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>.
struct nettle_cipher name context_size block_size key_size set_encrypt_key set_decrypt_key encrypt decryptThe last four attributes are function pointers, of types
nettle_set_key_funcandnettle_crypt_func. The first argument to these functions is avoid *pointer to a context struct, which is of sizecontext_size.
Nettle includes such structs for all the regular ciphers, i.e. ones without weak keys or other oddities.
Nettle also exports a list of all these ciphers without weak keys or other oddities.
This list can be used to dynamically enumerate or search the supported algorithms. NULL-terminated.
Cipher modes of operation specifies the procedure to use when encrypting a message that is larger than the cipher's block size. As explained in See Cipher functions, splitting the message into blocks and processing them independently with the block cipher (Electronic Code Book mode, ECB) leaks information. Besides ECB, Nettle provides three other modes of operation: Cipher Block Chaining (CBC), Counter mode (CTR), and Galois/Counter mode (GCM). CBC is widely used, but there are a few subtle issues of information leakage, see, e.g., SSH CBC vulnerability. CTR and GCM were standardized more recently, and are believed to be more secure. GCM includes message authentication; for the other modes, one should always use a MAC (see Keyed hash functions) or signature to authenticate the message.
When using CBC mode, plaintext 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 XORed with the plaintext 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 plaintext 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's includes two functions for applying a block cipher in Cipher
Block Chaining (CBC) mode, one for encryption and one for
decryption. These functions uses void * to pass cipher contexts
around.
Applies the encryption or decryption function f in CBC mode. The final ciphertext block processed is copied into iv before returning, so that large message be processed be a sequence of calls to
cbc_encrypt. The function f is of type
void f (void *ctx, unsignedlength, uint8_tdst, const uint8_t *src),and the
cbc_encryptandcbc_decryptfunctions pass their argument ctx on to f.
There are also some macros to help use these functions correctly.
Expands to
{ 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);
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.
A simpler way to invoke
cbc_encryptandcbc_decrypt. The first argument is a pointer to a context struct as defined byCBC_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.
Counter mode (CTR) uses the block cipher as a keyed pseudo-random generator. The output of the generator is XORed with the data to be encrypted. It can be understood as a way to transform a block cipher to a stream cipher.
The message is divided into n blocks M_1,...
M_n, where M_n is of size m which may be smaller
than the block size. Except for the last block, all the message blocks
must be of size equal to the cipher's block size.
If E_k is the encryption function of a block cipher, IC is
the initial counter, then the n plaintext blocks are
transformed into n ciphertext blocks C_1,...
C_n as follows:
C_1 = E_k(IC) XOR M_1
C_2 = E_k(IC + 1) XOR M_2
...
C_(n-1) = E_k(IC + n - 2) XOR M_(n-1)
C_n = E_k(IC + n - 1) [1..m] XOR M_n
The IC is the initial value for the counter, it plays a
similar rôle as the IV for CBC. When adding,
IC + x, IC is interpreted as an integer, in network
byte order. For the last block, E_k(IC + n - 1) [1..m] means that
the cipher output is truncated to m bytes.
Applies the encryption function f in CTR mode. Note that for CTR mode, encryption and decryption is the same operation, and hence f should always be the encryption function for the underlying block cipher.
When a message is encrypted using a sequence of calls to
ctr_crypt, all but the last call must use a length that is a multiple of the block size.
Like for CBC, there are also a couple of helper macros.
Expands to
{ context_type ctx; uint8_t ctr[block_size]; }
First argument is a pointer to a context struct as defined by
CTR_CTX, and the second is a pointer to an initial counter that is copied into that context.
A simpler way to invoke
ctr_crypt. The first argument is a pointer to a context struct as defined byCTR_CTX, and the second argument is an encryption function following Nettle's conventions. The last three arguments define the source and destination area for the operation.
Galois counter mode is the combination of counter mode with message authentication based on universal hashing. The main objective of the design is to provide high performance for hardware implementations, where other popular MAC algorithms (see Keyed hash functions becomes a bottleneck for high-speed hardware implementations. It was proposed by David A. McGrew and John Viega in 2005, and recommended by NIST in 2007, NIST Special Publication 800-38D. It is constructed on top of a block cipher which must have a block size of 128 bits.
GCM is applied to messages of arbitrary length. The inputs are:
The outputs are a ciphertext, of the same length as the plaintext, and a message digest of length 128 bits. Nettle's support for GCM consists of a low-level general interface, some convenience macros, and specific functions for GCM using AES as the underlying cipher. These interfaces are defined in <nettle/gcm.h>
Initializes key. cipher gives a context struct for the underlying cipher, which must have been previously initialized for encryption, and f is the encryption function.
Initializes ctx using the given IV. The key argument is actually needed only if length differs from
GCM_IV_SIZE.
Provides associated data to be authenticated. If used, must be called before
gcm_encryptorgcm_decrypt. All but the last call for each message must use a length that is a multiple of the block size.
Encrypts or decrypts the data of a message. cipher is the context struct for the underlying cipher and f is the encryption function. All but the last call for each message must use a length that is a multiple of the block size.
Extracts the message digest (also known “authentication tag”). This is the final operation when processing a message. length is usually equal to
GCM_BLOCK_SIZE, but if you provide a smaller value, only the first length octets of the digest are written.
