|Secure Hash Algorithms|
|hash functions · SHA · DSA|
|SHA-0 · SHA-1 · SHA-2 · SHA-3 |
|Designers||National Security Agency|
|Series||(SHA-0), SHA-1, SHA-2, SHA-3|
|Certification||FIPS PUB 180-4, CRYPTREC, NESSIE|
|Digest sizes||224, 256, 384, or 512 bits|
|Structure||Merkle–Damgård construction with Davies–Meyer compression function|
|Rounds||64 or 80|
|Best public cryptanalysis|
|A 2011 attack breaks preimage resistance for 57 out of 80 rounds of SHA-512, and 52 out of 64 rounds for SHA-256.
Pseudo-collision attack against up to 46 rounds of SHA-256.SHA-256 and SHA-512 are prone to length extension attacks. By guessing the hidden part of the state, length extension attacks on SHA-224 and SHA-384 succeed with probability 2−(256−224) = 2−32 > 2−224 and 2−(512−384) = 2−128 > 2−384 respectively.
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA). They are built using the Merkle–Damgård structure, from a one-way compression function itself built using the Davies–Meyer structure from a (classified) specialized block cipher.
Cryptographic hash functions are mathematical operations run on digital data; by comparing the computed "hash" (the output from execution of the algorithm) to a known and expected hash value, a person can determine the data's integrity. For example, computing the hash of a downloaded file and comparing the result to a previously published hash result can show whether the download has been modified or tampered with. A key aspect of cryptographic hash functions is their collision resistance: nobody should be able to find two different input values that result in the same hash output.
SHA-2 includes significant changes from its predecessor, SHA-1. The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256.
SHA-256 and SHA-512 are novel hash functions computed with 32-bit 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 SHA-256 and SHA-512 respectively, 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 Federal Information Processing Standards (FIPS) PUB 180-4. SHA-2 was published in 2001 by the National Institute of Standards and Technology (NIST) a U.S. federal standard (FIPS). The SHA-2 family of algorithms are patented in US patent 6829355. The United States has released the patent under a royalty-free license.
SHA-256 and SHA-512, and, to a lesser degree, SHA-224 and SHA-384 are prone to length extension attacks, rendering it insecure for some applications. It is thus generally recommended to switch to SHA-3 for 512-bit hashes and to use SHA-512/224 and SHA-512/256 instead of SHA-224 and SHA-256. This also happens to be faster than SHA-224 and SHA-256 on x86-64 processor architecture, since SHA-512 works on 64-bit instead of 32-bit words.
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 January 2011, NIST published SP800-131A, which specified a move from the then-current minimum of 80-bit security (provided by SHA-1) allowable for federal government use until the end of 2013, to 112-bit security (provided by SHA-2) being both the minimum requirement (starting in 2014) and the recommended security level (starting from the publication date in 2011).
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.
In July 2012, NIST revised SP800-57, which provides guidance for cryptographic key management. The publication disallowed creation of digital signatures with a hash security lower than 112 bits after 2013. The previous revision from 2007 specified the cutoff to be the end of 2010. In August 2012, NIST revised SP800-107 in the same manner.
The SHA-2 hash function is implemented in some widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, and IPsec.
SHA-256 partakes in the process of authenticating Debian 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.
Several cryptocurrencies like Bitcoin use SHA-256 for verifying transactions and calculating proof of work or proof of stake. The rise of ASIC SHA-2 accelerator chips has led to the use of scrypt-based proof-of-work schemes.
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 was hoped to accelerate migration away from SHA-1.
The SHA-2 functions were not quickly adopted initially, despite better security than SHA-1. Reasons might include lack of support for SHA-2 on systems running Windows XP SP2 or older and a lack of perceived urgency since SHA-1 collisions had not yet been found. The Google Chrome team announced a plan to make their web browser gradually stop honoring SHA-1-dependent TLS certificates over a period from late 2014 and early 2015. Similarly, Microsoft announced that Internet Explorer and Edge would stop honoring public SHA-1-signed TLS certificates from February 2017. Mozilla disabled SHA-1 in early January 2016, but had to re-enable it temporarily via a Firefox update, after problems with web-based user interfaces of some router models and security appliances.
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.
