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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 3.4), a low-level cryptographic library.
Originally written 2001 by Niels Möller, updated 2017.
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.
• Introduction: | What is Nettle? | |
• Copyright: | Your rights. | |
• Conventions: | General interface conventions. | |
• Example: | An example program. | |
• Linking: | Linking with libnettle and libhogweed. | |
• Compatibility: | On API and ABI compatibility between versions. | |
• Reference: | All Nettle functions and features. | |
• Nettle soup: | For the serious nettle hacker. | |
• Installation: | How to install Nettle. | |
• Index: | Function and concept index. | |
— The Detailed Node Listing — Reference | ||
---|---|---|
• Hash functions: | ||
• Cipher functions: | ||
• Cipher modes: | ||
• Keyed hash functions: | ||
• Key derivation functions: | ||
• Public-key algorithms: | ||
• Randomness: | ||
• ASCII encoding: | ||
• Miscellaneous functions: | ||
• Compatibility functions: | ||
Hash functions | ||
• Recommended hash functions: | ||
• Miscellaneous hash functions: | ||
• Legacy hash functions: | ||
• nettle_hash abstraction: | ||
Cipher modes | ||
• CBC: | ||
• CTR: | ||
• CFB and CFB8: | ||
• XTS: | ||
Authenticated encryption with associated data | ||
• EAX: | ||
• GCM: | ||
• CCM: | ||
• ChaCha-Poly1305: | ||
• SIV-CMAC: | ||
• nettle_aead abstraction: | ||
Keyed Hash Functions | ||
• HMAC: | ||
• UMAC: | ||
• CMAC: | ||
• Poly1305: | ||
Public-key algorithms | ||
• RSA: | The RSA public key algorithm. | |
• DSA: | The DSA digital signature algorithm. | |
• Elliptic curves: | Elliptic curves and ECDSA | |
Elliptic curves | ||
• Side-channel silence: | ||
• ECDSA: | ||
• GOSTDSA: | ||
• Curve 25519 and Curve 448: | ||
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.
Next: Conventions, Previous: Introduction, Up: Top [Contents][Index]
Nettle is dual licenced under the GNU General Public License version 2 or later, and the GNU Lesser General Public License version 3 or later. When using Nettle, you must comply fully with all conditions of at least one of these licenses. A few of the individual files are licensed under more permissive terms, or in the public domain. To find the current status of particular files, you have to read the copyright notices at the top of the files.
This manual is in the public domain. You may freely copy it in whole or in part, e.g., into documentation of programs that build on Nettle. Attribution, as well as contribution of improvements to the text, is of course appreciated, but it is not required.
A list of the supported algorithms, their origins, and exceptions to the above licensing:
The implementation of the AES cipher (also known as rijndael) is written by Rafael Sevilla. Assembler for x86 by Rafael Sevilla and Niels Möller, Sparc assembler by Niels Möller.
The implementation of the ARCFOUR (also known as RC4) cipher is written by Niels Möller.
The implementation of the ARCTWO (also known as RC2) cipher is written by Nikos Mavroyanopoulos and modified by Werner Koch and Simon Josefsson.
The implementation of the BLOWFISH cipher is written by Werner Koch, copyright owned by the Free Software Foundation. Also hacked by Simon Josefsson and Niels Möller.
The C implementation is by Nippon Telegraph and Telephone Corporation (NTT), heavily modified by Niels Möller. Assembler for x86 and x86_64 by Niels Möller.
The implementation of the CAST128 cipher is written by Steve Reid. Released into the public domain.
Implemented by Joachim Strömbergson, based on the implementation of SALSA20 (see below). Assembly for x86_64 by Niels Möller.
The implementation of the DES cipher is written by Dana L. How, and released under the LGPL, version 2 or later.
The C implementation of the GOST94 message digest is written by Aleksey Kravchenko and was ported from the rhash library by Nikos Mavrogiannopoulos. It is released under the MIT license.
The implementation of MD2 is written by Andrew Kuchling, and hacked some by Andreas Sigfridsson and Niels Möller. Python Cryptography Toolkit license (essentially public domain).
This is almost the same code as for MD5 below, with modifications by Marcus Comstedt. Released into the public domain.
The implementation of the MD5 message digest is written by Colin Plumb. It has been hacked some more by Andrew Kuchling and Niels Möller. Released into the public domain.
The C implementation of PBKDF2 is based on earlier work for Shishi and GnuTLS by Simon Josefsson.
The implementation of RIPEMD160 message digest is based on the code in libgcrypt, copyright owned by the Free Software Foundation. Ported to Nettle by Andres Mejia.
The C implementation of SALSA20 is based on D. J. Bernstein’s reference implementation (in the public domain), adapted to Nettle by Simon Josefsson, and heavily modified by Niels Möller. Assembly for x86_64 and ARM by Niels Möller.
The implementation of the SERPENT cipher is based on the code in libgcrypt, copyright owned by the Free Software Foundation. Adapted to Nettle by Simon Josefsson and heavily modified by Niels Möller. Assembly for x86_64 by Niels Möller.
Based on the implementation by Andrew M. (floodyberry), modified by Nikos Mavrogiannopoulos and Niels Möller. Assembly for x86_64 by Niels Möller.
The C implementation of the SHA1 message digest is written by Peter Gutmann, and hacked some more by Andrew Kuchling and Niels Möller. Released into the public domain. Assembler for x86, x86_64 and ARM by Niels Möller, released under the LGPL.
Written by Niels Möller, using Peter Gutmann’s SHA1 code as a model.
Written by Niels Möller.
The implementation of the TWOFISH cipher is written by Ruud de Rooij.
Written by Niels Möller.
Written by Nikos Mavrogiannopoulos, Niels Möller, Jeremy Allison, Michael Adam and Stefan Metzmacher.
Written by Niels Möller. Uses the GMP library for bignum operations.
Written by Niels Möller. Uses the GMP library for bignum operations.
Written by Niels Möller. Uses the GMP library for bignum operations. Development of Nettle’s ECC support was funded by the .SE Internet Fund.
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 size_t
, 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 usually of the same length.
When they differ, e.g., for ccm_encrypt_message
, the length
argument specifies the size of the destination area. Source and
destination pointers may be equal, so that you can process strings in
place, but source and destination areas 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.
Next: Linking, Previous: Conventions, Up: Top [Contents][Index]
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
Next: Compatibility, Previous: Example, Up: Top [Contents][Index]
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.
When you write a program using the Nettle library, it’s desirable to have it work together not only with exactly the same version of Nettle you had at hand, but with other current and future versions. If a different version of Nettle is used at compile time, i.e., you recompile it using the header and library files belonging to a different version, we talk about API compatibility (for Application Programming Interface). If a different version of Nettle isn’t used until link time, we talk about ABI compatibility (Application Binary Interface) or binary compatibility. ABI compatibility matters mainly when using dynamic linking with a shared library. E.g., a user has an executable linking at run-time with libnettle.so, and then updates to a later version of the shared library, without updating or recompiling the executable.
Nettle aims to provide backwards compatibility, i.e., a program written for a particular version of the Nettle library should usually work fine with later version of the library. Note that the opposite is not supported: The program should not be expected to work with older versions of the Nettle library; and ABI breakage can be unobvious. E.g, the later version may define a new library symbol, and let header files redefine an old API name as an alias for the new symbol. If the later version ensures that the old symbol is still defined in the library, this change is backwards compatible: A program compiled using headers from the older version can be successfully linked with either version of the library. But if you compile the same program using headers from the later version of the library, and attempt to link with the older version, you’ll get an undefined reference to the new symbol.
API compatibility is rarely broken; exceptions are noted in the NEWS
file. For example, the key size argument to the function
cast128_set_key
was dropped in the Nettle-3.0 release, and all
programs using that function had to be updated to work with the new
version.
ABI compatibility is broken occasionally. This is also noted in the NEWS file, and the name of the shared library is updated to prevent accidental run-time linking with the wrong version. All programs have to be recompiled before they can link with the new version. Since names are different, multiple versions can be installed on the same system, with a mix of programs linking to one version or the other.
Under some circumstances, it is possible to have a single program linking dynamically with two binary incompatible versions of the Nettle library, thanks to the use of symbol versioning. Consider a program calling functions in both Nettle and GnuTLS. For the direct dependency on Nettle, the program is linked with a particular version of the Nettle shared library. GnuTLS uses Nettle internally, but does not expose any Nettle data structures or the like in its own ABI. In this situation, the GnuTLS shared library may link with a different version of the Nettle library. Then both versions of the Nettle library will be loaded into the program’s address space, and each reference to a symbol will be resolved to the correct version.
Finally, some of Nettle’s symbols are internal. They carry a leading underscore, and are not declared in installed header files. They can be used for local or experimental purposes, but programs referring directly to those symbols get neither API nor ABI compatibility, not even between minor versions.
Next: Nettle soup, Previous: Compatibility, Up: Top [Contents][Index]
This chapter describes all the Nettle functions, grouped by family.
Next: Cipher functions, Previous: Reference, Up: Reference [Contents][Index]
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:
Given a hash value H(x)
it is hard to find a string x
that hashes to that value.
It is hard to find two different strings, x
and y
, such
that H(x)
= H(y)
.
Hash functions are useful as building blocks for digital signatures, message authentication codes, pseudo random generators, association of unique ids to documents, and many other things.
The most commonly used hash functions are MD5 and SHA1. Unfortunately, both these fail the collision-resistance requirement; cryptologists have found ways to construct colliding inputs. The recommended hash functions for new applications are SHA2 (with main variants SHA256 and SHA512). At the time of this writing (Autumn 2015), SHA3 has recently been standardized, and the new SHA3 and other top SHA3 candidates may also be reasonable alternatives.
• Recommended hash functions: | ||
• Miscellaneous hash functions: | ||
• Legacy hash functions: | ||
• nettle_hash abstraction: |
Next: Miscellaneous hash functions, Up: Hash functions [Contents][Index]
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 size of a SHA256 digest, i.e. 32.
The internal block size of SHA256. Useful for some special constructions, in particular HMAC-SHA256.
Initialize the SHA256 state.
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 size of a SHA224 digest, i.e. 28.
The internal block size of SHA224. Useful for some special constructions, in particular HMAC-SHA224.
Initialize the SHA224 state.
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 size of a SHA512 digest, i.e. 64.
The internal block size of SHA512, 128. Useful for some special constructions, in particular HMAC-SHA512.
Initialize the SHA512 state.
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
.
Several variants of SHA512 have been defined, with a different initial state, and with the output truncated to shorter length than 512 bits. Naming is a bit confused, these algorithms are called SHA512-224, SHA512-256 and SHA384, for output sizes of 224, 256 and 384 bits, respectively. Nettle defines these in <nettle/sha2.h> (and in <nettle/sha.h>, for backwards compatibility).
These context structs are all the same as sha512_ctx. They are defined as simple preprocessor aliases, which may cause some problems if used as identifiers for other purposes. So avoid doing that.