To encrypt a message using GCM, first initialize a context for
the underlying block cipher with a key to use for encryption. Then call
the above functions in the following order: gcm_set_key,
gcm_set_iv, gcm_update, gcm_encrypt,
gcm_digest. The decryption procedure is analogous, just calling
gcm_decrypt instead of gcm_encrypt (note that
GCM decryption still uses the encryption function of the
underlying block cipher). To process a new message, using the same key,
call gcm_set_iv with a new iv.
The following macros are defined.
This defines an all-in-one context struct, including the context of the underlying cipher, the hash sub-key, and the per-message state. It expands to
{ context_type cipher; struct gcm_key key; struct gcm_ctx gcm; }
Example use:
struct gcm_aes_ctx GCM_CTX(struct aes_ctx);
The following macros operate on context structs of this form.
First argument, ctx, is a context struct as defined by
GCM_CTX. set_key and encrypt are functions for setting the encryption key and for encrypting data using the underlying cipher. length and data give the key.
First argument is a context struct as defined by
GCM_CTX. length and data give the initialization vector (IV).
Simpler way to call
gcm_update. First argument is a context struct as defined byGCM_CTX
Simpler way to call
gcm_encrypt,gcm_decryptorgcm_digest. First argument is a context struct as defined byGCM_CTX. Second argument, encrypt, is a pointer to the encryption function of the underlying cipher.
The following functions implement the common case of GCM using AES as the underlying cipher.
Initializes ctx using the given key. All valid AES key sizes can be used.
Initializes the per-message state, using the given IV.
Provides associated data to be authenticated. If used, must be called before
gcm_aes_encryptorgcm_aes_decrypt. All but the last call for each message must use a length that is a multiple of the block size.
Encrypts or decrypts the data of a message. All but the last call for each message must use a length that is a multiple of the block size.
Extracts the message digest (also known “authentication tag”). This is the final operation when processing a message. length is usually equal to
GCM_BLOCK_SIZE, but if you provide a smaller value, only the first length octets of the digest are written.
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 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 its 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 a MAC created by Alice and one created by Bob.
Keyed hash functions are typically a lot faster than digital signatures as well.
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 subkeys 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-RIPEMD160 HMAC-SHA1, HMAC-SHA256, and
HMAC-SHA512. First, the abstract functions:
Initializes the three context structs from the key. The outer and inner contexts corresponds to the subkeys
k_oandk_i. state is used for hashing the message, and is initialized as a copy of the inner context.
This function is called zero or more times to process the message. Actually,
hmac_update(state, H, length, data)is equivalent toH->update(state, length, data), so if you wish you can use the ordinary update function of the underlying hash function instead.
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.
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);
ctx is a pointer to a context struct as defined by
HMAC_CTX, H is a pointer to aconst struct nettle_hashdescribing the underlying hash function (so it must match the type of the components of ctx). The last two arguments specify the secret key.
ctx is a pointer to a context struct as defined by
HMAC_CTX, H is a pointer to aconst struct nettle_hashdescribing 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.
Now we come to the specialized HMAC functions, which are easier to use than the general HMAC functions.
Initializes the context with the key.
Process some more data.
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.
Initializes the context with the key.
Process some more data.
Extracts the MAC, writing it to digest. length may be smaller than
RIPEMD160_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.
Initializes the context with the key.
Process some more data.
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.
Initializes the context with the key.
Process some more data.
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.
Initializes the context with the key.
Process some more data.
Extracts the MAC, writing it to digest. length may be smaller than
SHA512_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.
UMAC is a message authentication code based on universal hashing, and designed for high performance on modern processors (in contrast to GCM, See GCM, which is designed primarily for hardware performance). On processors with good integer multiplication performance, it can be 10 times faster than SHA256 and SHA512. UMAC is specified in RFC 4418.
The secret key is always 128 bits (16 octets). The key is used as an encryption key for the AES block cipher. This cipher is used in counter mode to generate various internal subkeys needed in UMAC. Messages are of arbitrary size, and for each message, UMAC also needs a unique nonce. Nonce values must not be reused for two messages with the same key, but they need not be kept secret.
The nonce must be at least one octet, and at most 16; nonces shorter than 16 octets are zero-padded. Nettle's implementation of UMAC increments the nonce for automatically each message, so explicitly setting the nonce for each message is optional. This auto-increment uses network byte order and it takes the length of the nonce into acount. E.g., if the initial nonce is “abc” (3 octets), this value is zero-padded to 16 octets for the first message. For the next message, the nonce is incremented to “abd”, and this incremented value is zero-padded to 16 octets.
UMAC is defined in four variants, for different output sizes:
32 bits (4 octest), 64 bits (8 octets), 96 bits (12 octets) and 128 bits
(16 octets), corresponding to different tradeoffs between speed and
security. Using a shorter output size sometimes (but not always!) gives
the same result as using a longer output size and truncating the result.
So it is important to use the right variant. For consistency with other
hash and MAC functions, Nettle's _digest functions for
UMAC accept a length parameter so that the output can be
truncated to any desired size, but it is recommended to stick to the
specified output size and select the umac variant
corresponding to the desired size.
