|Designers||National Security Agency|
|Series||(SHA-0), SHA-1, SHA-2, SHA-3|
|Certification||FIPS PUB 180-4, CRYPTREC, NESSIE|
|Digest sizes||224/256 bits or 384/512 bits|
|Rounds||64 or 80|
|Best public cryptanalysis|
SHA-2 is a set of cryptographic hash functions (SHA-224, SHA-256, SHA-384, SHA-512) designed by the U.S. National Security Agency (NSA) and published in 2001 by the NIST as a U.S. Federal Information Processing Standard (FIPS). A hash function is an algorithm that transforms (hashes) an arbitrary set of data elements, such as a text file, into a single fixed length value (the hash). The computed hash value may then be used to verify the integrity of copies of the original data without providing any means to derive said original data. Irreversible, a hash value may be freely distributed, stored. and used for comparative purposes. SHA stands for Secure Hash Algorithm. SHA-2 includes a significant number of changes from its predecessor, SHA-1. SHA-2 consists of a set of four hash functions with digests that are 224, 256, 384 or 512 bits.
The security provided by a hashing algorithm is entirely dependent upon its ability to produce a unique value for any specific set of data. When a hash function produces the same hash value for two different sets of data then a collision is said to occur. Collision raises the possibility that an attacker may be able to computationally craft sets of data which provide access to information secured by the hashed values of pass codes or to alter computer data files in a fashion that would not change the resulting hash value and would thereby escape detection. A strong hash function is one that is resistant to such computational attacks. A weak hash function is one where a computational approach to producing collisions is believed to be possible. A broken hash function is one where a computational method for producing collisions is known to exist.
In 2005, security flaws were identified in SHA-1, namely that a mathematical weakness might exist, indicating that a stronger hash function would be desirable. Although SHA-2 bears some similarity to the SHA-1 algorithm, these attacks have not been successfully extended to SHA-2.
With the publication of FIPS PUB 180-2, NIST added three additional hash functions in the SHA family. The algorithms are collectively known as SHA-2, named after their digest lengths (in bits): SHA-256, SHA-384, and SHA-512.
The algorithms were first published in 2001 in the draft FIPS PUB 180-2, at which time public review and comments were accepted. In August 2002, FIPS PUB 180-2 became the new Secure Hash Standard, replacing FIPS PUB 180-1, which was released in April 1995. The updated standard included the original SHA-1 algorithm, with updated technical notation consistent with that describing the inner workings of the SHA-2 family.
In February 2004, a change notice was published for FIPS PUB 180-2, specifying an additional variant, SHA-224, defined to match the key length of two-key Triple DES. In October 2008, the standard was updated in FIPS PUB 180-3, including SHA-224 from the change notice, but otherwise making no fundamental changes to the standard. The primary motivation for updating the standard was relocating security information about the hash algorithms and recommendations for their use to Special Publications 800-107 and 800-57. Detailed test data and example message digests were also removed from the standard, and provided as separate documents.
In March 2012, the standard was updated in FIPS PUB 180-4, adding the hash functions SHA-512/224 and SHA-512/256, and describing a method for generating initial values for truncated versions of SHA-512. Additionally, a restriction on padding the input data prior to hash calculation was removed, allowing hash data to be calculated simultaneously with content generation, such as a real-time video or audio feed. Padding the final data block must still occur prior to hash output.
SHA-256 and SHA-512 are novel hash functions computed with 32- and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are simply truncated versions of the first two, computed with different initial values. SHA-512/224 and SHA-512/256 are also truncated versions of SHA-512, but the initial values are generated using the method described in FIPS PUB 180-4. The SHA-2 family of algorithms are patented in US 6829355 . The United States has released the patent under a royalty-free license.
Comparison of SHA functions
In the table below, internal state means the "internal hash sum" after each compression of a data block.
|Output size (bits)||Internal state size (bits)||Block size (bits)||Max message size (bits)||Word size (bits)||Rounds||Operations||Collisions found||Example Performance (MiB/s)|
|MD5 (as reference)||128||128||512||264 − 1||32||64||+,and,or,xor,rot||Yes||335|
|SHA-0||160||160||512||264 − 1||32||80||+,and,or,xor,rot||Yes||-|
|SHA-1||160||160||512||264 − 1||32||80||+,and,or,xor,rot||Theoretical attack (260)||192|
|256||512||264 − 1||32||64||+,and,or,xor,shr,rot||None||139|
|512||1024||2128 − 1||64||80||+,and,or,xor,shr,rot||None||154|
(5×5 array of 64-bit words)
The performance numbers above were for a single-threaded implementation on an AMD Opteron 8354 running at 2.2 GHz under Linux in 64-bit mode, and serve only as a rough point for general comparison. More detailed performance measurements on modern processor architectures are given in the table below.