The digest size for each variant, i.e., 28, 32, and 48, respectively.
The internal block size, same as SHA512_BLOCK_SIZE, i.e., 128. Useful for some special constructions, in particular HMAC-SHA384.
Initialize the context struct.
Hash some more data. These are all aliases for sha512_update, which does the same thing.
Performs final processing and extracts the message digest, writing it to digest. length may be smaller than the specified digest size, in which case only the first length octets of the digest are written.
These function also reset the context in the same way as the corresponding init function.
The SHA3 hash functions were specified by NIST in response to weaknesses in SHA1, and doubts about SHA2 hash functions which structurally are very similar to SHA1. SHA3 is a result of a competition, where the winner, also known as Keccak, was designed by Guido Bertoni, Joan Daemen, Michaël Peeters and Gilles Van Assche. It is structurally very different from all widely used earlier hash functions. Like SHA2, there are several variants, with output sizes of 224, 256, 384 and 512 bits (28, 32, 48 and 64 octets, respectively). In August 2015, it was formally standardized by NIST, as FIPS 202, http://dx.doi.org/10.6028/NIST.FIPS.202.
Note that the SHA3 implementation in earlier versions of Nettle was
based on the specification at the time Keccak was announced as the
winner of the competition, which is incompatible with the final standard
and hence with current versions of Nettle. The nette/sha3.h
defines a preprocessor symbol NETTLE_SHA3_FIPS202
to indicate
conformance with the standard.
Defined to 1 in Nettle versions supporting FIPS 202. Undefined in earlier versions.
Nettle defines SHA3-224 in <nettle/sha3.h>.
The size of a SHA3_224 digest, i.e., 28.
The internal block size of SHA3_224.
Initialize the SHA3-224 state.
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>.
The size of a SHA3_256 digest, i.e., 32.
The internal block size of SHA3_256.
Initialize the SHA3-256 state.
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>.
The size of a SHA3_384 digest, i.e., 48.
The internal block size of SHA3_384.
Initialize the SHA3-384 state.
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>.
The size of a SHA3_512 digest, i.e. 64.
The internal block size of SHA3_512.
Initialize the SHA3-512 state.
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.
In addition to those SHA-3 hash functions, Nettle also provides a SHA-3 extendable-output function (XOF), SHAKE-256. Unlike SHA-3 hash functions, SHAKE can produce an output digest of any desired length.
To use SHAKE256, the context struct, init and update functions are the
same as for SHA3-256. To get a SHAKE256 digest, the following function
is used instead of sha3_256_digest
. For an output size of
SHA3_256_DIGEST_SIZE
, security is equivalent to SHA3-256 (but the
digest is different). Increasing output size further does not increase
security in terms of collision or preimage resistance. It can be seen as
a built in pseudorandomness generator.
Performs final processing and produces a SHAKE256 digest, writing it to digest. length can be of arbitrary size.
This function also resets the context.
Next: Legacy hash functions, Previous: Recommended hash functions, Up: Hash functions [Contents][Index]
STREEBOG512 is a member of the Streebog (GOST R 34.11-2012) family. It outputs hash values of 512 bits, or 64 octets. Nettle defines STREEBOG512 in <nettle/streebog.h>.
The size of a STREEBOG512 digest, i.e. 64.
The internal block size of STREEBOG512. Useful for some special constructions, in particular HMAC-STREEBOG512.
Initialize the STREEBOG512 state.
Hash some more data.
Performs final processing and extracts the message digest, writing it
to digest. length may be smaller than
STREEBOG512_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
streebog512_init
.
STREEBOG256 is a variant of STREEBOG512, with a different initial state, and with the output truncated to 256 bits, or 32 octets. Nettle defines STREEBOG256 in <nettle/streebog.h>.
The size of a STREEBOG256 digest, i.e. 32.
The internal block size of STREEBOG256. Useful for some special constructions, in particular HMAC-STREEBOG256.
Initialize the STREEBOG256 state.
Hash some more data.
Performs final processing and extracts the message digest, writing it
to digest. length may be smaller than
STREEBOG256_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
streebog256_init
.
Next: nettle_hash abstraction, Previous: Miscellaneous hash functions, Up: Hash functions [Contents][Index]
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 size of an MD5 digest, i.e. 16.
The internal block size of MD5. Useful for some special constructions, in particular HMAC-MD5.
Initialize the MD5 state.
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>.
The size of an MD2 digest, i.e. 16.
The internal block size of MD2.
Initialize the MD2 state.
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.
The size of an MD4 digest, i.e. 16.
The internal block size of MD4.
Initialize the MD4 state.
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.
The size of a RIPEMD160 digest, i.e. 20.
The internal block size of RIPEMD160.
Initialize the RIPEMD160 state.
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 size of a SHA1 digest, i.e. 20.
The internal block size of SHA1. Useful for some special constructions, in particular HMAC-SHA1.
Initialize the SHA1 state.
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. The standard itself does not fix the S-box used by the hash algorith, so there are two popular variants (the testing S-box from the standard itself and the S-box defined by CryptoPro company, see RFC 4357). Nettle provides support for the former S-box in the form of GOSTHASH94 hash algorithm and for the latter in the form of GOSTHASH94CP hash algorithm. Nettle defines GOSTHASH94 and GOSTHASH94CP in <nettle/gosthash94.h>.
The size of a GOSTHASH94 digest, i.e. 32.
The internal block size of GOSTHASH94, i.e., 32.
Initialize the GOSTHASH94 state.
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
.
The size of a GOSTHASH94CP digest, i.e. 32.
The internal block size of GOSTHASH94CP, i.e., 32.
Initialize the GOSTHASH94CP state.
Hash some more data.
Performs final processing and extracts the message digest, writing it
to digest. length may be smaller than
GOSTHASH94CP_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
gosthash94cp_init
.
Previous: Legacy hash functions, Up: Hash functions [Contents][Index]
struct nettle_hash
abstractionNettle 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 *
, and
nettle_hash_digest_func *
. The first argument to these functions is
void *
pointer to a context struct, which is of size
context_size
.
These are all the hash functions that Nettle implements.
Nettle also exports a list of all these hashes.
Returns a NULL-terminated list of pointers to supported hash functions. This list can be used to dynamically enumerate or search the supported algorithms.
A macro expanding to a call to nettle_get_hashes, so that one could
write, e.g., nettle_hashes[0]->name
for the name of the first
hash function on the list. In earlier versions, this was not a macro but
the actual array of pointers. However, referring directly to the array
makes the array size leak into the ABI in some cases.
Next: Cipher modes, Previous: Hash functions, Up: Reference [Contents][Index]
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 three possible key-size, 128, 192 and 256 bits
(16, 24 and 32 octets) being the allowed key sizes. It does not have any
weak keys. Nettle defines AES in <nettle/aes.h>, and there is one
context struct for each key size. (Earlier versions of Nettle used a
single context struct, struct aes_ctx
, for all key sizes. This
interface kept for backwards compatibility).
Alternative struct, for the old AES interface.
The AES block-size, 16.
Default AES key size, 32.
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 src
and dst
, it is
converted in place. These functions are mainly useful for applications
which needs to both encrypt and decrypt using the same key,
because calling, e.g., aes128_set_encrypt_key
and
aes128_invert_key
, is more efficient than calling
aes128_set_encrypt_key
and aes128_set_decrypt_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. src
and dst
may be equal, but they must not overlap
in any other way.
Analogous to the encryption functions above.
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, size_t length, const uint8_t *key) { struct sha256_ctx hash; uint8_t digest[SHA256_DIGEST_SIZE]; uint8_t buffer[0x200]; sha256_init(&hash); sha256_update(&hash, length, key); sha256_digest(&hash, SHA256_DIGEST_SIZE, digest); arcfour_set_key(ctx, SHA256_DIGEST_SIZE, digest); arcfour_crypt(ctx, sizeof(buffer), buffer, buffer); }
Nettle defines ARCFOUR in <nettle/arcfour.h>.
Minimum key size, 1.
Maximum key size, 256.
Default ARCFOUR key size, 16.
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_crypt
only 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.
The ARCTWO block-size, 8.
Default ARCTWO key size, 8.
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 = 0
has the same effect as ekb = 1024
.
arctwo_set_key(ctx, length, key)
is equivalent to
arctwo_set_key_ekb(ctx, length, key, 8*length)
, and
arctwo_set_key_gutmann(ctx, length, key)
is equivalent to
arctwo_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. src
and dst
may 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>.
The BLOWFISH block-size, 8.
Minimum BLOWFISH key size, 8.
Maximum BLOWFISH key size, 56.
Default BLOWFISH key size, 16.
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_encrypt
or blowfish_decrypt
with 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. src
and dst
may be equal, but they must not overlap
in any other way.
Analogous to blowfish_encrypt
Compute the bcrypt password hash.
The function will return 0
if the hash cannot be computed
due to invalid input.
The function will return 1
and store the computed hash
in the array pointed to by dst. The hash is computed based
on the chosen scheme, number of rounds log2rounds and
specified salt.
dst must point to a character array of at least
BLOWFISH_BCRYPT_HASH_SIZE
bytes.
key contains the plaintext password string of size lenkey.
scheme is of size lenscheme and contains either just the
chosen scheme (valid schemes
are: 2a
, 2b
, 2x
or 2y
), or
(the prefix of) an existing hashed password (typically $2b$10$...
).
log2rounds contains the log2 of the number of encryption rounds
that must be used to compute the hash. If it is -1
the value
will be extracted from scheme.
salt should point to an array of BLOWFISH_BCRYPT_BINSALT_SIZE
random bytes to be used to perturb the hash computation. If it is NULL
the salt will be extracted from scheme.
Sample code to generate a bcrypt hash:
char cleartxtpassword[] = "ExamplePassword"; char scheme[] = "2b"; uint8_t salt[BLOWFISH_BCRYPT_BINSALT_SIZE]; … /* Make sure that salt is filled with random bytes */ … char hashedresult[BLOWFISH_BCRYPT_HASH_SIZE]; int result = blowfish_bcrypt(hashedresult, sizeof(cleartxtpassword) - 1, cleartxtpassword, sizeof(scheme) - 1, scheme, 10, salt); if (result) printf("%s\n", hashedresult);
Verifies the bcrypt password hash against the supplied plaintext password.
The function will return 0
if the password does not match.
The function will return 1
if the password matches.
key contains the plaintext password string of size lenkey.
hashed contains the hashed string of size lenhashed to compare with.