The internal block size of UMAC is 1024 octets, and it also generates more than 1024 bytes of subkeys. This makes the size of the context struct a bit larger than other hash functions and MAC algorithms in Nettle.
Nettle defines UMAC in <nettle/umac.h>.
Each UMAC variant uses its own context struct.
These functions initialize the UMAC context struct. They also initialize the nonce to zero (with length 16, for auto-increment).
Sets the nonce to be used for the next message. In general, nonces should be set before processing of the message. This is not strictly required for UMAC (the nonce only affects the final processing generating the digest), but it is nevertheless recommended that this function is called before the first
_updatecall for the message.
These functions are called zero or more times to process the message.
Extracts the MAC of the message, writing it to digest. length is usually equal to the specified output size, but if you provide a smaller value, only the first length octets of the MAC are written. These functions reset the context for processing of a new message with the same key. The nonce is incremented as described above, the new value is used unless you call the
_set_noncefunction explicitly for each message.
A key derivation function (KDF) is a function that from a given symmetric key derives other symmetric keys. A sub-class of KDFs is the password-based key derivation functions (PBKDFs), which take as input a password or passphrase, and its purpose is typically to strengthen it and protect against certain pre-computation attacks by using salting and expensive computation.
The most well known PBKDF is the PKCS #5 PBKDF2 described in
RFC 2898 which uses a pseudo-random function such as
HMAC-SHA1.
Nettle's PBKDF2 functions are defined in
<nettle/pbkdf2.h>. There is an abstract function that operate on
any PRF implemented via the nettle_hash_update_func,
nettle_hash_digest_func interfaces. There is also helper macros
and concrete functions PBKDF2-HMAC-SHA1 and PBKDF2-HMAC-SHA256. First,
the abstract function:
Derive symmetric key from a password according to PKCS #5 PBKDF2. The PRF is assumed to have been initialized and this function will call the update and digest functions passing the mac_ctx context parameter as an argument in order to compute digest of size digest_size. Inputs are the salt salt of length salt_length, the iteration counter iterations (> 0), and the desired derived output length length. The output buffer is dst which must have room for at least length octets.
Like for CBC and HMAC, there is a macro to help use the function correctly.
ctx is a pointer to a context struct passed to the update and digest functions (of the types
nettle_hash_update_funcandnettle_hash_digest_funcrespectively) to implement the underlying PRF with digest size of digest_size. Inputs are the salt salt of length salt_length, the iteration counter iterations (> 0), and the desired derived output length length. The output buffer is dst which must have room for at least length octets.
Now we come to the specialized PBKDF2 functions, which are easier to use than the general PBKDF2 function.
PBKDF2 with HMAC-SHA1. Derive length bytes of key into buffer dst using the password key of length key_length and salt salt of length salt_length, with iteration counter iterations (> 0). The output buffer is dst which must have room for at least length octets.
PBKDF2 with HMAC-SHA256. Derive length bytes of key into buffer dst using the password key of length key_length and salt salt of length salt_length, with iteration counter iterations (> 0). The output buffer is dst which must have room for at least length octets.
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 -lhogweed -lnettle
-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. The public-key encryption functions in Nettle are not yet documented; the rest of this chapter is about digital signatures.
To use a digital signature algorithm, one must first create a 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”.
The RSA algorithm was the first practical digital signature algorithm that was constructed. It was described 1978 in a paper by Ronald Rivest, Adi Shamir and L.M. Adleman, and the technique was also patented in the USA in 1983. The patent expired on September 20, 2000, and since that day, RSA can be used freely, even in the USA.
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 n1. 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 represents RSA keys using two structures that contain
large numbers (of type mpz_t).
sizeis the size, in octets, of the modulo, and is used internally.nandeis the public key.
sizeis the size, in octets, of the modulo, and is used internally.dis the secret exponent, but it is not actually used when signing. Instead, the factorspandq, and the parametersa,bandcare used. They are computed fromp,qandesuch thata 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
Calls
mpz_initon all numbers in the key struct.
and when finished with them, the space for the numbers must be deallocated by calling one of
Calls
mpz_clearon 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 See GMP Allocation.
When you have assigned values to the attributes of a key, you must call
Computes the octet size of the key (stored in the
sizeattribute, and may also do other basic sanity checks. Returns one if successful, or zero if the key can't be used, for instance if the modulo is smaller than the minimum size needed for RSA operations 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 signature function, and it will extract the message digest and do the rest of the work. There are also alternative functions that take the hash digest as argument.
There is currently no support for using SHA224 or SHA384 with RSA signatures, since there's no gain in either computation time nor message size compared to using SHA256 and SHA512, respectively.
Creation and verification of signatures is done with the following functions:
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. Returns one on success, or zero on failure. Signing fails if the key is too small for the given hash size, e.g., it's not possible to create a signature using SHA512 and a 512-bit RSA key.
Creates a signature from the given hash digest. digest should point to a digest of size
MD5_DIGEST_SIZE,SHA1_DIGEST_SIZE, orSHA256_DIGEST_SIZE, respectively. The signature is stored in signature (which must have beenmpz_init:ed earlier). Returns one on success, or zero on failure.
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.
Returns 1 if the signature is valid, or 0 if it isn't. digest should point to a digest of size
MD5_DIGEST_SIZE,SHA1_DIGEST_SIZE, orSHA256_DIGEST_SIZE, respectively.