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 which would be accepted by widely used web browsers.
Increased interest in cryptographic hash analysis during the SHA-3 competition produced several new attacks on the SHA-2 family, the best of which are given in the table below. Only the collision attacks are of practical complexity; none of the attacks extend to the full round hash function.
At FSE 2012, researchers at Sony gave a presentation suggesting pseudo-collision attacks could be extended to 52 rounds on SHA-256 and 57 rounds on SHA-512 by building upon the biclique pseudo-preimage attack.
|Published in||Year||Attack method||Attack||Variant||Rounds||Complexity|
|New Collision Attacks Against
Up To 24-step SHA-2
|Preimages for step-reduced SHA-2||2009||Meet-in-the-middle||Preimage||SHA-256||42/64||2251.7|
|Higher-Order Differential Attack
on Reduced SHA-256
|Bicliques for Preimages: Attacks on
Skein-512 and the SHA-2 family
|Improving Local Collisions: New
Attacks on Reduced SHA-256
|Branching Heuristics in Differential Collision
Search with Applications to SHA-512
|Analysis of SHA-512/224 and SHA-512/256||2016||Differential||Collision||SHA-256||28/64||practical|
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 the formal CMVP validation, which is required by law for certain applications.
As of December 2013[update], there are over 1300 validated implementations of SHA-256 and over 900 of SHA-512, with only 5 of them being capable of handling messages with a length in bits not a multiple of eight while supporting both variants.
Hash values of an empty string (i.e., a zero-length input text).
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 this sentence changes almost half (111 out of 224) of the bits in the hash:
SHA224("The quick brown fox jumps over the lazy dog") 0x 730e109bd7a8a32b1cb9d9a09aa2325d2430587ddbc0c38bad911525 SHA224("The quick brown fox jumps over the lazy dog.") 0x 619cba8e8e05826e9b8c519c0a5c68f4fb653e8a3d8aa04bb2c8cd4c
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 (Padding): begin with the original message of length L bits append a single '1' bit append K '0' bits, where K is the minimum number >= 0 such that L + 1 + K + 64 is a multiple of 512 append L as a 64-bit big-endian integer, making the total 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 message schedule array w has 80 64-bit words instead of 64 32-bit words,
- to extend the message schedule array w, the loop is from 16 to 79 instead of from 16 to 63,
- 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.
The SHA-512/t IV generation function evaluates a modified SHA-512 on the ASCII string "SHA-512/t", substituted with the decimal representation of t. The modified SHA-512 is the same as SHA-512 except its initial values
h7 have each been XORed with the hexadecimal constant
Sample C implementation for SHA-2 family of hash functions can be found in RFC 6234.
Comparison of SHA functions
In the table below, internal state means the "internal hash sum" after each compression of a data block.
|Algorithm and variant||Output size
|Internal state size
|Rounds||Operations||Security (in bits) against collision attacks||Capacity
against length extension attacks
|Performance on Skylake (median cpb)||First published|
|long messages||8 bytes|
|MD5 (as reference)||128||128
(4 × 32)
|512||64||And, Xor, Rot, Add (mod 232), Or||≤18
(5 × 32)
|512||80||And, Xor, Rot, Add (mod 232), Or||<34
|0||≈ SHA-1||≈ SHA-1||1993|
(8 × 32)
|512||64||And, Xor, Rot, Add (mod 232), Or, Shr||112
(8 × 64)
|1024||80||And, Xor, Rot, Add (mod 264), Or, Shr||192
|128 (≤ 384)
|≈ SHA-384||≈ SHA-384||2012|
(5 × 5 × 64)
|24||And, Xor, Rot, Not||112
In the bitwise operations column, "Rot" stands for rotate no carry, and "Shr" stands for right logical shift. All of these algorithms employ modular addition in some fashion except for SHA-3.
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||16.80||199||13.05||256|
|AMD Piledriver APU||3.8 GHz||SHA-256||32||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 on the x86 architecture. 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 APU at a clock speed of 3.8 GHz. The referenced cycles per byte speeds above are the median performance of an algorithm digesting a 4,096 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.