Sample code to verify a bcrypt hash:
char cleartxtpassword[] = "ExamplePassword"; char existinghashed[] = "$2y$" /* Hash algorithm version */ "10" /* 2^10 hash rounds (strength) */ "$" /* separator */ "1b2lPgo4XumibnJGN3r3sO" /* base64 encoded 16-byte salt */ "u7wE7xNfYDKlAxZffJDCJdVfFTAyevu"; /* Hashedpart */ if (blowfish_bcrypt_verify(sizeof(cleartxtpassword) - 1, cleartxtpassword, sizeof(existinghashed) - 1, existinghashed)) printf("Password is correct."); else printf("Password is incorrect.");
Camellia is a block cipher developed by Mitsubishi and Nippon Telegraph and Telephone Corporation, described in RFC3713. It is recommended by some Japanese and European authorities as an alternative to AES, and it is one of the selected algorithms in the New European Schemes for Signatures, Integrity and Encryption (NESSIE) project. The algorithm is patented. The implementation in Nettle is derived from the implementation released by NTT under the GNU LGPL (v2.1 or later), and relies on the implicit patent license of the LGPL. There is also a statement of royalty-free licensing for Camellia at 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. The variants with 192 and 256 bit keys are identical, except
for the key setup. Nettle defines Camellia in
<nettle/camellia.h>, and there is one context struct for each key
size. (Earlier versions of Nettle used a single context struct,
struct camellia_ctx
, for all key sizes. This interface kept for
backwards compatibility).
Contexts structs. Actually, camellia192_ctx
is an alias for
camellia256_ctx
.
Alternative struct, for the old Camellia interface.
The CAMELLIA block-size, 16.
Default CAMELLIA key size, 32.
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 src
and dst
, it is
converted in place. These functions are 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. src
and
dst
may 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 key size of 128 bits. It is possible, but discouraged, to use the same algorithm with shorter keys. Nettle refers to the variant with variable key size as CAST-5. Keys for CAST-5 are zero padded to 128 bits, and with very short keys, less than 80 bits, encryption also uses fewer rounds than CAST128. Nettle defines cast128 in <nettle/cast128.h>.
The CAST128 block-size, 8.
The CAST128 key size, 16.
Minimum CAST5 key size, 5.
Maximum CAST5 key size, 16. With 16 octets key (128 bits), CAST-5 is the same as CAST-128.
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. src
and dst
may be equal, but they must not overlap
in any other way.
Analogous to cast128_encrypt
Initialize the cipher. This variant of the key setup takes the key size as argument. The same function is used for both encryption and decryption.
ChaCha is a variant of the stream cipher Salsa20, also designed by D. J. Bernstein. For more information on Salsa20, see below. Nettle defines ChaCha in <nettle/chacha.h>.
ChaCha key size, 32.
ChaCha block size, 64.
Size of the nonce, 8.
Size of the counter, 8.
Initialize the cipher. The same function is used for both encryption and
decryption. Before using the cipher,
you must also call chacha_set_nonce
, see below.
Sets the nonce. It is always of size CHACHA_NONCE_SIZE
, 8
octets. This function also initializes the block counter, setting it to
zero.
Sets the block counter. It is always of size CHACHA_COUNTER_SIZE
,
8 octets. This is rarely needed since chacha_set_nonce
initializes the block counter to zero. When it is still necessary, this
function must be called after chacha_set_nonce
.
Encrypts or decrypts the data of a message, using ChaCha. When a
message is encrypted using a sequence of calls to chacha_crypt
,
all but the last call must use a length that is a multiple of
CHACHA_BLOCK_SIZE
.
While the original paper uses 64-bit counter value, the variant defined in RFC 8439 uses 32-bit counter value. This variant is particularly useful for see ChaCha-Poly1305 AEAD construction, which supports 12-octet nonces.
Size of the nonce, 12.
Size of the counter, 4.
Sets the nonce. This is similar to the above chacha_set_nonce
,
but the input is always of size CHACHA_NONCE96_SIZE
, 12 octets.
Sets the block counter. This is similar to the above chacha_set_counter
,
but the input is always of size CHACHA_COUNTER32_SIZE
, 4 octets.
Encrypts or decrypts the data of a message, using ChaCha. This is similar to the
above chacha_crypt
, but it assumes the internal counter value is 32-bit
long and the nonce is 96-bit long.
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>.
The DES block-size, 8.
DES key size, 8.
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. src
and dst
may 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>.
The DES3 block-size is the same as DES_BLOCK_SIZE, 8.
DES key size, 24.
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. src
and dst
may 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. 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.
Recommended key size, 32.
Salsa20 block size, 64.
Size of the nonce, 8.
Initialize the cipher. The same function is used for both encryption and
decryption. salsa20_128_set_key
and salsa20_128_set_key
use a fix key size each, 16 and 32 octets, respectively. The function
salsa20_set_key
is provided for backwards compatibility, and the
length argument must be either 16 or 32. Before using the cipher,
you must also call salsa20_set_nonce
, see below.
Sets the nonce. It is always of size SALSA20_NONCE_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 of
SALSA20_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>.
The SERPENT block-size, 16.
Minimum SERPENT key size, 16.
Maximum SERPENT key size, 32.
Default SERPENT key size, 32.
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. src
and dst
may 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>.
The TWOFISH block-size, 16.
Minimum TWOFISH key size, 16.
Maximum TWOFISH key size, 32.
Default TWOFISH key size, 32.
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. src
and dst
may be equal, but they must not overlap
in any other way.
Analogous to twofish_encrypt
struct nettle_cipher
abstractionNettle includes a struct including information about some of the more regular cipher functions. It can be useful for applications that need a simple way to handle various algorithms. Nettle defines these structs in <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_func *
and nettle_cipher_func *
. The first
argument to these functions is a const void *
pointer to a context
struct, which is of size context_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.
Returns a NULL-terminated list of pointers to supported block ciphers. This list can be used to dynamically enumerate or search the supported algorithms.
A macro expanding to a call to nettle_get_ciphers. In earlier versions, this was not a macro but the actual array of pointers.
Next: Authenticated encryption, Previous: Cipher functions, Up: Reference [Contents][Index]
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 several other modes of operation: Cipher Block Chaining (CBC), Counter mode (CTR), Cipher Feedback (CFB and CFB8), XEX-based tweaked-codebook mode with ciphertext stealing (XTS) and a couple of AEAD modes (see Authenticated encryption). CBC is widely used, but there are a few subtle issues of information leakage, see, e.g., SSH CBC vulnerability. Today, CTR is usually preferred over CBC.
Modes like CBC, CTR, CFB and CFB8 provide no message authentication, and should always be used together with a MAC (see Keyed hash functions) or signature to authenticate the message.
• CBC: | ||
• CTR: | ||
• CFB and CFB8: | ||
• XTS: |
Next: CTR, Previous: Cipher modes, Up: Cipher modes [Contents][Index]
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 a large message can be processed by a sequence of
calls to cbc_encrypt
. The function f is of type
void f (void *ctx, size_t length, uint8_t dst,
const uint8_t *src)
,
and the cbc_encrypt
and cbc_decrypt
functions pass their
argument ctx on to f.
There are also some macros to help use these functions correctly.
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_encrypt
and cbc_decrypt
. The
first argument is a pointer to a context struct as defined by
CBC_CTX
, and the second argument is an encryption or decryption
function following Nettle’s conventions. The last three arguments define
the source and destination area for the operation.
These macros use some tricks to make the compiler display a warning if
the types of f and ctx don’t match, e.g. if you try to use
an struct aes_ctx
context with the des_encrypt
function.
Next: CFB and CFB8, Previous: CBC, Up: Cipher modes [Contents][Index]
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 by CTR_CTX
, and the second
argument is an encryption function following Nettle’s conventions. The
last three arguments define the source and destination area for the
operation.
Next: XTS, Previous: CTR, Up: Cipher modes [Contents][Index]
Cipher Feedback mode (CFB) and Cipher Feedback 8-bit mode (CFB8) being close relatives to both CBC mode and CTR mode borrow some characteristics from stream ciphers.
For CFB 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, IV
is
the initialization vector, then the n
plaintext blocks 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-1) = E_k(C_(n - 2)) XOR M_(n-1) C_n = E_k(C_(n - 1)) [1..m] XOR M_n
Cipher Feedback 8-bit mode (CFB8) transforms block cipher into a stream cipher. The message is encrypted byte after byte, not requiring any padding.
If E_k
is the encryption function of a block cipher, b
is
E_k
block size, IV
is the initialization vector, then the
n
plaintext bytes are transformed into n
ciphertext bytes
C_1
,… C_n
as follows:
I_1 = IV C_1 = E_k(I_1) [1..8] XOR M_1 I_2 = I_1 [9..b] << 8 | C_1 C_2 = E_k(I_2) [1..8] XOR M_2 … I_(n-1) = I_(n-2) [9..b] << 8 | C_(n-2) C_(n-1) = E_k(I_(n-1)) [1..8] XOR M_(n-1) I_n = I_(n-1) [9..b] << 8 | C_(n-1) C_n = E_k(I_n) [1..8] XOR M_n
Nettle’s includes functions for applying a block cipher in Cipher
Feedback (CFB) and Cipher Feedback 8-bit (CFB8)
modes. These functions uses void *
to pass cipher contexts around.
Applies the encryption or decryption function f in CFB
mode. The final ciphertext block processed is copied into iv
before returning, so that a large message can be processed by a sequence
of calls to cfb_encrypt
. Note that for CFB mode
internally uses encryption only function 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
cfb_encrypt
, all but the last call must use a length that
is a multiple of the block size.
Applies the encryption or decryption function f in CFB8
mode. The final IV block processed is copied into iv
before returning, so that a large message can be processed by a sequence of
calls to cfb8_encrypt
. Note that for CFB8 mode internally
uses encryption only function and hence f should always be the
encryption function for the underlying block cipher.
Like for CBC, there are also a couple of helper macros.
Expands to
{ context_type ctx; uint8_t iv[block_size]; }
First argument is a pointer to a context struct as defined by
CFB_CTX
, and the second is a pointer to an initialization vector
that is copied into that context.
A simpler way to invoke cfb_encrypt
. The first argument is a
pointer to a context struct as defined by CFB_CTX
, and the second
argument is an encryption function following Nettle’s conventions. The
last three arguments define the source and destination area for the
operation.
A simpler way to invoke cfb_decrypt
. The first argument is a
pointer to a context struct as defined by CFB_CTX
, and the second
argument is an encryption function following Nettle’s conventions. The
last three arguments define the source and destination area for the
operation.
Expands to
{ context_type ctx; uint8_t iv[block_size]; }
First argument is a pointer to a context struct as defined by
CFB8_CTX
, and the second is a pointer to an initialization vector
that is copied into that context.
A simpler way to invoke cfb8_encrypt
. The first argument is a
pointer to a context struct as defined by CFB8_CTX
, and the
second argument is an encryption function following Nettle’s
conventions. The last three arguments define the source and destination
area for the operation.
A simpler way to invoke cfb8_decrypt
. The first argument is a
pointer to a context struct as defined by CFB8_CTX
, and the
second argument is an encryption function following Nettle’s
conventions. The last three arguments define the source and destination
area for the operation.