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.
Computes
x = m^d, efficiently.
At last, how do you create new keys?
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_public_key_prepareorrsa_private_key_prepareafter key generation.random_ctx and random is a randomness generator.
random(random_ctx, length, dst)should generatelengthrandom octets and store them atdst. For advice, see See 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 one on success, and zero on failure. The function can fail for example if if n_size is too small, or if e_size is zero andpub->eis an even number.
The DSA digital signature algorithm is more complex than RSA. It was specified during the early 1990s, and in 1994 NIST published FIPS 186 which is the authoritative specification. Sometimes DSA is referred to using the acronym DSS, for Digital Signature Standard. The most recent revision of the specification, FIPS186-3, was issued in 2009, and it adds support for larger hash functions than sha1.
For DSA, the underlying mathematical problem is the
computation of discrete logarithms. The public key consists of a large
prime p, a small prime q which is a factor of p-1,
a number g which generates a subgroup of order q modulo
p, and an element y in that subgroup.
In the original DSA, the size of q is fixed to 160
bits, to match with the SHA1 hash algorithm. The size of
p is in principle unlimited, but the
standard specifies only nine specific sizes: 512 + l*64, where
l is between 0 and 8. Thus, the maximum size of p is 1024
bits, and sizes less than 1024 bits are considered obsolete and not
secure.
The subgroup requirement means that if you compute
g^t mod p
for all possible integers t, you will get precisely q
distinct values.
The private key is a secret exponent x, such that
g^x = y mod p
In mathematical speak, x is the discrete logarithm of
y mod p, with respect to the generator g. The size
of x will also be about the same size as q. The security of the
DSA algorithm relies on the difficulty of the discrete
logarithm problem. Current algorithms to compute discrete logarithms in
this setting, and hence crack DSA, are of two types. The first
type works directly in the (multiplicative) group of integers mod
p. The best known algorithm of this type is the Number Field
Sieve, and it's complexity is similar to the complexity of factoring
numbers of the same size as p. The other type works in the
smaller q-sized subgroup generated by g, which has a more
difficult group structure. One good algorithm is Pollard-rho, which has
complexity sqrt(q).
The important point is that security depends on the size of both
p and q, and they should be chosen so that the difficulty
of both discrete logarithm methods are comparable. Today, the security
margin of the original DSA may be uncomfortably small. Using a
p of 1024 bits implies that cracking using the number field sieve
is expected to take about the same time as factoring a 1024-bit
RSA modulo, and using a q of size 160 bits implies
that cracking using Pollard-rho will take roughly 2^80 group
operations. With the size of q fixed, tied to the SHA1
digest size, it may be tempting to increase the size of p to,
say, 4096 bits. This will provide excellent resistance against attacks
like the number field sieve which works in the large group. But it will
do very little to defend against Pollard-rho attacking the small
subgroup; the attacker is slowed down at most by a single factor of 10
due to the more expensive group operation. And the attacker will surely
choose the latter attack.
The signature generation algorithm is randomized; in order to create a
DSA signature, you need a good source for random numbers
(see Randomness). Let us describe the common case of a 160-bit
q.
To create a signature, one starts with the hash digest of the message,
h, which is a 160 bit number, and a random number k,
0<k<q, also 160 bits. Next, one computes
r = (g^k mod p) mod q
s = k^-1 (h + x r) mod q
The signature is the pair (r, s), two 160 bit numbers. Note the
two different mod operations when computing r, and the use of the
secret exponent x.
To verify a signature, one first checks that 0 < r,s < q, and
then one computes backwards,
w = s^-1 mod q
v = (g^(w h) y^(w r) mod p) mod q
The signature is valid if v = r. This works out because w =
s^-1 mod q = k (h + x r)^-1 mod q, so that
g^(w h) y^(w r) = g^(w h) (g^x)^(w r) = g^(w (h + x r)) = g^k
When reducing mod q this yields r. Note that when
verifying a signature, we don't know either k or x: those
numbers are secret.
If you can choose between RSA and DSA, which one is
best? Both are believed to be secure. DSA gained popularity in
the late 1990s, as a patent free alternative to RSA. Now that
the RSA patents have expired, there's no compelling reason to
want to use DSA. Today, the original DSA key size
does not provide a large security margin, and it should probably be
phased out together with RSA keys of 1024 bits. Using the
revised DSA algorithm with a larger hash function, in
particular, SHA256, a 256-bit q, and p of size
2048 bits or more, should provide for a more comfortable security
margin, but these variants are not yet in wide use.
DSA signatures are smaller than RSA signatures, which is important for some specialized applications.
From a practical point of view, DSA's need for a good
randomness source is a serious disadvantage. If you ever use the same
k (and r) for two different message, you leak your private
key.
Like for RSA, Nettle represents DSA keys using two
structures, containing values of type mpz_t. For information on
how to customize allocation, see See GMP Allocation.
Most of the DSA functions are very similar to the
corresponding RSA functions, but there are a few differences
pointed out below. For a start, there are no functions corresponding to
rsa_public_key_prepare and rsa_private_key_prepare.
Before use, these structs must be initialized by calling one of
Calls
mpz_initon all numbers in the key struct.