|CPU Architecture||Frequency||Algorithm||Word size (bits)||Cycles/Byte x86||MiB/s x86||Cycles/Byte x86-64||MiB/s x86-64|
|Intel Ivy Bridge||3.5 GHz||SHA-256||32-bit||16.80||199||13.05||256|
|AMD Piledriver||3.8 GHz||SHA-256||32-bit||22.87||158||18.47||196|
The performance numbers labeled 'x86' were running using 32-bit code on 64-bit processors, whereas the 'x86-64' numbers are native 64-bit code. While SHA-256 is designed for 32-bit calculations, it does benefit from code optimized for 64-bit processors. 32-bit implementations of SHA-512 are significantly slower than their 64-bit counterparts. Variants of both algorithms with different output sizes will perform similarly, since the message expansion and compression functions are identical, and only the initial hash values and output sizes are different. The best implementations of MD5 and SHA-1 perform between 4.5 and 6 cycles per byte on modern processors.
Testing was performed by the University of Illinois at Chicago on their hydra8 system running an Intel Xeon E3-1275 V2 at a clock speed of 3.5 GHz, and on their hydra9 system running an AMD A10-5800K at a clock speed of 3.8 GHz. The referenced cycles per byte speeds above are the median performance of an algorithm digesting a 4096 byte message using the SUPERCOP cryptographic benchmarking software. The MiB/s performance is extrapolated from the CPU clockspeed on a single core, real world performance will vary due to a variety of factors.
The cryptocurrency Bitcoin relies heavily on a double round of SHA-256. SHA-256 is used to authenticate Debian GNU/Linux software packages and in the DKIM message signing standard; SHA-512 is part of a system to authenticate archival video from the International Criminal Tribunal of the Rwandan genocide. SHA-256 and SHA-512 are proposed for use in DNSSEC. Unix and Linux vendors are moving to using 256- and 512-bit SHA-2 for secure password hashing.
SHA-1 and SHA-2 are the secure hash algorithms required by law for use in certain U.S. Government applications, including use within other cryptographic algorithms and protocols, for the protection of sensitive unclassified information. FIPS PUB 180-1 also encouraged adoption and use of SHA-1 by private and commercial organizations. SHA-1 is being retired for most government uses; the U.S. National Institute of Standards and Technology says, "Federal agencies should stop using SHA-1 for...applications that require collision resistance as soon as practical, and must use the SHA-2 family of hash functions for these applications after 2010" (emphasis in original). NIST's directive that U.S. government agencies must stop uses of SHA-1 after 2010 and the completion of SHA-3 may accelerate migration away from SHA-1.
The SHA-2 functions are not as widely used as SHA-1, despite their better security. Reasons might include lack of support for SHA-2 on systems running Windows XP SP2 or older, or a lack of perceived urgency since SHA-1 collisions have not yet been found.
Cryptanalysis and validation
For a hash function for which L is the number of bits in the message digest, finding a message that corresponds to a given message digest can always be done using a brute force search in 2L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as a collision, requires on average only 2L/2 evaluations using a birthday attack.
In terms of practical security, a major concern about these[which?] new attacks is that they might pave the way to more efficient ones. Whether this is the case has yet to be seen, but a migration to stronger hashes is believed to be prudent.[by whom?] Some of the applications that use cryptographic hashes, such as password storage, are only minimally affected by a collision attack. Constructing a password that works for a given account requires a preimage attack, as well as access to the hash of the original password (typically in the shadow file) which may or may not be trivial. Reversing password encryption (e.g., to obtain a password to try against a user's account elsewhere) is not made possible by the attacks. (However, even a secure password hash cannot prevent brute-force attacks on weak passwords.)
In the case of document signing, an attacker could not simply fake a signature from an existing document—the attacker would have to produce a pair of documents, one innocuous and one damaging, and get the private key holder to sign the innocuous document. There are practical circumstances in which this is possible; until the end of 2008, it was possible to create forged SSL certificates using an MD5 collision.