Previous: CFB and CFB8, Up: Cipher modes [Contents][Index]
XEX-based tweaked-codebook mode with ciphertext stealing (XTS) is a block mode like (CBC) but tweaked to be able to encrypt partial blocks via a technique called ciphertext stealing, where the last complete block of ciphertext is split and part returned as the last block and part used as plaintext for the second to last block. This mode is principally used to encrypt data at rest where it is not possible to store additional metadata or blocks larger than the plain text. The most common usage is for disk encryption. Due to the fact that ciphertext expansion is not possible, data is not authenticated. This mode should not be used where authentication is critical.
The message is divided into n
blocks M_1
,… M_n
,
where M_n
is of size m
which may be smaller than the block size.
XTS always uses a fixed blocksize of 128 bit (16 bytes) length.
Unlike other modes, the key is double the size of that for the used cipher mode (for example 256bit for AES-128 and 512bit for AES-256).
XTS encryption mode operates given:
MUL a^j
here represents the multiplication, where j
is the power
of alpha, and the input value is converted into a 16 bytes array
a_0[k], k = 0,1,..,15
. The multiplication is calculated as
a_(j+1)[0] = (2(a_j[0] mod 128)) XOR (135 * floor(a_j[15]/128)
a_(j+1)[k] = (2(a_j[k] mod 128)) XOR (floor(a_j[k-1]/128), k = 1,2,..15
Note that this operation is practically a 1 bit left shift operation with carry
propagating from one byte to the next, and if the last bit shift results in a
carry the decimal value 135 is XORed into the first byte.
Key = K1 | K2
, where |
denotes string concatenation.
E_k1
is the encryption function of the block cipher using K1
as
the key, and E_k2
is the same encryption function using K2
IV
The n
plaintext blocks are transformed into n
ciphertext blocks
C_1
,… C_n
as follows.
For a plaintext length that is a perfect multiple of the XTS block size:
T_1 = E_k2(IV) C_1 = E_k1(P_1 XOR T_1) XOR T_1 … T_n = T_(n-1) MUL a C_n = E_k1(P_n XOR T_n) XOR T_n
For any other plaintext lengths:
T_1 = E_k2(IV) C_1 = E_k1(P_1 XOR T_1) XOR T_1 … T_(n-2) = T_(n-3) MUL a C_(n-2) = E_k1(P_(n-2) XOR T_(n-2)) XOR T_(n-2) T_(n-1) = T_(n-2) MUL a CC_(n-1) = E_k1(P_(n-1) XOR T_(n-1)) XOR T_(n-1) T_n = T_(n-1) MUL a PP = [1..m]Pn | [m+1..128]CC_(n-1) C_(n-1) = E_k1(PP XOR T_n) XOR T_n C_n = [1..m]CC_(n-1)
The two general functions to encrypt and decrypt using the XTS block cipher mode are the following:
Applies the encryption function encf or the decryption function decf in XTS mode. At least one block (16 bytes) worth of data must be available therefore specifying a length less than 16 bytes is illegal.
The functions encf decf are of type
void f (const void *ctx, size_t length, uint8_t *dst,
const uint8_t *src)
,
and the xts_encrypt_message
and xts_decrypt_message
functions pass their arguments enc_ctx, twk_ctx and dec_ctx
to the functions encf, decf as ctx.
The AES XTS functions provide an API for using the XTS mode with the AES block ciphers. The parameters all have the same meaning as the general interface, except that the enc_ctx, dec_ctx, twk_ctx, encf and decf are replaced with an AES context structure called ctx, and a appropriate set-key function must be called before using any of the encryption or decryption functions in this interface.
Holds state corresponding to the AES-128 block cipher.
Holds state corresponding to the AES-256 block cipher.
Initializes the encryption or decryption key for the AES block cipher. The length of the key must be double the size of the key for the corresponding cipher (256 bits for AES-128 and 512 bits for AES-256). One of these functions must be called before any of the other functions.
These are identical to xts_encrypt_message
and
xts_decrypt_message
, except that enc_ctx, dec_ctx,
twk_ctx, encf and decf are replaced by the ctx context
structure.
Next: Keyed hash functions, Previous: Cipher modes, Up: Reference [Contents][Index]
Since there are some subtle design choices to be made when combining a block cipher mode with out authentication with a MAC. In recent years, several constructions that combine encryption and authentication have been defined. These constructions typically also have an additional input, the “associated data”, which is authenticated but not included with the message. A simple example is an implicit message number which is available at both sender and receiver, and which needs authentication in order to detect deletions or replay of messages. This family of building blocks are therefore called AEAD, Authenticated encryption with associated data.
The aim is to provide building blocks that it is easier for designers of protocols and applications to use correctly. There is also some potential for improved performance, if encryption and authentication can be done in a single step, although that potential is not realized for the constructions currently supported by Nettle.
For encryption, the inputs are:
The outputs are:
Decryption works the same, but with cleartext and ciphertext interchanged. All currently supported AEAD algorithms always use the encryption function of the underlying block cipher, for both encryption and decryption.
Usually, the authentication tag should be appended at the end of the ciphertext, producing an encrypted message which is slightly longer than the cleartext. However, Nettle’s low level AEAD functions produce the authentication tag as a separate output for both encryption and decryption.
Both associated data and the message data (cleartext or ciphertext) can be processed incrementally. In general, all associated data must be processed before the message data, and all calls but the last one must use a length that is a multiple of the block size, although some AEAD may implement more liberal conventions. The CCM mode is a bit special in that it requires the message lengths up front, other AEAD constructions don’t have this restriction.
The supported AEAD constructions are Galois/Counter mode (GCM), EAX, ChaCha-Poly1305, and Counter with CBC-MAC (CCM). There are some weaknesses in GCM authentication, see http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf. CCM and EAX use the same building blocks, but the EAX design is cleaner and avoids a couple of inconveniences of CCM. Therefore, EAX seems like a good conservative choice. The more recent ChaCha-Poly1305 may also be an attractive but more adventurous alternative, in particular if performance is important.
• EAX: | ||
• GCM: | ||
• CCM: | ||
• ChaCha-Poly1305: | ||
• SIV-CMAC: | ||
• nettle_aead abstraction: |
Next: GCM, Previous: Authenticated encryption, Up: Authenticated encryption [Contents][Index]
The EAX mode is an AEAD mode which combines CTR mode encryption, See CTR, with a message authentication based on CBC, See CBC. The implementation in Nettle is restricted to ciphers with a block size of 128 bits (16 octets). EAX was defined as a reaction to the CCM mode, See CCM, which uses the same primitives but has some undesirable and inelegant properties.
EAX supports arbitrary nonce size; it’s even possible to use an empty nonce in case only a single message is encrypted for each key.
Nettle’s support for EAX consists of a low-level general interface, some convenience macros, and specific functions for EAX using AES-128 as the underlying cipher. These interfaces are defined in <nettle/eax.h>
EAX state which depends only on the key, but not on the nonce or the message.
Holds state corresponding to a particular message.
EAX’s block size, 16.
Size of the EAX digest, also 16.
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 for processing a new message, using the given nonce.
Process associated data for authentication. All but the last call for each message must use a length that is a multiple of the block size. Unlike many other AEAD constructions, for EAX it’s not necessary to complete the processing of all associated data before encrypting or decrypting the message data.
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. If length is
smaller than EAX_DIGEST_SIZE
, only the first length octets
of the digest are written.
The following macros are defined.
This defines an all-in-one context struct, including the context of the underlying cipher and all EAX state. It expands to
{ struct eax_key key; struct eax_ctx eax; context_type cipher; }
For all these macros, ctx, is a context struct as defined by
EAX_CTX
, and encrypt is the encryption function of the
underlying cipher.
set_key is the function for setting the encryption key for the underlying cipher, and key is the key.
Sets the nonce to be used for the message.
Process associated data for authentication.
Process message data for encryption or decryption.
Extract the authentication tag for the message.
The following functions implement EAX using AES-128 as the underlying cipher.
The context struct, defined using EAX_CTX
.
Initializes ctx using the given key.
Initializes the per-message state, using the given nonce.
Process associated data for authentication. 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. If length is
smaller than EAX_DIGEST_SIZE
, only the first length octets
of the digest are written.
Next: CCM, Previous: EAX, Up: Authenticated encryption [Contents][Index]
Galois counter mode is an AEAD constructions combining counter mode with message authentication based on universal hashing. The main objective of the design is to provide high performance for hardware implementations, where other popular MAC algorithms (see Keyed hash functions) become a bottleneck for high-speed hardware implementations. It was proposed by David A. McGrew and John Viega in 2005, and recommended by NIST in 2007, NIST Special Publication 800-38D. It is constructed on top of a block cipher which must have a block size of 128 bits.
The authentication in GCM has some known weaknesses, see http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf. In particular, don’t use GCM with short authentication tags.
Nettle’s support for GCM consists of a low-level general interface, some convenience macros, and specific functions for GCM using AES or Camellia as the underlying cipher. These interfaces are defined in <nettle/gcm.h>
Message independent hash sub-key, and related tables.
Holds state corresponding to a particular message.
GCM’s block size, 16.
Size of the GCM digest, also 16.
Recommended size of the IV, 12. Arbitrary sizes are allowed.
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_encrypt
or gcm_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. It’s strongly recommended
that length is GCM_DIGEST_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
{ struct gcm_key key; struct gcm_ctx gcm; context_type cipher; }
Example use:
struct gcm_aes128_ctx GCM_CTX(struct aes128_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.
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 by GCM_CTX
Simpler way to call gcm_encrypt
, gcm_decrypt
or
gcm_digest
. First argument is a context struct as defined by
GCM_CTX
. Second argument, encrypt, is the encryption
function of the underlying cipher.
The following functions implement the common case of GCM using
AES as the underlying cipher. The variants with a specific
AES flavor are recommended, while the fucntinos using
struct gcm_aes_ctx
are kept for compatibility with older versiosn
of Nettle.
Context structs, defined using GCM_CTX
.
Alternative context struct, using the old AES interface.
Initializes ctx using the given key.
Corresponding function, using the old AES interface. 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_encrypt
or gcm_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. It’s strongly recommended
that length is GCM_DIGEST_SIZE
, but if you provide a smaller
value, only the first length octets of the digest are written.
The following functions implement the case of GCM using Camellia as the underlying cipher.
Context structs, defined using GCM_CTX
.
Initializes ctx using the given key.
Initializes the per-message state, using the given IV.
Provides associated data to be authenticated. If used, must be called
before gcm_camellia_encrypt
or gcm_camellia_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. It’s strongly recommended
that length is GCM_DIGEST_SIZE
, but if you provide a smaller
value, only the first length octets of the digest are written.
Next: ChaCha-Poly1305, Previous: GCM, Up: Authenticated encryption [Contents][Index]
CCM mode is a combination of counter mode with message authentication based on cipher block chaining, the same building blocks as EAX, see EAX. It is constructed on top of a block cipher which must have a block size of 128 bits. CCM mode is recommended by NIST in NIST Special Publication 800-38C. Nettle’s support for CCM consists of a low-level general interface, a message encryption and authentication interface, and specific functions for CCM using AES as the underlying block cipher. These interfaces are defined in <nettle/ccm.h>.