When finished with them, the space for the numbers must be deallocated by calling one of
Calls
mpz_clearon all numbers in the key struct.
Signatures are represented using the structure below, and need to be initialized and cleared in the same way as the key structs.
You must call
dsa_signature_initbefore creating or using a signature, and calldsa_signature_clearwhen you are finished with it.
For signing, you need to provide both the public and the private key (unlike RSA, where the private key struct includes all information needed for signing), and a source for random numbers. Signatures can use the SHA1 or the SHA256 hash function, although the implementation of DSA with SHA256 should be considered somewhat experimental due to lack of official test vectors and interoperability testing.
Creates a signature from the given hash context or digest. random_ctx and random is a randomness generator.
random(random_ctx, length, dst)should generatelengthrandom octets and store them atdst. For advice, see See Randomness. Returns one on success, or zero on failure. Signing fails if the key size and the hash size don't match.
Verifying signatures is a little easier, since no randomness generator is needed. The functions are
Verifies a signature. Returns 1 if the signature is valid, otherwise 0.
Key generation uses mostly the same parameters as the corresponding RSA function.
pub and key is where the resulting key pair is stored. The structs should be initialized before you call this function.
random_ctx and random is a randomness generator.
random(random_ctx, length, dst)should generatelengthrandom octets and store them atdst. For advice, see See 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.
p_bits and q_bits are the desired sizes of
pandq. To generate keys that conform to the original DSA standard, you must useq_bits = 160and select p_bits of the formp_bits = 512 + l*64, for0 <= l <= 8, where the smaller sizes are no longer recommended, so you should most likely stick top_bits = 1024. Non-standard sizes are possible, in particularp_bitslarger than 1024, although DSA implementations can not in general be expected to support such keys. Also note that using very large p_bits, with q_bits fixed at 160, doesn't make much sense, because the security is also limited by the size of the smaller prime. Using a largerq_bitsrequires switching to a larger hash function. To generate DSA keys for use with SHA256, useq_bits = 256and, e.g.,p_bits = 2048.Returns one on success, and zero on failure. The function will fail if q_bits is neither 160 nor 256, or if p_bits is unreasonably small.
For cryptographic purposes, an elliptic curve is a mathematical group of points, and computing logarithms in this group is computationally difficult problem. Nettle uses additive notation for elliptic curve groups. If P and Q are two points, and k is an integer, the point sum, P + Q, and the multiple k P can be computed efficiently, but given only two points P and Q, finding an integer k such that Q = k P is the elliptic curve discrete logarithm problem.
Nettle supports standard curves which are all of the form y^2 =
x^3 - 3 x + b (mod p), i.e., the points have coordinates (x,y),
both considered as integers modulo a specified prime p. Curves
are represented as a struct ecc_curve. Supported curves are
declared in <nettle/ecc-curve.h>, e.g., nettle_secp_256r1
for a standardized curve using the 256-bit prime p = 2^256 -
2^224 + 2^192 + 2^96 - 1. The contents of these structs is not
visible to nettle users. The “bitsize of the curve” is used as a
shorthand for the bitsize of the curve's prime p, e.g., 256 bits
for nettle_secp_256r1.
Nettle's implementation of the elliptic curve operations is intended to be side-channel silent. The side-channel attacks considered are:
Nettle's ECC implementation is designed to be side-channel silent, and not leak any information to these attacks. Timing and memory accesses depend only on the size of the input data and its location in memory, not on the actual data bits. This implies a performance penalty in several of the building blocks.
ECDSA is a variant of the DSA digital signature scheme (see DSA), which works over an elliptic curve group rather than over a (subgroup of) integers modulo p. Like DSA, creating a signature requires a unique random nonce (repeating the nonce with two different messages reveals the private key, and any leak or bias in the generation of the nonce also leaks information about the key).
Unlike DSA, signatures are in general not tied to any particular hash function or even hash size. Any hash function can be used, and the hash value is truncated or padded as needed to get a size matching the curve being used. It is recommended to use a strong cryptographic hash function with digest size close to the bit size of the curve, e.g., SHA256 is a reasonable choice when using ECDSA signature over the curve secp256r1. A protocol or application using ECDSA has to specify which curve and which hash function to use, or provide some mechanism for negotiating.
Nettle defines ECDSA in <nettle/ecdsa.h>. We first need to define the data types used to represent public and private keys.
Represents a point on an elliptic curve. In particular, it is used to represent an ECDSA public key.
Initializes p to represent points on the given curve ecc. Allocates storage for the coordinates, using the same allocation functions as GMP.
Check that the given coordinates represent a point on the curve. If so, the coordinates are copied and converted to internal representation, and the function returns 1. Otherwise, it returns 0. Currently, the infinity point (or zero point, with additive notation) i snot allowed.
Extracts the coordinate of the point p. The output parameters x or y may be NULL if the caller doesn't want that coordinate.
Represents an integer in the range 0 < x < group order, where the “group order” refers to the order of an ECC group. In particular, it is used to represent an ECDSA private key.
Initializes s to represent a scalar suitable for the given curve ecc. Allocates storage using the same allocation functions as GMP.
Check that z is in the correct range. If so, copies the value to s and returns 1, otherwise returns 0.
Extracts the scalar, in GMP
mpz_trepresentation.
