This page uses content from Wikipedia and is licensed under CC BYSA.
Secure Hash Algorithms  

Concepts  
hash functions · SHA · DSA  
Main standards  
SHA0 · SHA1 · SHA2 · SHA3


General  

Designers  National Security Agency 
First published  2001 
Series  (SHA0), SHA1, SHA2, SHA3 
Certification  FIPS PUB 1804, CRYPTREC, NESSIE 
Detail  
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 SHA512, and 52 out of 64 rounds for SHA256.^{[1]} Pseudocollision attack against up to 46 rounds of SHA256.^{[2]} SHA256 and SHA512 are prone to length extension attacks. By guessing the hidden part of the state, length extension attacks on SHA224 and SHA384 succeed with probability 2^{−(256−224)} = 2^{−32} > 2^{−224} and 2^{−(512−384)} = 2^{−128} > 2^{−384} respectively. 
SHA2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA).^{[3]}. They are built using the Merkle–Damgård structure, from a Oneway compression function itself built using the DaviesMeyer 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.^{[4]} 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.
SHA2 includes significant changes from its predecessor, SHA1. The SHA2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA224, SHA256, SHA384, SHA512, SHA512/224, SHA512/256.
SHA256 and SHA512 are novel hash functions computed with 32bit and 64bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA224 and SHA384 are simply truncated versions of the first two, computed with different initial values. SHA512/224 and SHA512/256 are also truncated versions of SHA512, but the initial values are generated using the method described in Federal Information Processing Standards (FIPS) PUB 1804. SHA2 was published in 2001 by the National Institute of Standards and Technology (NIST) a U.S. federal standard (FIPS). The SHA2 family of algorithms are patented in US patent 6829355.^{[5]} The United States has released the patent under a royaltyfree license.^{[6]}
Currently, the best public attacks break preimage resistance for 52 out of 64 rounds of SHA256 or 57 out of 80 rounds of SHA512, and collision resistance for 46 out of 64 rounds of SHA256.^{[1]}^{[2]}
SHA256 and SHA512, and, to a lesser degree, SHA224 and SHA384 are prone to length extension attacks,^{[7]} rendering it insecure for some applications. It is thus generally recommended to switch to SHA3 for 512 bit hashes and to use SHA512/224 and SHA512/256 instead of SHA224 and SHA256. This also happens to be faster than SHA224 and SHA256 on x8664, since SHA512 works on 64 bit instead of 32 bit words.^{[8]}
With the publication of FIPS PUB 1802, NIST added three additional hash functions in the SHA family. The algorithms are collectively known as SHA2, named after their digest lengths (in bits): SHA256, SHA384, and SHA512.
The algorithms were first published in 2001 in the draft FIPS PUB 1802, at which time public review and comments were accepted. In August 2002, FIPS PUB 1802 became the new Secure Hash Standard, replacing FIPS PUB 1801, which was released in April 1995. The updated standard included the original SHA1 algorithm, with updated technical notation consistent with that describing the inner workings of the SHA2 family.^{[9]}
In February 2004, a change notice was published for FIPS PUB 1802, specifying an additional variant, SHA224, defined to match the key length of twokey Triple DES.^{[10]} In October 2008, the standard was updated in FIPS PUB 1803, including SHA224 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 800107 and 80057.^{[11]}^{[12]}^{[13]} Detailed test data and example message digests were also removed from the standard, and provided as separate documents.^{[14]}
In January 2011, NIST published SP800131A, which specified a move from the current minimum security of 80bits (provided by SHA1) allowable for federal government use until the end of 2013, with 112bit security (provided by SHA2) being the minimum requirement current thereafter, and the recommended security level from the publication date.^{[15]}
In March 2012, the standard was updated in FIPS PUB 1804, adding the hash functions SHA512/224 and SHA512/256, and describing a method for generating initial values for truncated versions of SHA512. 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 realtime video or audio feed. Padding the final data block must still occur prior to hash output.^{[16]}
In July 2012, NIST revised SP80057, which provides guidance for cryptographic key management. The publication disallows creation of digital signatures with a hash security lower than 112bits after 2013. The previous revision from 2007 specified the cutoff to be the end of 2010.^{[13]} In August 2012, NIST revised SP800107 in the same manner.^{[12]}
The NIST hash function competition selected a new hash function, SHA3, in 2012.^{[17]} The SHA3 algorithm is not derived from SHA2.
The SHA2 hash function is implemented in some widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, and IPsec.
SHA256 partakes in the process of authenticating Debian software packages^{[18]} and in the DKIM message signing standard; SHA512 is part of a system to authenticate archival video from the International Criminal Tribunal of the Rwandan genocide.^{[19]} SHA256 and SHA512 are proposed for use in DNSSEC.^{[20]} Unix and Linux vendors are moving to using 256 and 512bit SHA2 for secure password hashing.^{[21]}
Several cryptocurrencies like Bitcoin use SHA256 for verifying transactions and calculating proofofwork or proofofstake. The rise of ASIC SHA2 accelerator chips has led to the use of scryptbased proofofwork schemes.
SHA1 and SHA2 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 1801 also encouraged adoption and use of SHA1 by private and commercial organizations. SHA1 is being retired for most government uses; the U.S. National Institute of Standards and Technology says, "Federal agencies should stop using SHA1 for...applications that require collision resistance as soon as practical, and must use the SHA2 family of hash functions for these applications after 2010" (emphasis in original).^{[22]} NIST's directive that U.S. government agencies must stop uses of SHA1 after 2010^{[23]} was hoped to accelerate migration away from SHA1.
The SHA2 functions were not quickly adopted initially, despite better security than SHA1. Reasons might include lack of support for SHA2 on systems running Windows XP SP2 or older^{[24]} and a lack of perceived urgency since SHA1 collisions had not yet been found. The Google Chrome team announced a plan to make their web browser gradually stop honoring SHA1dependent TLS certificates over a period from late 2014 and early 2015.^{[25]}^{[26]}^{[27]} Similarly, Microsoft announced^{[28]} that Internet Explorer and Edge would stop honoring public SHA1signed TLS certificates from February 2017. Mozilla disabled SHA1 in early January 2016, but had to reenable it temporarily via a Firefox update, after problems with webbased user interfaces of some router models and security appliances.^{[29]}
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 2^{L} 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 2^{L/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 bruteforce 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.^{[30]}
Increased interest in cryptographic hash analysis during the SHA3 competition produced several new attacks on the SHA2 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 pseudocollision attacks could be extended to 52 rounds on SHA256 and 57 rounds on SHA512 by building upon the biclique pseudopreimage attack.^{[31]}
Published in  Year  Attack method  Attack  Variant  Rounds  Complexity 