There are two meet-in-the-middle preimage attacks against SHA-2 with a reduced number of rounds. The first one attacks 41-round SHA-256 out of 64 rounds with time complexity of 2253.5 and space complexity of 216, and 46-round SHA-512 out of 80 rounds with time 2511.5 and space 23. The second one attacks 42-round SHA-256 with time complexity of 2251.7 and space complexity of 212, and 42-round SHA-512 with time 2502 and space 222.
Implementations of all FIPS-approved security functions can be officially validated through the CMVP program, jointly run by the National Institute of Standards and Technology (NIST) and the Communications Security Establishment (CSE). For informal verification, a package to generate a high number of test vectors is made available for download on the NIST site; the resulting verification however does not replace in any way the formal CMVP validation, which is required by law for certain applications.
Examples of SHA-2 variants
Hash values of empty string.
SHA224("") 0x d14a028c2a3a2bc9476102bb288234c415a2b01f828ea62ac5b3e42f SHA256("") 0x e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855 SHA384("") 0x 38b060a751ac96384cd9327eb1b1e36a21fdb71114be07434c0cc7bf63f6e1da274edebfe76f65fbd51ad2f14898b95b SHA512("") 0x cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e SHA512/224("") 0x 6ed0dd02806fa89e25de060c19d3ac86cabb87d6a0ddd05c333b84f4 SHA512/256("") 0x c672b8d1ef56ed28ab87c3622c5114069bdd3ad7b8f9737498d0c01ecef0967a
Even a small change in the message will (with overwhelming probability) result in a mostly different hash, due to the avalanche effect. For example, adding a period to the end of the sentence:
SHA224("The quick brown fox jumps over the lazy dog") 0x 730e109bd7a8a32b1cb9d9a09aa2325d2430587ddbc0c38bad911525 SHA224("The quick brown fox jumps over the lazy dog.") 0x 619cba8e8e05826e9b8c519c0a5c68f4fb653e8a3d8aa04bb2c8cd4c SHA256("The quick brown fox jumps over the lazy dog") 0x d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592 SHA256("The quick brown fox jumps over the lazy dog.") 0x ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c SHA384("The quick brown fox jumps over the lazy dog") 0x ca737f1014a48f4c0b6dd43cb177b0afd9e5169367544c494011e3317dbf9a509cb1e5dc1e85a941bbee3d7f2afbc9b1 SHA384("The quick brown fox jumps over the lazy dog.") 0x ed892481d8272ca6df370bf706e4d7bc1b5739fa2177aae6c50e946678718fc67a7af2819a021c2fc34e91bdb63409d7 SHA512("The quick brown fox jumps over the lazy dog") 0x 07e547d9586f6a73f73fbac0435ed76951218fb7d0c8d788a309d785436bbb642e93a252a954f23912547d1e8a3b5ed6e1bfd7097821233fa0538f3db854fee6 SHA512("The quick brown fox jumps over the lazy dog.") 0x 91ea1245f20d46ae9a037a989f54f1f790f0a47607eeb8a14d12890cea77a1bbc6c7ed9cf205e67b7f2b8fd4c7dfd3a7a8617e45f3c463d481c7e586c39ac1ed SHA512/224("The quick brown fox jumps over the lazy dog") 0x 944cd2847fb54558d4775db0485a50003111c8e5daa63fe722c6aa37 SHA512/224("The quick brown fox jumps over the lazy dog.") 0x 6d6a9279495ec4061769752e7ff9c68b6b0b3c5a281b7917ce0572de SHA512/256("The quick brown fox jumps over the lazy dog") 0x dd9d67b371519c339ed8dbd25af90e976a1eeefd4ad3d889005e532fc5bef04d SHA512/256("The quick brown fox jumps over the lazy dog.") 0x 1546741840f8a492b959d9b8b2344b9b0eb51b004bba35c0aebaac86d45264c3
Pseudocode for the SHA-256 algorithm follows. Note the great increase in mixing between bits of the
w[16..63] words compared to SHA-1.