In CCM, the length of the message must be known before processing. The maximum message size depends on the size of the nonce, since the message size is encoded in a field which must fit in a single block, together with the nonce and a flag byte. E.g., with a nonce size of 12 octets, there are three octets left for encoding the message length, the maximum message length is 2^24 - 1 octets.
CCM mode encryption operates as follows:
B_0 = flags | nonce | mlength
B = L(adata) | adata | padding | plaintext | padding
with
padding
being the shortest string of zero bytes such that the
length of the string is a multiple of the block size, and
L(adata)
is an encoding of the length of adata
.
B
is separated into blocks B_1
...
B_n
T
is calculated as
T=0, for i=0 to n, do T = E_k(B_i XOR T)
IC = flags | nonce | padding
, where padding
is the
shortest string of zero bytes such that IC
is exactly one block
in length.
MAC = E_k(IC) XOR T
IC+1
.
CCM mode decryption operates similarly, except that the ciphertext and MAC are first decrypted using CTR mode to retrieve the plaintext and authentication tag. The authentication tag can then be recalculated from the authenticated data and plaintext, and compared to the value in the message to check for authenticity.
For all of the functions in the CCM interface, cipher is the context struct for the underlying cipher and f is the encryption function. The cipher’s encryption key must be set before calling any of the CCM functions. The cipher’s decryption function and key are never used.
Holds state corresponding to a particular message.
CCM’s block size, 16.
Size of the CCM digest, 16.
The the minimum and maximum sizes for an CCM nonce, 7 and 14, respectively.
The largest allowed plaintext length, when using CCM with a nonce of the given size.
Initializes ctx using the given nonce and the sizes of the authenticated data, message, and MAC to be processed.
Provides associated data to be authenticated. Must be called after
ccm_set_nonce
, and before ccm_encrypt
, ccm_decrypt
, or
ccm_digest
.
Encrypts or decrypts the message data. Must be called after
ccm_set_nonce
and before ccm_digest
. 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 the taglen parameter supplied to ccm_set_nonce
,
but if you provide a smaller value, only the first length octets
of the digest are written.
To encrypt a message using the general CCM interface, set the
message nonce and length using ccm_set_nonce
and then call
ccm_update
to generate the digest of any authenticated data.
After all of the authenticated data has been digested use
ccm_encrypt
to encrypt the plaintext. Finally, use
ccm_digest
to return the encrypted MAC.
To decrypt a message, use ccm_set_nonce
and ccm_update
the
same as you would for encryption, and then call ccm_decrypt
to
decrypt the ciphertext. After decrypting the ciphertext
ccm_digest
will return the encrypted MAC which should
be identical to the MAC in the received message.
The CCM message fuctions provides a simple interface that will perform authentication and message encryption in a single function call. The length of the cleartext is given by mlength and the length of the ciphertext is given by clength, always exactly tlength bytes longer than the corresponding plaintext. The length argument passed to a function is always the size for the result, clength for the encryption functions, and mlength for the decryption functions.
Computes the message digest from the adata and src parameters, encrypts the plaintext from src, appends the encrypted MAC to ciphertext and outputs it to dst.
Decrypts the ciphertext from src, outputs the plaintext to dst, recalculates the MAC from adata and the plaintext, and compares it to the final tlength bytes of src. If the values of the received and calculated MACs are equal, this will return 1 indicating a valid and authenticated message. Otherwise, this function will return zero.
The AES CCM functions provide an API for using CCM mode with the AES block ciphers. The parameters all have the same meaning as the general and message interfaces, except that the cipher, f, and ctx parameters are replaced with an AES context structure, and a set-key function must be called before using any of the other functions in this interface.
Holds state corresponding to a particular message encrypted using the AES-128 block cipher.
Holds state corresponding to a particular message encrypted using the AES-192 block cipher.
Holds state corresponding to a particular message encrypted using the AES-256 block cipher.
Initializes the encryption key for the AES block cipher. One of these functions must be called before any of the other functions in the AES CCM interface.
These are identical to ccm_set_nonce
, except that cipher,
f, and ctx are replaced with a context structure.
These are identical to ccm_set_update
, except that cipher,
f, and ctx are replaced with a context structure.
These are identical to ccm_set_encrypt
and ccm_set_decrypt
, except
that cipher, f, and ctx are replaced with a context structure.
These are identical to ccm_set_digest
, except that cipher,
f, and ctx are replaced with a context structure.
These are identical to ccm_encrypt_message
and ccm_decrypt_message
except that cipher and f are replaced with a context structure.
Next: SIV-CMAC, Previous: CCM, Up: Authenticated encryption [Contents][Index]
ChaCha-Poly1305 is a combination of the ChaCha stream cipher and the poly1305 message authentication code (see Poly1305). It originates from the NaCl cryptographic library by D. J. Bernstein et al, which defines a similar construction but with Salsa20 instead of ChaCha.
Nettle’s implementation of ChaCha-Poly1305 follows RFC 8439, where the ChaCha cipher is initialized with a 12-byte nonce and a 4-byte block counter. This allows up to 256 gigabytes of data to be encrypted using the same key and nonce.
For ChaCha-Poly1305, the ChaCha cipher is initialized with a key, of 256 bits, and a per-message nonce. The first block of the key stream (counter all zero) is set aside for the authentication subkeys. Of this 64-octet block, the first 16 octets specify the poly1305 evaluation point, and the next 16 bytes specify the value to add in for the final digest. The final 32 bytes of this block are unused. Note that unlike poly1305-aes, the evaluation point depends on the nonce. This is preferable, because it leaks less information in case the attacker for some reason is lucky enough to forge a valid authentication tag, and observe (from the receiver’s behaviour) that the forgery succeeded.
The ChaCha key stream, starting with counter value 1, is then used to encrypt the message. For authentication, poly1305 is applied to the concatenation of the associated data, the cryptotext, and the lengths of the associated data and the message, each a 64-bit number (eight octets, little-endian). Nettle defines ChaCha-Poly1305 in <nettle/chacha-poly1305.h>.
Same as the ChaCha block size, 64.
ChaCha-Poly1305 key size, 32.
ChaCha-Poly1305 nonce size, 12.
Digest size, 16.
Initializes ctx using the given key. Before using the context, you
must also call chacha_poly1305_set_nonce
, see below.
Initializes the per-message state, using the given nonce.
Process associated data for authentication.
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. If length is
smaller than CHACHA_POLY1305_DIGEST_SIZE
, only the first
length octets of the digest are written.
Next: nettle_aead abstraction, Previous: ChaCha-Poly1305, Up: Authenticated encryption [Contents][Index]
SIV-CMAC mode is a combination of counter mode with message authentication based on CMAC. Unlike other counter AEAD modes, it provides protection against accidental nonce misuse, making it a good choice for stateless-servers that cannot ensure nonce uniqueness. It is constructed on top of a block cipher which must have a block size of 128 bits. Nettle’s support for SIV-CMAC consists of a message encryption and authentication interface, for SIV-CMAC using AES as the underlying block cipher. When a nonce is re-used with this mode, message authenticity is retained however an attacker can determine whether the same plaintext was protected with the two messages sharing the nonce. These interfaces are defined in <nettle/siv-cmac.h>.
Unlike other AEAD mode in SIV-CMAC the initialization vector serves as the tag. That means that in the generated ciphertext the tag precedes the ciphertext.
Note also, that the SIV-CMAC algorithm, as specified in
RFC 5297, introduces the notion of authenticated data which
consist of multiple components. For example with SIV-CMAC the
authentication tag of data X
followed by Y
, is different
than the concatenated data X || Y
. The interfaces described below
follow the AEAD paradigm and do not allow access to this
feature and also require the use of a non-empty nonce. In the
terminology of the RFC, the input to the S2V function is always a vector
of three elements, where S1 is the authenticated data, S2 is the nonce,
and S3 is the plaintext.
SIV-CMAC’s block size, 16.
Size of the SIV-CMAC digest or initialization vector, 16.
The the minimum size for an SIV-CMAC nonce, 1.
The AES SIV-CMAC functions provide an API for using SIV-CMAC mode with the AES block ciphers. The parameters all have the same meaning as the general and message interfaces, except that the cipher, f, and ctx parameters are replaced with an AES context structure, and a set-key function must be called before using any of the other functions in this interface.
Holds state corresponding to a particular message encrypted using the AES-128 block cipher.
Holds state corresponding to a particular message encrypted using the AES-256 block cipher.
Initializes the encryption key for the AES block cipher. One of these functions must be called before any of the other functions in the AES SIV-CMAC interface.
Computes the message digest from the adata and src
parameters, encrypts the plaintext from src, prepends the
initialization vector to the ciphertext and outputs it to dst.
The clength variable must be equal to the length of src
plus SIV_DIGEST_SIZE
.
Decrypts the ciphertext from src, outputs the plaintext to dst, recalculates the initialization vector from adata and the plaintext. If the values of the received and calculated initialization vector are equal, this will return 1 indicating a valid and authenticated message. Otherwise, this function will return zero.
Previous: ChaCha-Poly1305, Up: Authenticated encryption [Contents][Index]
struct nettle_aead
abstractionNettle includes a struct including information about the supported hash functions. It is defined in <nettle/nettle-meta.h>.
struct nettle_aead
name context_size block_size key_size nonce_size digest_size set_encrypt_key set_decrypt_key set_nonce update encrypt decrypt digestThe last seven attributes are function pointers.
These are most of the AEAD constructions that Nettle
implements. Note that CCM is missing; it requirement that the
message size is specified in advance makes it incompatible with the
nettle_aead
abstraction.
Nettle also exports a list of all these constructions.
Returns a NULL-terminated list of pointers to supported algorithms.This list can be used to dynamically enumerate or search the supported algorithms.
A macro expanding to a call to nettle_get_aeads. In earlier versions, this was not a macro but the actual array of pointers.
Next: Key derivation functions, Previous: Authenticated encryption, Up: Reference [Contents][Index]
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.
• HMAC: | ||
• UMAC: | ||
• CMAC: | ||
• Poly1305: |
Next: UMAC, Previous: Keyed hash functions, Up: Keyed hash functions [Contents][Index]
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_o
and
k_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 to
H->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.
Expands to
{ type outer; type inner; type state; }
It can be used to define a HMAC context struct, either directly,
struct HMAC_CTX(struct md5_ctx) ctx;
or to give it a struct tag,
struct hmac_md5_ctx HMAC_CTX (struct md5_ctx);
ctx is a pointer to a context struct as defined by
HMAC_CTX
, H is a pointer to a const struct
nettle_hash
describing the underlying hash function (so it must match
the type of the components of ctx). The last two arguments specify
the secret key.
ctx is a pointer to a context struct as defined by
HMAC_CTX
, H is a pointer to a const struct
nettle_hash
describing the underlying hash function. The last two
arguments specify where the digest is written.
Note that there is no HMAC_UPDATE
macro; simply call
hmac_update
function directly, or the update function of the
underlying hash function.
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.