To create and verify ECDSA signatures, the following functions are used.
Uses the private key key to create a signature on digest. random_ctx and random is a randomness generator.
random(random_ctx, length, dst)should generatelengthrandom octets and store them atdst. The signature is stored in signature, in the same was as for plain DSA.
Uses the public key pub to verify that signature is a valid signature for the message digest digest (of length octets). Returns 1 if the signature is valid, otherwise 0.
Finally, to generation of new an ECDSA key pairs
pub and key is where the resulting key pair is stored. The structs should be initialized, for the desired ECC curve, before you call this function.
random_ctx and random is a randomness generator.
random(random_ctx, length, dst)should generatelengthrandom octets and store them atdst. For advice, see See 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:
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:
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:
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 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 for the details of Yarrow-256, as implemented by Nettle, you have to consult the source code. Maybe a complete specification can be written later.
Yarrow can use many sources (at least two are needed for proper reseeding), and two randomness “pools”, referred to as the “slow pool” and the “fast pool”. Input from the sources is fed alternatingly into the two pools. When one of the sources has contributed 100 bits of entropy to the fast pool, a “fast reseed” happens and the fast pool is mixed into the internal state. When at least two of the sources have contributed at least 160 bits each to the slow pool, a “slow reseed” takes place. The contents of both pools are mixed into the internal state. These procedures should ensure that the generator will eventually recover after a key compromise.
The output is generated by using 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>.
Initializes the yarrow context, and its nsources sources. It's possible to call it with nsources=0 and sources=NULL, if you don't need the update features.
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 newly generated data from
yarrow256_random. If it's possible for several processes to read the seed file at about the same time, access must be coordinated using some locking mechanism.
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 an application using a seed file may want to generate new seed data with
yarrow256_randomand overwrite the seed file. Otherwise, the function returns 0.
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.
Returns 1 if the generator is seeded and ready to generate output, otherwise 0.
Returns the number of sources that must reach the threshold before a slow reseed will happen. Useful primarily when the generator is unseeded.
Causes a fast or 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.
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
gettimeofdayon 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.
Encryption will transform your data from text into binary format, and that may be a problem if you want, for example, to send the data as if it was plain text in an email (or store it along with descriptive text in a file). You may then use an encoding from binary to text: each binary byte is translated into a number of bytes of plain text.
A base-N encoding of data is one representation of data that only uses N different symbols (instead of the 256 possible values of a byte).
The base64 encoding will always use alphanumeric (upper and lower case) characters and the '+', '/' and '=' symbols to represent the data. Four output characters are generated for each three bytes of input. In case the length of the input is not a multiple of three, padding characters are added at the end.
The base16 encoding, also known as “hexadecimal”, uses the decimal digits and the letters from A to F. Two hexadecimal digits are generated for each input byte. Base16 may be useful if you want to use the data for filenames or URLs, for example.
Nettle supports both base64 and base16 encoding and decoding.
Encoding and decoding uses a context struct to maintain its state (with the exception of base16 encoding, which doesn't need any). To encode or decode the your data, first initialize the context, then call the update function as many times as necessary, and complete the operation by calling the final function.
The following functions can be used to perform base64 encoding and decoding. They are defined in <nettle/base64.h>.
Initializes a base64 context. This is necessary before starting an encoding session.
Encodes a single byte. Returns amount of output (always 1 or 2).
The maximum number of output bytes when passing length input bytes to
base64_encode_update.
After ctx is initialized, this function may be called to encode length bytes from src. The result will be placed in dst, and the return value will be the number of bytes generated. Note that dst must be at least of size BASE64_ENCODE_LENGTH(length).
After calling base64_encode_update one or more times, this function should be called to generate the final output bytes, including any needed paddding. The return value is the number of output bytes generated.
Initializes a base64 decoding context. This is necessary before starting a decoding session.
Decodes a single byte (src) and stores the result in dst. Returns amount of output (0 or 1), or -1 on errors.
The maximum number of output bytes when passing length input bytes to
base64_decode_update.
After ctx is initialized, this function may be called to decode src_length bytes from src. dst should point to an area of size at least BASE64_DECODE_LENGTH(length), and for sanity checking, dst_length should be initialized to the size of that area before the call. dst_length is updated to the amount of decoded output. The function will return 1 on success and 0 on error.
Check that final padding is correct. Returns 1 on success, and 0 on error.
Similarly to the base64 functions, the following functions perform base16 encoding, and are defined in <nettle/base16.h>. Note that there is no encoding context necessary for doing base16 encoding.
Encodes a single byte. Always stores two digits in dst[0] and dst[1].
The number of output bytes when passing length input bytes to
base16_encode_update.
Always stores BASE16_ENCODE_LENGTH(length) digits in dst.
Initializes a base16 decoding context. This is necessary before starting a decoding session.
Decodes a single byte from src into dst. Returns amount of output (0 or 1), or -1 on errors.
The maximum number of output bytes when passing length input bytes to
base16_decode_update.
After ctx is initialized, this function may be called to decode src_length bytes from src. dst should point to an area of size at least BASE16_DECODE_LENGTH(length), and for sanity checking, dst_length should be initialized to the size of that area before the call. dst_length is updated to the amount of decoded output. The function will return 1 on success and 0 on error.