Note 1: All variables are 32 bit unsigned integers and addition is calculated modulo 232 Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63 Note 3: The compression function uses 8 working variables, a through h Note 4: Big-endian convention is used when expressing the constants in this pseudocode, and when parsing message block data from bytes to words, for example, the first word of the input message "abc" after padding is 0x61626380 Initialize hash values: (first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19): h0 := 0x6a09e667 h1 := 0xbb67ae85 h2 := 0x3c6ef372 h3 := 0xa54ff53a h4 := 0x510e527f h5 := 0x9b05688c h6 := 0x1f83d9ab h7 := 0x5be0cd19 Initialize array of round constants: (first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311): k[0..63] := 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2 Pre-processing: append the bit '1' to the message (by appending a byte 0x80, i.e. bits are considered in big-endian order too) append k bits '0', where k is the minimum number >= 0 such that the resulting message length (modulo 512 in bits) is 448. append length of message (without the '1' bit or padding), in bits, as 64-bit big-endian integer (this will make the entire post-processed length a multiple of 512 bits) Process the message in successive 512-bit chunks: break message into 512-bit chunks for each chunk create a 64-entry message schedule array w[0..63] of 32-bit words (The initial values in w[0..63] don't matter, so many implementations zero them here) copy chunk into first 16 words w[0..15] of the message schedule array Extend the first 16 words into the remaining 48 words w[16..63] of the message schedule array: for i from 16 to 63 s0 := (w[i-15] rightrotate 7) xor (w[i-15] rightrotate 18) xor (w[i-15] rightshift 3) s1 := (w[i-2] rightrotate 17) xor (w[i-2] rightrotate 19) xor (w[i-2] rightshift 10) w[i] := w[i-16] + s0 + w[i-7] + s1 Initialize working variables to current hash value: a := h0 b := h1 c := h2 d := h3 e := h4 f := h5 g := h6 h := h7 Compression function main loop: for i from 0 to 63 S1 := (e rightrotate 6) xor (e rightrotate 11) xor (e rightrotate 25) ch := (e and f) xor ((not e) and g) temp1 := h + S1 + ch + k[i] + w[i] S0 := (a rightrotate 2) xor (a rightrotate 13) xor (a rightrotate 22) maj := (a and b) xor (a and c) xor (b and c) temp2 := S0 + maj h := g g := f f := e e := d + temp1 d := c c := b b := a a := temp1 + temp2 Add the compressed chunk to the current hash value: h0 := h0 + a h1 := h1 + b h2 := h2 + c h3 := h3 + d h4 := h4 + e h5 := h5 + f h6 := h6 + g h7 := h7 + h Produce the final hash value (big-endian): digest := hash := h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7
The computation of the
maj values can be optimized the same way as described for SHA-1.
SHA-224 is identical to SHA-256, except that:
- the initial hash values
h7are different, and
- the output is constructed by omitting
SHA-224 initial hash values (in big endian): (The second 32 bits of the fractional parts of the square roots of the 9th through 16th primes 23..53) h[0..7] := 0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939, 0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4
SHA-512 is identical in structure to SHA-256, but:
- the message is broken into 1024-bit chunks,
- the initial hash values and round constants are extended to 64 bits,
- there are 80 rounds instead of 64,
- the round constants are based on the first 80 primes 2..409,
- the word size used for calculations is 64 bits long,
- the appended length of the message (before pre-processing), in bits, is a 128-bit big-endian integer, and
- the shift and rotate amounts used are different.
SHA-512 initial hash values (in big-endian): h[0..7] := 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179
SHA-512 round constants: k[0..79] := [ 0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118, 0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694, 0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65, 0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5, 0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4, 0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70, 0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df, 0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b, 0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30, 0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8, 0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8, 0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3, 0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec, 0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b, 0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178, 0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b, 0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c, 0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817]
SHA-512 Sum & Sigma: S0 := (a rightrotate 28) xor (a rightrotate 34) xor (a rightrotate 39) S1 := (e rightrotate 14) xor (e rightrotate 18) xor (e rightrotate 41) s0 := (w[i-15] rightrotate 1) xor (w[i-15] rightrotate 8) xor (w[i-15] rightshift 7) s1 := (w[i-2] rightrotate 19) xor (w[i-2] rightrotate 61) xor (w[i-2] rightshift 6)
SHA-384 is identical to SHA-512, except that:
- the initial hash values
h7are different (taken from the 9th through 16th primes), and
- the output is constructed by omitting
SHA-384 initial hash values (in big-endian): h[0..7] := 0xcbbb9d5dc1059ed8, 0x629a292a367cd507, 0x9159015a3070dd17, 0x152fecd8f70e5939, 0x67332667ffc00b31, 0x8eb44a8768581511, 0xdb0c2e0d64f98fa7, 0x47b5481dbefa4fa4
SHA-512/t is identical to SHA-512 except that:
- the initial hash values
h7are given by the SHA-512/t IV generation function,
- the output is constructed by truncating the concatenation of
h7at t bits,
- t equal to 384 is not allowed, instead SHA-384 should be used as specified, and
- t values 224 and 256 are especially mentioned as approved.