Next: Poly1305, Previous: HMAC, Up: Keyed hash functions [Contents][Index]
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 automatically for each message, so explicitly setting the nonce for each message is optional. This auto-increment uses network byte order and it takes the length of the nonce into account. E.g., if the initial nonce is “abc” (3 octets), this value is zero-padded to 16 octets for the first message. For the next message, the nonce is incremented to “abd”, and this incremented value is zero-padded to 16 octets.
UMAC is defined in four variants, for different output sizes:
32 bits (4 octets), 64 bits (8 octets), 96 bits (12 octets) and 128 bits
(16 octets), corresponding to different trade-offs between speed and
security. Using a shorter output size sometimes (but not always!) gives
the same result as using a longer output size and truncating the result.
So it is important to use the right variant. For consistency with other
hash and 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 quite 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.
The UMAC key size, 16.
The the minimum and maximum sizes for an UMAC nonce, 1 and 16, respectively.
The size of an UMAC32 digest, 4.
The size of an UMAC64 digest, 8.
The size of an UMAC96 digest, 12.
The size of an UMAC128 digest, 16.
The internal block size of UMAC.
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 _update
call 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_nonce
function explicitly for each message.
Previous: UMAC, Up: Keyed hash functions [Contents][Index]
CMAC is a message authentication code based on CBC encryption mode. It is suitable for systems where block ciphers are preferrable and perform better than hash functions. CMAC-128 is specified in RFC4493. The block size is always 128 bits (16 octets). CMAC-64 is specified by NIST Special Publication 800-38B. The block size is always 64 bits (8 octets).
Nettle provides helper functions for CMAC-128 with the AES block cipher and for CMAC-64 with the Tripple-DES block cipher.
Nettle defines CMAC in <nettle/cmac.h>.
The size of an CMAC-128 digest, 16.
This function initializes the CMAC context struct for AES-128.
This function is 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. This function resets the context for processing of a new message with the same key.
This function initializes the CMAC context struct for AES-256.
This function is 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. This function resets the context for processing of a new message with the same key.
The size of an CMAC-64 digest, 8.
This function initializes the CMAC context struct for Tripple-DES.
This function is 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. This function resets the context for processing of a new message with the same key.
Previous: CMAC, Up: Keyed hash functions [Contents][Index]
Poly1305-AES is a message authentication code designed by D. J. Bernstein. It treats the message as a polynomial modulo the prime number 2^130 - 5.
The key, 256 bits, consists of two parts, where the first half is an
AES-128 key, and the second half specifies the point where the
polynomial is evaluated. Of the latter half, 22 bits are set to zero, to
enable high-performance implementation, leaving 106 bits for specifying
an evaluation point r
. For each message, one must also provide a
128-bit nonce. The nonce is encrypted using the AES key, and
that’s the only thing AES is used for.
The message is split into 128-bit chunks (with final chunk possibly
being shorter), each read as a little-endian integer. Each chunk has a
one-bit appended at the high end. The resulting integers are treated as
polynomial coefficients modulo 2^130 - 5, and the polynomial is
evaluated at the point r
. Finally, this value is reduced modulo
2^128, and added (also modulo 2^128) to the encrypted
nonce, to produce an 128-bit authenticator for the message. See
http://cr.yp.to/mac/poly1305-20050329.pdf for further details.
Clearly, variants using a different cipher than AES could be defined. Another variant is the ChaCha-Poly1305 AEAD construction (see ChaCha-Poly1305). Nettle defines Poly1305-AES in nettle/poly1305.h.
Key size, 32 octets.
Size of the digest or “authenticator”, 16 octets.
Nonce size, 16 octets.
The poly1305-aes context struct.
Initialize the context struct. Also sets the nonce to zero.
Sets the nonce. Calling this function is optional, since the nonce is incremented automatically for each message.
Process more data.
Extracts the digest. If length is smaller than
POLY1305_AES_DIGEST_SIZE
, only the first length octets are
written. Also increments the nonce, and prepares the context for
processing a new message.
Next: Public-key algorithms, Previous: Keyed hash functions, Up: Reference [Contents][Index]
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.
HKDF is a key derivation function used as a building block of higher-level protocols like TLS 1.3. It is a derivation function based on HMAC described in RFC 5869, and is split into two logical modules, called ’extract’ and ’expand’. The extract module takes an initial secret and a random salt to "extract" a fixed-length pseudorandom key (PRK). The second stage takes as input the previous PRK and some informational data (e.g., text) and expands them into multiple keys.
Nettle’s HKDF functions are defined in
<nettle/hkdf.h>. There are two abstract functions for the extract
and expand operations that operate on any HMAC implemented via the nettle_hash_update_func
,
and nettle_hash_digest_func
interfaces.
Extract a Pseudorandom Key (PRK) from a secret and a salt according to HKDF. The HMAC must have been initialized, with its key being the salt for the Extract operation. This function will call the 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 secret secret of length secret_length. The output length is fixed to digest_size octets, thus the output buffer dst must have room for at least digest_size octets.
Expand a Pseudorandom Key (PRK) to an arbitrary size according to HKDF. The HMAC must have been initialized, with its key being the PRK from the Extract operation. This function will call the 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 info info of length info_length, and the desired derived output length length. The output buffer is dst which must have room for at least length octets.
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_func
and nettle_hash_digest_func
respectively) 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.
Next: Randomness, Previous: Key derivation functions, Up: Reference [Contents][Index]
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”.
• RSA: | The RSA public key algorithm. | |
• DSA: | The DSA digital signature algorithm. | |
• Elliptic curves: | Elliptic curves and ECDSA |
Next: DSA, Previous: Public-key algorithms, Up: Public-key algorithms [Contents][Index]
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 2000
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 2000 bits,
p
and q
are about 1000 bits each). One also computes the
number phi = (p-1)(q-1)
, in mathematical speak, phi
is the
order of the multiplicative group of integers modulo n.
Next, e
is chosen. It must have no factors in common with phi
(in
particular, it must be odd), but can otherwise be chosen more or less
randomly. e = 65537
is a popular choice, because it makes raising
to the e
’th power particularly efficient, and being prime, it
usually has no factors common with phi
.
Finally, a number d
, d < n
is computed such that e d
mod phi = 1
. It can be shown that such a number exists (this is why
e
and phi
must have no common factors), and that for all x,
(x^e)^d mod n = x^(ed) mod n = (x^d)^e mod n = x
Using Euclid’s algorithm, d
can be computed quite easily from
phi
and e
. But it is still hard to get d
without
knowing phi
, which depends on the factorization of n
.
So d
is the trapdoor, if we know d
and y = F(x)
, we can
recover x as y^d mod n
. d
is also the private half of
the RSA key-pair.
The most common signature operation for RSA is defined in
PKCS#1, a specification by RSA Laboratories. The message to be
signed is first hashed using a cryptographic hash function, e.g.
MD5 or SHA1. Next, some padding, the ASN.1
“Algorithm Identifier” for the hash function, and the message digest
itself, are concatenated and converted to a number x
. The
signature is computed from x
and the private key as s = x^d
mod n
^{1}. The signature, s
is a
number of about the same size of n
, and it usually encoded as a
sequence of octets, most significant octet first.
The verification operation is straight-forward, x
is computed
from the message in the same way as above. Then s^e mod n
is
computed, the operation returns true if and only if the result equals
x
.
The RSA algorithm can also be used for encryption. RSA encryption uses
the public key (n,e)
to compute the ciphertext m^e mod n
.
The PKCS#1 padding scheme will use at least 8 random and non-zero
octets, using m of the form [00 02 padding 00 plaintext]
.
It is required that m < n
, and therefor the plaintext must be
smaller than the octet size of the modulo n
, with some margin.
To decrypt the message, one needs the private key to compute m =
c^e mod n
followed by checking and removing the padding.
Nettle represents RSA keys using two structures that contain
large numbers (of type mpz_t
).
size
is the size, in octets, of the modulo, and is used internally.
n
and e
is the public key.
size
is the size, in octets, of the modulo, and is used internally.
d
is the secret exponent, but it is not actually used when
signing. Instead, the factors p
and q
, and the parameters
a
, b
and c
are used. They are computed from p
,
q
and e
such that a e mod (p - 1) = 1, b e mod (q -
1) = 1, c q mod p = 1
.
Before use, these structs must be initialized by calling one of
Calls mpz_init
on all numbers in the key struct.
and when finished with them, the space for the numbers must be deallocated by calling one of
Calls mpz_clear
on all numbers in the key struct.
In general, Nettle’s RSA functions deviates from Nettle’s “no memory allocation”-policy. Space for all the numbers, both in the key structs above, and temporaries, are allocated dynamically. For information on how to customize allocation, see See GMP Allocation in GMP Manual.
When you have assigned values to the attributes of a key, you must call
Computes the octet size of the key (stored in the size
attribute,
and may also do other basic sanity checks. Returns one if successful, or
zero if the key can’t be used, for instance if the modulo is smaller
than the minimum size needed for RSA operations specified by PKCS#1.
For each operation using the private key, there are two variants, e.g.,
rsa_sha256_sign
and rsa_sha256_sign_tr
. The former
function is older, and it should be avoided, because it provides no
defenses against side-channel attacks. The latter function use
randomized RSA blinding, which defends against timing attacks
using chosen-ciphertext, and it also checks the correctness of the
private key computation using the public key, which defends against
software or hardware errors which could leak the private key.
Before signing or verifying a message, you first hash it with the appropriate hash function. You pass the hash function’s context struct to the 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.
Creating an RSA signature is done with one of 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. The random_ctx and random pointers
are used to generate the RSA blinding. Returns one on success,
or zero on failure. Signing fails if an error in the computation was
detected, or if the key is too small for the given hash size, e.g., it’s
not possible to create a signature using SHA512 and a 512-bit
RSA key.
Creates a signature from the given hash digest. digest should
point to a digest of size MD5_DIGEST_SIZE
,
SHA1_DIGEST_SIZE
, SHA256_DIGEST_SIZE
, or
SHA512_DIGEST_SIZE
respectively. The signature is stored in
signature (which must have been mpz_init
:ed earlier).
Returns one on success, or zero on failure.
Similar to the above _sign_digest_tr
functions, but the input is not the
plain hash digest, but a PKCS#1 “DigestInfo”, an ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
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; otherwise analoguous to
the above signing functions. digest should point to a digest of
size MD5_DIGEST_SIZE
, SHA1_DIGEST_SIZE
,
SHA256_DIGEST_SIZE
, or SHA512_DIGEST_SIZE
, respectively.
The signature is stored in signature (which must have been
mpz_init
:ed earlier). Returns one on success, or zero on failure.
Similar to the above _sign_digest functions, but the input is not the plain hash digest, but a PKCS#1 “DigestInfo”, an ASN.1 DER-encoding of the digest together with an object identifier for the used hash algorithm.
Verifying an RSA signature is done with one of the following functions:
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
, SHA256_DIGEST_SIZE
, or
SHA512_DIGEST_SIZE
respectively.