Checks that the end of data is correct (i.e., an even number of hexadecimal digits have been seen). Returns 1 on success, and 0 on error.
XORs the source area on top of the destination area. The interface doesn't follow the Nettle conventions, because it is intended to be similar to the ANSI-C
memcpyfunction.
memxor is declared in <nettle/memxor.h>.
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 its 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.
For the serious nettle hacker, here is a recipe for nettle soup. 4 servings.
Gather 1 liter fresh nettles. Use gloves! Small, tender shoots are preferable but the tops of larger nettles can also be used.
Rinse the nettles very well. Boil them for 10 minutes in lightly salted water. Strain the nettles and save the water. Hack the nettles. Melt the butter and mix in the flour. Dilute with stock and the nettle-water you saved earlier. Add the hacked nettles. If you wish you can add some milk or cream at this stage. Bring to a boil and let boil for a few minutes. Season with salt and pepper.
Serve with boiled egg-halves.
Nettle uses autoconf. To build it, unpack the source and run
./configure
make
make check
make install
to install in under the default prefix, /usr/local.
To get a list of configure options, use ./configure --help.
By default, both static and shared libraries are built and installed. To omit building the shared libraries, use the --disable-shared option to ./configure.
Using GNU make is recommended. For other make programs, in particular BSD make, you may have to use the --disable-dependency-tracking option to ./configure.
aes_decrypt: Cipher functionsaes_encrypt: Cipher functionsaes_invert_key: Cipher functionsaes_set_decrypt_key: Cipher functionsaes_set_encrypt_key: Cipher functionsarcfour_crypt: Cipher functionsarcfour_set_key: Cipher functionsarctwo_decrypt: Cipher functionsarctwo_encrypt: Cipher functionsarctwo_set_key: Cipher functionsarctwo_set_key_ekb: Cipher functionsarctwo_set_key_gutmann: Cipher functionsbase16_decode_final: ASCII encodingbase16_decode_init: ASCII encodingBASE16_DECODE_LENGTH: ASCII encodingbase16_decode_single: ASCII encodingbase16_decode_update: ASCII encodingBASE16_ENCODE_LENGTH: ASCII encodingbase16_encode_single: ASCII encodingbase16_encode_update: ASCII encodingbase64_decode_final: ASCII encodingbase64_decode_init: ASCII encodingBASE64_DECODE_LENGTH: ASCII encodingbase64_decode_single: ASCII encodingbase64_decode_update: ASCII encodingbase64_encode_final: ASCII encodingbase64_encode_init: ASCII encodingBASE64_ENCODE_LENGTH: ASCII encodingbase64_encode_single: ASCII encodingbase64_encode_update: ASCII encodingblowfish_decrypt: Cipher functionsblowfish_encrypt: Cipher functionsblowfish_set_key: Cipher functionscamellia_crypt: Cipher functionscamellia_invert_key: Cipher functionscamellia_set_decrypt_key: Cipher functionscamellia_set_encrypt_key: Cipher functionscast128_decrypt: Cipher functionscast128_encrypt: Cipher functionscast128_set_key: Cipher functionsCBC_CTX: CBCCBC_DECRYPT: CBCcbc_decrypt: CBCCBC_ENCRYPT: CBCcbc_encrypt: CBCCBC_SET_IV: CBCCTR_CRYPT: CTRctr_crypt: CTRCTR_CTX: CTRCTR_SET_COUNTER: CTRdes3_decrypt: Cipher functionsdes3_encrypt: Cipher functionsdes3_set_key: Cipher functionsdes_check_parity: Cipher functionsdes_decrypt: Cipher functionsdes_encrypt: Cipher functionsdes_fix_parity: Cipher functionsdes_set_key: Cipher functionsdsa_generate_keypair: DSAdsa_private_key_clear: DSAdsa_private_key_init: DSAdsa_public_key_clear: DSAdsa_public_key_init: DSAdsa_sha1_sign: DSAdsa_sha1_sign_digest: DSAdsa_sha1_verify: DSAdsa_sha1_verify_digest: DSAdsa_sha256_sign: DSAdsa_sha256_sign_digest: DSAdsa_sha256_verify: DSAdsa_sha256_verify_digest: DSAdsa_signature_clear: DSAdsa_signature_init: DSAecc_point_clear: Elliptic curvesecc_point_get: Elliptic curvesecc_point_init: Elliptic curvesecc_point_set: Elliptic curvesecc_scalar_clear: Elliptic curvesecc_scalar_get: Elliptic curvesecc_scalar_init: Elliptic curvesecc_scalar_set: Elliptic curvesecdsa_generate_keypair: Elliptic curvesecdsa_sign: Elliptic curvesecdsa_verify: Elliptic curvesgcm_aes_decrypt: GCMgcm_aes_digest: GCMgcm_aes_encrypt: GCMgcm_aes_set_iv: GCMgcm_aes_set_key: GCMgcm_aes_update: GCMGCM_CTX: GCMGCM_DECRYPT: GCMgcm_decrypt: GCMGCM_DIGEST: GCMgcm_digest: GCMGCM_ENCRYPT: GCMgcm_encrypt: GCMGCM_SET_IV: GCMgcm_set_iv: GCMGCM_SET_KEY: GCMgcm_set_key: GCMGCM_UPDATE: GCMgcm_update: GCMgosthash94_digest: Legacy hash functionsgosthash94_init: Legacy hash functionsgosthash94_update: Legacy hash functionsHMAC_CTX: Keyed hash functionsHMAC_DIGEST: Keyed hash functionshmac_digest: Keyed hash functionshmac_md5_digest: Keyed hash functionshmac_md5_set_key: Keyed hash functionshmac_md5_update: Keyed hash functionshmac_ripemd160_digest: Keyed hash functionshmac_ripemd160_set_key: Keyed hash functionshmac_ripemd160_update: Keyed hash functionsHMAC_SET_KEY: Keyed hash functionshmac_set_key: Keyed hash functionshmac_sha1_digest: Keyed hash functionshmac_sha1_set_key: Keyed hash functionshmac_sha1_update: Keyed hash functionshmac_sha256_digest: Keyed hash functionshmac_sha256_set_key: Keyed hash functionshmac_sha256_update: Keyed hash functionshmac_sha512_digest: Keyed hash functionshmac_sha512_set_key: Keyed hash functionshmac_sha512_update: Keyed hash functionshmac_update: Keyed hash functionsmd2_digest: Legacy hash functionsmd2_init: Legacy hash functionsmd2_update: Legacy hash functionsmd4_digest: Legacy hash functionsmd4_init: Legacy hash functionsmd4_update: Legacy hash functionsmd5_digest: Legacy hash functionsmd5_init: Legacy hash functionsmd5_update: Legacy hash functionsmemxor: Miscellaneous functionsPBKDF2: Key derivation functionspbkdf2: Key derivation functionspbkdf2_hmac_sha1: Key derivation functionspbkdf2_hmac_sha256: Key derivation functionsripemd160_digest: Legacy hash functionsripemd160_init: Legacy hash functionsripemd160_update: Legacy hash functionsrsa_compute_root: RSArsa_generate_keypair: RSArsa_md5_sign: RSArsa_md5_sign_digest: RSArsa_md5_verify: RSArsa_md5_verify_digest: RSArsa_private_key_clear: RSArsa_private_key_init: RSArsa_private_key_prepare: RSArsa_public_key_clear: RSArsa_public_key_init: RSArsa_public_key_prepare: RSArsa_sha1_sign: RSArsa_sha1_sign_digest: RSArsa_sha1_verify: RSArsa_sha1_verify_digest: RSArsa_sha256_sign: RSArsa_sha256_sign_digest: RSArsa_sha256_verify: RSArsa_sha256_verify_digest: RSArsa_sha512_sign: RSArsa_sha512_sign_digest: RSArsa_sha512_verify: RSArsa_sha512_verify_digest: RSAsalsa20_crypt: Cipher functionssalsa20_set_iv: Cipher functionssalsa20_set_key: Cipher functionssalsa20r12_crypt: Cipher functionsserpent_decrypt: Cipher functionsserpent_encrypt: Cipher functionsserpent_set_key: Cipher functionssha1_digest: Legacy hash functionssha1_init: Legacy hash functionssha1_update: Legacy hash functionssha224_digest: Recommended hash functionssha224_init: Recommended hash functionssha224_update: Recommended hash functionssha256_digest: Recommended hash functionssha256_init: Recommended hash functionssha256_update: Recommended hash functionssha384_digest: Recommended hash functionssha384_init: Recommended hash functionssha384_update: Recommended hash functionssha3_224_digest: Recommended hash functionssha3_224_init: Recommended hash functionssha3_224_update: Recommended hash functionssha3_256_digest: Recommended hash functionssha3_256_init: Recommended hash functionssha3_256_update: Recommended hash functionssha3_384_digest: Recommended hash functionssha3_384_init: Recommended hash functionssha3_384_update: Recommended hash functionssha3_512_digest: Recommended hash functionssha3_512_init: Recommended hash functionssha3_512_update: Recommended hash functionssha512_digest: Recommended hash functionssha512_init: Recommended hash functionssha512_update: Recommended hash functionstwofish_decrypt: Cipher functionstwofish_encrypt: Cipher functionstwofish_set_key: Cipher functionsumac128_digest: Keyed hash functionsumac128_set_key: Keyed hash functionsumac128_set_nonce: Keyed hash functionsumac128_update: Keyed hash functionsumac32_digest: Keyed hash functionsumac32_set_key: Keyed hash functionsumac32_set_nonce: Keyed hash functionsumac32_update: Keyed hash functionsumac64_digest: Keyed hash functionsumac64_set_key: Keyed hash functionsumac64_set_nonce: Keyed hash functionsumac64_update: Keyed hash functionsumac96_digest: Keyed hash functionsumac96_set_key: Keyed hash functionsumac96_set_nonce: Keyed hash functionsumac96_update: Keyed hash functionsyarrow256_fast_reseed: Randomnessyarrow256_init: Randomnessyarrow256_is_seeded: Randomnessyarrow256_needed_sources: Randomnessyarrow256_random: Randomnessyarrow256_seed: Randomnessyarrow256_slow_reseed: Randomnessyarrow256_update: Randomnessyarrow_key_event_estimate: Randomnessyarrow_key_event_init: Randomness[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.