Below is a list of cryptography libraries that support SHA-2:
- Bouncy Castle
Other articles of the topic Cryptography : Zclassic, Pasaffe, BoxyCoin, Peercoin, Datacoin, SafeWallet Password Manager, Securebear
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- Comparison of cryptographic hash functions
- Comparison of cryptography libraries
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- Ji Li, Takanori Isobe and Kyoji Shibutani, Sony China Research Laboratory and Sony Corporation, Converting Meet-in-the-Middle Preimage Attack into Pseudo Collision Attack: Application to SHA-2
- Somitra Kumar Sanadhya & Palash Sarkar (2008). "New Collision Attacks Against Up To 24-step SHA-2" (PDF). IACR Cryptology ePrint Archive. 2008:270.
- Kazumaro Aoki; Jian Guo; Krystian Matusiewicz; Yu Sasaki & Lei Wang (2009). "Preimages for step-reduced SHA-2". Advances in Cryptology – ASIACRYPT 2009. Lecture Notes in Computer Science. Springer Berlin Heidelberg. 5912: 578–597. doi:10.1007/978-3-642-10366-7_34. ISBN 978-3-642-10366-7. ISSN 0302-9743.
- Jian Guo; San Ling; Christian Rechberger & Huaxiong Wang (2010). "Advanced meet-in-the-middle preimage attacks: First results on full Tiger, and improved results on MD4 and SHA-2" (PDF). Advances in Cryptology – ASIACRYPT 2010. Lecture Notes in Computer Science. Springer Berlin Heidelberg. 6477: 56–75. doi:10.1007/978-3-642-17373-8_4. ISBN 978-3-642-17373-8. ISSN 0302-9743.
- Florian Mendel; Tomislav Nad; Martin Schläffer (2013). "Improving Local Collisions: New Attacks on Reduced SHA-256". Advances in Cryptology – EUROCRYPT 2013. Lecture Notes in Computer Science. Springer Berlin Heidelberg. 7881: 262–278. doi:10.1007/978-3-642-38348-9_16. ISBN 978-3-642-38348-9. ISSN 0302-9743.
- Maria Eichlseder and Florian Mendel and Martin Schläffer (2014). "Branching Heuristics in Differential Collision Search with Applications to SHA-512" (PDF). IACR Cryptology ePrint Archive. 2014:302.
- Christoph Dobraunig; Maria Eichlseder & Florian Mendel (2016). "Analysis of SHA-512/224 and SHA-512/256" (PDF).
- "SHS Validation List". NIST. 2017-06-16. Archived from the original on 2017-06-17.
- "Measurements table". bench.cr.yp.to.
- Xie Tao; Fanbao Liu & Dengguo Feng (2013). "Fast Collision Attack on MD5 <img src=x>" (PDF).
- "Announcing the first SHA1 collision". Retrieved 2017-02-23.
- "The Keccak sponge function family". Retrieved 2016-01-27.
- SUPERCOP Benchmarks Measurements of hash functions, indexed by machine
- "SUPERCOP". Retrieved 24 February 2015.
- Henri Gilbert, Helena Handschuh: Security Analysis of SHA-256 and Sisters. Selected Areas in Cryptography 2003: pp175–193
- "Proposed Revision of Federal Information Processing Standard (FIPS) 180, Secure Hash Standard". Federal Register. 59 (131): 35317–35318. 1994-07-11. Retrieved 2007-04-26.[permanent dead link]
- Descriptions of SHA-256, SHA-384, and SHA-512 from NIST
- SHA-2 Checker – SHAChecker to check one's SSL compatibility for SHA-2
- Specifications for a Secure Hash Standard (SHS) – Draft for proposed SHS (SHA-0)
- Secure Hash Standard (SHS) – Proposed SHS (SHA-0)
- CSRC Cryptographic Toolkit – Official NIST site for the Secure Hash Standard
- FIPS PUB 180-4: Secure Hash Standard (SHS) (PDF, 834 KB) – Current version of the Secure Hash Standard (SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512), August 2015
- Test vectors for SHA-256/384/512 from the NESSIE project
- Test vectors for SHA-1, SHA-2 from NIST site
- NIST Cryptographic Hash Project – SHA-3 competition
- RFC 3874: "A 224-bit One-way Hash Function: SHA-224"
- RFC 6234: "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)"; contains sample C implementation
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