Similar to the above _verify_digest functions, but the input is not the plain hash digest, but a PKCS#1 “DigestInfo”, and ASN.1 DER-encoding of the digest together with an object identifier for the used hash algorithm.
While the above functions for the RSA signature operations use the PKCS#1 padding scheme, Nettle also provides the variants based on the PSS padding scheme, specified in RFC 3447. These variants take advantage of a randomly choosen salt value, which could enhance the security by causing output to be different for equivalent inputs. However, assuming the same security level as inverting the RSA algorithm, a longer salt value does not always mean a better security http://www.iacr.org/archive/eurocrypt2002/23320268/coron.pdf. The typical choices of the length are between 0 and the digest size of the underlying hash function.
Creating an RSA signature with the PSS padding scheme is done with one of the following functions:
Creates a signature using the PSS padding scheme. salt should
point to a salt string of size salt_length. digest should
point to a digest of size SHA256_DIGEST_SIZE
,
SHA384_DIGEST_SIZE
, or SHA512_DIGEST_SIZE
respectively. The
signature is stored in signature (which must have been
mpz_init
:ed earlier).
Returns one on success, or zero on failure.
Verifying an RSA signature with the PSS padding scheme is done with one of the following functions:
Returns 1 if the signature is valid, or 0 if it isn’t. digest
should point to a digest of size SHA256_DIGEST_SIZE
,
SHA384_DIGEST_SIZE
, or SHA512_DIGEST_SIZE
respectively.
The following function is used to encrypt a clear text message using RSA.
Returns 1 on success, 0 on failure. If the message is too long then this will lead to a failure.
The following function is used to decrypt a cipher text message using RSA.
Returns 1 on success, 0 on failure. Causes of failure include decryption failing or the resulting message being to large. The message buffer pointed to by cleartext must be of size *length. After decryption, *length will be updated with the size of the message.
There is also a timing resistant version of decryption that utilizes randomized RSA blinding.
Returns 1 on success, 0 on failure.
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
. Returns one on success, or zero if a failure in
the computation was detected.
Computes x = m^d
.
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_prepare
or
rsa_private_key_prepare
after key generation.
random_ctx and random is a randomness generator.
random(random_ctx, length, dst)
should generate length
random octets and store them at dst
. For advice, see
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 and
pub->e
is an even number.
Next: Elliptic curves, Previous: RSA, Up: Public-key algorithms [Contents][Index]
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 in GMP Manual. Nettle’s DSA interface is defined
in <nettle/dsa.h>.
A DSA group is represented using the following struct.
Parameters of the DSA group.
Calls mpz_init
on all numbers in the struct.
Calls mpz_clear
on all numbers in the struct.
Generates parameters of a new group. The params struct should be initialized before you call this function.
random_ctx and random is a randomness generator.
random(random_ctx, length, dst)
should generate length
random octets and store them at dst
. For advice, see
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 p
and
q
. To generate keys that conform to the original DSA
standard, you must use q_bits = 160
and select p_bits of
the form p_bits = 512 + l*64
, for 0 <= l <= 8
, where the
smaller sizes are no longer recommended, so you should most likely stick
to p_bits = 1024
. Non-standard sizes are possible, in particular
p_bits
larger 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. To generate DSA keys for use with
SHA256, use q_bits = 256
and, e.g., p_bits =
2048
.
Returns one on success, and zero on failure. The function will fail if q_bits is too small, or too close to p_bits.
Signatures are represented using the structure below.
You must call dsa_signature_init
before creating or using a
signature, and call dsa_signature_clear
when you are finished
with it.
Keys are represented as bignums, of type mpz_t
. A public key
represents a group element, and is of the same size as p
, while a
private key is an exponent, of the same size as q
.
Creates a signature from the given hash digest, using the private key
x. random_ctx and random is a randomness generator.
random(random_ctx, length, dst)
should generate length
random octets and store them at dst
. For advice, see
See Randomness. Returns one on success, or zero on failure. Signing
can fail only if the key is invalid, so that inversion modulo q
fails.
Verifies a signature, using the public key y. Returns 1 if the signature is valid, otherwise 0.
To generate a keypair, first generate a DSA group using
dsa_generate_params
. A keypair in this group is then created
using
Generates a new keypair, using the group params. The public key is
stored in pub, and the private key in key. Both variables
must be initialized using mpz_init
before this call.
random_ctx and random is a randomness generator.
random(random_ctx, length, dst)
should generate length
random octets and store them at dst
. For advice, see
See Randomness.
Versions before nettle-3.0 used a different interface for DSA
signatures, where the group parameters and the public key was packed
together as struct dsa_public_key
. Most of this interface is kept
for backwards compatibility, and declared in nettle/dsa-compat.h.
Below is the old documentation. The old and new interface use distinct
names and don’t confict, with one exception: The key generation
function. The nettle/dsa-compat.h redefines
dsa_generate_keypair
as an alias for
dsa_compat_generate_keypair
, compatible with the old interface
and documented below.
The old 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
.
The public parameters described above.
The private key x
.
Before use, these structs must be initialized by calling one of
Calls mpz_init
on all numbers in the key struct.
When finished with them, the space for the numbers must be deallocated by calling one of
Calls mpz_clear
on all numbers in the key struct.
Signatures are represented using struct dsa_signature
, described
earlier.
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 generate length
random octets and store them at dst
. 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 generate length
random octets and store them at dst
. 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 p
and
q
. See dsa_generate_keypair
for details.
Previous: DSA, Up: Public-key algorithms [Contents][Index]
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
. It also supports
curve25519, which uses a different form of curve. Supported curves are
declared in <nettle/ecc-curve.h>, e.g., call
nettle_get_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 the SECP 256R1 curve.
• Side-channel silence: | ||
• ECDSA: | ||
• GOSTDSA: | ||
• Curve 25519 and Curve 448: |
Next: ECDSA, Up: Elliptic curves [Contents][Index]
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.
Next: GOSTDSA, Previous: Side-channel silence, Up: Elliptic curves [Contents][Index]
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.
Deallocate storage.
Check that the given coordinates represent a point on the curve. If so, the coordinates are copied and converted to internal representation, and the function returns 1. Otherwise, it returns 0. Currently, the infinity point (or zero point, with additive notation) is not allowed.
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.
Deallocate storage.
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_t
representation.
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 generate length
random octets and store them at dst
. 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, generating a new ECDSA key pair:
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 generate length
random octets and store them at dst
. For advice, see
See Randomness.
Next: Curve 25519 and Curve 448, Previous: ECDSA, Up: Elliptic curves [Contents][Index]
GOSTDSA (GOST R 34.10-2001, GOST R 34.10-2012) is a variant of the DSA (see DSA) and ECDSA (see ECDSA) digital signature schemes, which works over an elliptic curve group. Original documents are written in Russian. English translations are provided in RFC 5832 and RFC 7091. While technically nothing stops one from using GOSTDSA over any curve, it is defined only over several 256 and 512-bit curves. Like DSA and ECDSA, creating a signature requires a unique random nonce (repeating the nonce with two different messages reveals the private key, and any leak or bias in the generation of the nonce also leaks information about the key).
GOST R 34.10-2001 was defined to use GOST R 34.11-94 hash function (GOSTHASH94 and GOSTHASH94CP, RFC 5831). GOST R 34.10-2012 is defined to use GOST R 34.11-2012 hash function (Streebog, RFC 6986) of corresponding size (256 or 512) depending on curve size.
Nettle defines GOSTDSA in <nettle/gostdsa.h>. GOSTDSA reuses ECDSA
data types (struct ecc_point
, struct ecc_scalar
) to
represent public and private keys. Also to generate a new GOSTDSA key
pair one has to use ecdsa_generate_keypair()
function.
To create and verify GOSTDSA 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 generate length
random octets and store them at dst
. 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.
For historical reason several curve IDs (OIDs) may correspond to a single curve/generator combination. Following list defines correspondence between nettle’s view on curves and actual identifiers defined in RFC 4357 and RFC 7836.
Returns curve corresponding to following identifiers:
Returns curve corresponding to following identifiers:
For GOST key pairs key derivation/key agreement function (VKO) is defined in RFC 4357 and RFC 7836. Basically shared key is equal to hash(cofactor * ukm * priv * pub). Nettle library provides a function that does multiplication. Caller should do hashing on his own (it will be either GOST R 34.11-94 (see GOSTHASH94CP) or GOST R 34.11-2012, Streebog, which nor part of the library yet).
Uses private key priv, public ket pub and shared key material ukm to generate shared secret, written to buffer out. The buffer should be of the size equal to 2 private key lengths: 64 bytes for 256 bit curves and 128 bytes for 512 bit ones. UKM is a shared key material, usually transferred in cleartext. It does not have to be secret.
Previous: ECDSA, Up: Elliptic curves [Contents][Index]
Curve25519 is an elliptic curve of Montgomery type, y^2 = x^3 + 486662 x^2 + x (mod p), with p = 2^255 - 19. Montgomery curves have the advantage of simple and efficient point addition based on the x-coordinate only. This particular curve was proposed by D. J. Bernstein in 2006, for fast Diffie-Hellman key exchange, and is also described in RFC 7748. The group generator is defined by x = 9 (there are actually two points with x = 9, differing by the sign of the y-coordinate, but that doesn’t matter for the curve25519 operations which work with the x-coordinate only).
The curve25519 functions are defined as operations on octet strings, representing 255-bit scalars or x-coordinates, in little-endian byte order. The most significant input bit, i.e, the most significant bit of the last octet, is always ignored.
For scalars, in addition, the least significant three bits are ignored, and treated as zero, and the second most significant bit is ignored too, and treated as one. Then the scalar input string always represents 8 times a number in the range 2^251 <= s < 2^252.
Of all the possible input strings, only about half correspond to
x-coordinates of points on curve25519, i.e., a value x for which
the the curve equation can be solved for y. The other half
correspond to points on a related “twist curve”. The function
curve25519_mul
uses a Montgomery ladder for the scalar
multiplication, as suggested in the curve25519 literature, and required
by RFC 7748. The output is therefore well defined for
all possible inputs, no matter if the input string represents a
valid point on the curve or not.
Note that the curve25519 implementation in earlier versions of Nettle
deviates slightly from RFC 7748, in that bit 255 of the x
coordinate of the point input to curve25519_mul was not ignored. The
nette/curve25519.h defines a preprocessor symbol
NETTLE_CURVE25519_RFC7748
to indicate conformance with the
standard.
Nettle defines Curve 25519 in <nettle/curve25519.h>.
Defined to 1 in Nettle versions conforming to RFC 7748. Undefined in earlier versions.
The size of the strings representing curve25519 points and scalars, 32.
Computes Q = N G, where G is the group generator and
N is an integer. The input argument n and the output
argument q use a little-endian representation of the scalar and
the x-coordinate, respectively. They are both of size
CURVE25519_SIZE
.
This function is intended to be compatible with the function
crypto_scalar_mult_base
in the NaCl library.