Implementations in common languages
- Bouncy Castle
- The Bouncy Castle Library is a free Java and C# class library that contains implementations of the SHA-1, SHA-224, SHA-256, SHA-384 and SHA-512 algorithms as well as other algorithms like Whirlpool, Tiger, RIPEMD, GOST-3411, MD2, MD4 and MD5.
- an open source cross-platform software security toolkit library.
- An open source, permissively licensed, C++ class library of cryptographic schemes, including implementations of the SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 algorithms.
- A formally verified implementation of several widely used symmetric cryptographic algorithms using the SPARK programming language and toolset, complete library proofs of the absence of run-time errors like type range violations, division by zero and numerical overflows are available.
- A portable ISO C cryptographic toolkit, Public Domain.
- A general purpose cryptographic library based on the code from GNU Privacy Guard.
- A set of programs to compute MD5, SHA-1, SHA-256, Tiger, or Whirlpool cryptographic message digests on an arbitrary number of files. It is used in computer security, system administration and computer forensics communities for purposes of running large numbers of files through any of several different cryptographic digests. It is similar to sha1sum from GNU Core Utilities and md5sum.
- The widely used OpenSSL
cryptolibrary includes free, open-source – implementations of SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512.
- The small PolarSSL
SSLlibrary includes open-source – implementations of SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512.
- A free, open-source library which implements many hash functions, including SHA-1 and SHA-2, both in portable (but optimized) C and in Java.
- A free, open-source collection of hardware implementations of hash functions (including SHA-1 and SHA-2) in portable (but optimized) VHDL.
- Comparison of cryptographic hash functions
- Digital timestamping
- Hash based Message Authentication Code (HMAC) or Keyed Hash
- International Association for Cryptologic Research (IACR)
- sha1sum (sha224sum, sha256sum, sha384sum and sha512sum) commands
- Yu Sasaki, Lei Wang, and Kazumaro Aoki (2008-11-25). Preimage Attacks on 41-Step SHA-256 and 46-Step SHA-512.
- "Schneier on Security: Cryptanalysis of SHA-1". Schneier.com. Retrieved 2011-11-08.
- NIST Selects Winner of Secure Hash Algorithm (SHA-3) Competition
- Federal Register Notice 02-21599, Announcing Approval of FIPS Publication 180-2
- FIPS 180-2 with Change Notice 1
- Federal Register Notice E8-24743, Announcing Approval of FIPS Publication 180-3
- FIPS SP 800-107 Recommendation for Applications Using Approved Hash Algorithms
- FIPS SP 800-57 Recommendation for Key Management: Part 1: General
- NIST Algorithm Examples, Secure Hashing
- Federal Register Notice 2012-5400, Announcing Approval of FIPS Publication 180-4
- Licensing Declaration for US patent 6829355.. Retrieved 2008-02-17.
- Mario Lamberger and Florian Mendel, Higher-Order Differential Attack on Reduced SHA-256, accessed August 24, 2012.
- Yu Sasaki, Lei Wang, and Kazumaro Aoki, Preimage Attacks on 41-Step SHA-256 and 46-Step SHA-512, accessed January 3, 2010.
- "Crypto++ 5.6.0 Benchmarks". Retrieved 2013-06-13.
- "Cryptanalysis of MD5 & SHA-1" (PDF). Retrieved 2013-04-25.
- SUPERCOP Benchmarks Measurements of hash functions, indexed by machine
- SUPERCOP Benchmarking Toolkit
- "Debian codebase in Google Code". Google. Retrieved 2011-11-08.[dead link]
- John Markoff, A Tool to Verify Digital Records, Even as Technology Shifts, New York Times, January 26, 2009
- RFC 5702,RFC-Editor.org
- Ulrich Drepper, Unix crypt with SHA-256/512
- National Institute on Standards and Technology Computer Security Resource Center, NIST's Policy on Hash Functions, accessed March 29, 2009.
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- Microsoft Corporation,Overview of Windows XP Service Pack 3
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