Computes Q = N P, where P is an input point and N
is an integer. The input arguments n and p and the output
argument q use a little-endian representation of the scalar and
the x-coordinates, respectively. They are all of size
CURVE25519_SIZE
.
This function is intended to be compatible with the function
crypto_scalar_mult
in the NaCl library.
Similarly, Nettle also implements Curve448, an elliptic curve of Montgomery type, y^2 = x^3 + 156326 x^2 + x (mod p), with p = 2^448 - 2^224 - 1. This particular curve was proposed by Mike Hamburg in 2015, for fast Diffie-Hellman key exchange, and is also described in RFC 7748.
Nettle defines Curve 448 in <nettle/curve448.h>.
The octet length of the strings representing curve448 points and scalars, 56.
Computes Q = N G, where G is the group generator and
N is an integer. The input argument n and the output
argument q use a little-endian representation of the scalar and
the x-coordinate, respectively. They are both of size
CURVE448_SIZE
.
This function is intended to be compatible with the function
crypto_scalar_mult_base
in the NaCl library.
Computes Q = N P, where P is an input point and N
is an integer. The input arguments n and p and the output
argument q use a little-endian representation of the scalar and
the x-coordinates, respectively. They are all of size
CURVE448_SIZE
.
This function is intended to be compatible with the function
crypto_scalar_mult
in the NaCl library.
EdDSA is a signature scheme proposed by D. J. Bernstein et al. in 2011. It is defined using a “Twisted Edwards curve”, of the form -x^2 + y^2 = 1 + d x^2 y^2. The specific signature scheme Ed25519 uses a curve which is equivalent to curve25519: The two groups used differ only by a simple change of coordinates, so that the discrete logarithm problem is of equal difficulty in both groups.
Unlike other signature schemes in Nettle, the input to the EdDSA sign and verify functions is the possibly large message itself, not a hash digest. EdDSA is a variant of Schnorr signatures, where the message is hashed together with other data during the signature process, providing resilience to hash-collisions: A successful attack finding collisions in the hash function does not automatically translate into an attack to forge signatures. EdDSA also avoids the use of a randomness source by generating the needed signature nonce from a hash of the private key and the message, which means that the message is actually hashed twice when creating a signature. If signing huge messages, it is possible to hash the message first and pass the short message digest as input to the sign and verify functions, however, the resilience to hash collision is then lost.
The size of a private or public Ed25519 key, 32 octets.
The size of an Ed25519 signature, 64 octets.
Computes the public key corresponding to the given private key. Both
input and output are of size ED25519_KEY_SIZE
.
Signs a message using the provided key pair.
Verifies a message using the provided public key. Returns 1 if the signature is valid, otherwise 0.
Nettle also provides Ed448, an EdDSA signature scheme based on an Edwards curve equivalent to curve448.
The size of a private or public Ed448 key, 57 octets.
The size of an Ed448 signature, 114 octets.
Computes the public key corresponding to the given private key. Both
input and output are of size ED448_KEY_SIZE
.
Signs a message using the provided key pair.
Verifies a message using the provided public key. Returns 1 if the signature is valid, otherwise 0.
Next: ASCII encoding, Previous: Public-key algorithms, Up: Reference [Contents][Index]
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:
Such as completed blocks from spinning hard disks, network packets, etc. Getting access to such information is quite system dependent, and not all systems include suitable hardware. If available, it’s one of the better randomness source one can find in a digital, mostly predictable, computer.
Timing and contents of user interaction events is another popular source that is available for interactive programs (even if I suspect that it is sometimes used in order to make the user feel good, not because the quality of the input is needed or used properly). Obviously, not available when a machine is unattended. Also beware of networks: User interaction that happens across a long serial cable, TELNET session, or even SSH session may be visible to an attacker, in full or partially.
Any room, or even a microphone input that’s left unconnected, is a source of some random background noise, which can be fed into the seeding process.
Hardware devices with the sole purpose of generating random data have been designed. They range from radioactive samples with an attached Geiger counter, to amplification of the inherent noise in electronic components such as diodes and resistors, to low-frequency sampling of chaotic systems. Hashing successive images of a Lava lamp is a spectacular example of the latter type.
Secret information, such as user passwords or keys, or private files stored on disk, can provide some unguessability. A problem is that if the information is revealed at a later time, the unguessability vanishes. Another problem is that this kind of information tends to be fairly constant, so if you rely on it and seed your generator regularly, you risk constructing almost similar seeds or even constructing the same seed more than once.
For all practical sources, it’s difficult but important to provide a reliable lower bound on the amount of unguessability that it provides. Two important points are to make sure that the attacker can’t observe your sources (so if you like the Lava lamp idea, remember that you have to get your own lamp, and not put it by a window or anywhere else where strangers can see it), and that hardware failures are detected. What if the bulb in the Lava lamp, which you keep locked into a cupboard following the above advice, breaks after a few months?
So let’s assume that we have been able to find an unguessable seed, which contains at least 80 bits of conditional entropy, relative to all attackers that we care about (typically, we must at the very least assume that no attacker has root privileges on our machine).
How do we generate output from this seed, and how much can we get? Some generators (notably the Linux /dev/random generator) tries to estimate available entropy and restrict the amount of output. The goal is that if you read 128 bits from /dev/random, you should get 128 “truly random” bits. This is a property that is useful in some specialized circumstances, for instance when generating key material for a one time pad, or when working with unconditional blinding, but in most cases, it doesn’t matter much. For most application, there’s no limit on the amount of useful “random” data that we can generate from a small seed; what matters is that the seed is unguessable and that the generator has good cryptographic properties.
At the heart of all generators lies its internal state. Future output is determined by the internal state alone. Let’s call it the generator’s key. The key is initialized from the unguessable seed. Important properties of a generator are:
An attacker observing the output should not be able to recover the generator’s key.
Observing some of the output should not help the attacker to guess previous or future output.
Even if an attacker compromises the generator’s key, he should not be able to guess the generator output before the key compromise.
If an attacker compromises the generator’s key, he can compute
all future output. This is inevitable if the generator is seeded
only once, at startup. However, the generator can provide a reseeding
mechanism, to achieve recovery from key compromise. More precisely: If
the attacker compromises the key at a particular time t_1
, there
is another later time t_2
, such that if the attacker observes all
output generated between t_1
and t_2
, he still can’t guess
what output is generated after t_2
.
Nettle includes one randomness generator that is believed to have all the above properties, and two simpler ones.
ARCFOUR, like any stream cipher, can be used as a randomness
generator. Its output should be of reasonable quality, if the seed is
hashed properly before it is used with arcfour_set_key
. There’s
no single natural way to reseed it, but if you need reseeding, you
should be using Yarrow instead.
The “lagged Fibonacci” generator in <nettle/knuth-lfib.h> is a fast generator with good statistical properties, but is not for cryptographic use, and therefore not documented here. It is included mostly because the Nettle test suite needs to generate some test data from a small seed.
The recommended generator to use is Yarrow, described below.
Yarrow 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>.
Information about a single source.
Recommended size of the Yarrow-256 seed file.
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_random
and 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.
Information about recent key events.
Initializes the context.
key is the id of the key (ASCII value, hardware key code, X
keysym, …, it doesn’t matter), and time is the timestamp of
the event. The time must be given in units matching the resolution by
which you read the clock. If you read the clock with microsecond
precision, time should be provided in units of microseconds. But
if you use gettimeofday
on a typical Unix system where the clock
ticks 10 or so microseconds at a time, time should be given in
units of 10 microseconds.
Returns an entropy estimate, in bits, suitable for calling
yarrow256_update
. Usually, 0, 1 or 2 bits.
Next: Miscellaneous functions, Previous: Randomness, Up: Reference [Contents][Index]
Encryption will transform your data from text into binary format, and that may be a problem if, for example, you want to send the data as if it was plain text in an email, or store it along with descriptive text in a file. You may then use an encoding from binary to text: each binary byte is translated into a number of bytes of plain text.
A base-N encoding of data is one representation of data that only uses N different symbols (instead of the 256 possible values of a byte).
The base64 encoding will always use alphanumeric (upper and lower case) characters and the ’+’, ’/’ and ’=’ symbols to represent the data. Four output characters are generated for each three bytes of input. In case the length of the input is not a multiple of three, padding characters are added at the end. There’s also a “URL safe” variant, which is useful for encoding binary data into URLs and filenames. See RFC 4648.
The base16 encoding, also known as “hexadecimal”, uses the decimal digits and the letters from A to F. Two hexadecimal digits are generated for each input byte.
Nettle supports both base64 and base16 encoding and decoding.
Encoding and decoding uses a context struct to maintain its state (with the exception of base16 encoding, which doesn’t need any). To encode or decode the data, first initialize the context, then call the update function as many times as necessary, and complete the operation by calling the final function.
The following functions can be used to perform base64 encoding and decoding. They are defined in <nettle/base64.h>.
Initializes a base64 context. This is necessary before starting an
encoding session. base64_encode_init
selects the standard base64
alphabet, while base64url_encode_init
selects the URL safe
alphabet.
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).
The maximum amount of output from base64_encode_final
.
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. base64_decode_init
selects the standard
base64 alphabet, while base64url_decode_init
selects the URL safe
alphabet.
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(src_length). The amount of data generated is returned in *dst_length. Returns 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(src_length). The amount of data generated is returned in *dst_length. Returns 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.
Next: Compatibility functions, Previous: ASCII encoding, Up: Reference [Contents][Index]
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 memcpy
function.
Like memxor
, but takes two source areas and separate
destination area.
Side-channel silent comparison of the n bytes at a and b. I.e., instructions executed and memory accesses are identical no matter where the areas differ, see Side-channel silence. Return non-zero if the areas are equal, and zero if they differ.
These functions are declared in <nettle/memops.h>. For
compatibility with earlier versions of Nettle, memxor
and
memxor3
are also declared in <nettle/memxor.h>.
Previous: Miscellaneous functions, Up: Reference [Contents][Index]
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
.
Next: Installation, Previous: Reference, Up: Top [Contents][Index]
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.
Next: Index, Previous: Nettle soup, Up: Top [Contents][Index]
Nettle uses autoconf
. To build it, unpack the source and run
./configure make make check make install
to install it under the default prefix, /usr/local. Using GNU make is strongly recommended. By default, both static and shared libraries are built and installed.
To get a list of configure options, use ./configure --help
. Some
of the more interesting are:
Include multiple versions of certain functions in the library, and select the ones to use at run-time, depending on available processor features. Supported for ARM and x86_64.
Use the smaller and slower “mini-gmp” implementation of the bignum functions needed for public-key cryptography, instead of the real GNU GMP library. This option is intended primarily for smaller embedded systems. Note that builds using mini-gmp are not binary compatible with regular builds of Nettle, and more likely to leak side-channel information.
Omit building the shared libraries.
Disable the automatic dependency tracking. You will likely need this option to be able to build with BSD make.
Previous: Installation, Up: Top [Contents][Index]
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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.