New Collision Attacks Against Up To 24step SHA2^{[32]} 
2008  Deterministic  Collision  SHA256  24/64  2^{28.5} 
SHA512  24/80  2^{32.5}  
Preimages for stepreduced SHA2^{[33]}  2009  Meetinthemiddle  Preimage  SHA256  42/64  2^{251.7} 
43/64  2^{254.9}  
SHA512  42/80  2^{502.3}  
46/80  2^{511.5}  
Advanced meetinthemiddle preimage attacks^{[34]} 
2010  Meetinthemiddle  Preimage  SHA256  42/64  2^{248.4} 
SHA512  42/80  2^{494.6}  
HigherOrder Differential Attack on Reduced SHA256^{[2]} 
2011  Differential  Pseudocollision  SHA256  46/64  2^{178} 
33/64  2^{46}  
Bicliques for Preimages: Attacks on Skein512 and the SHA2 family^{[1]} 
2011  Biclique  Preimage  SHA256  45/64  2^{255.5} 
SHA512  50/80  2^{511.5}  
Pseudopreimage  SHA256  52/64  2^{255}  
SHA512  57/80  2^{511}  
Improving Local Collisions: New Attacks on Reduced SHA256^{[35]} 
2013  Differential  Collision  SHA256  31/64  2^{65.5} 
Pseudocollision  SHA256  38/64  2^{37}  
Branching Heuristics in Differential Collision Search with Applications to SHA512^{[36]} 
2014  Heuristic differential  Pseudocollision  SHA512  38/80  2^{40.5} 
Analysis of SHA512/224 and SHA512/256^{[37]}  2016  Differential  Collision  SHA256  28/64  practical 
SHA512  27/80  practical  
Pseudocollision  SHA512  39/80  practical 
Implementations of all FIPSapproved 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 SHA256 and over 900 of SHA512, with only 5 of them being capable of handling messages with a length in bits not a multiple of eight while supporting both variants.^{[38]}
Hash values of an empty string (i.e., a zerolength 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 SHA256 algorithm follows. Note the great increase in mixing between bits of the w[16..63]
words compared to SHA1.
Note 1: All variables are 32 bit unsigned integers and addition is calculated modulo 2^{32} 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: Bigendian 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 Preprocessing: 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 64bit bigendian integer, making the total postprocessed length a multiple of 512 bits Process the message in successive 512bit chunks: break message into 512bit chunks for each chunk create a 64entry message schedule array w[0..63] of 32bit 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[i15] rightrotate 7) xor (w[i15] rightrotate 18) xor (w[i15] rightshift 3) s1 := (w[i2] rightrotate 17) xor (w[i2] rightrotate 19) xor (w[i2] rightshift 10) w[i] := w[i16] + s0 + w[i7] + 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 (bigendian): digest := hash := h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7
The computation of the ch
and maj
values can be optimized the same way as described for SHA1.
SHA224 is identical to SHA256, except that:
h0
through h7
are different, andh7
.SHA224 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
SHA512 is identical in structure to SHA256, but:
SHA512 initial hash values (in bigendian): h[0..7] := 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179 SHA512 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] SHA512 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[i15] rightrotate 1) xor (w[i15] rightrotate 8) xor (w[i15] rightshift 7) s1 := (w[i2] rightrotate 19) xor (w[i2] rightrotate 61) xor (w[i2] rightshift 6)
SHA384 is identical to SHA512, except that:
h0
through h7
are different (taken from the 9th through 16th primes), andh6
and h7
.SHA384 initial hash values (in bigendian):
h[0..7] := 0xcbbb9d5dc1059ed8, 0x629a292a367cd507, 0x9159015a3070dd17, 0x152fecd8f70e5939,
0x67332667ffc00b31, 0x8eb44a8768581511, 0xdb0c2e0d64f98fa7, 0x47b5481dbefa4fa4
SHA512/t is identical to SHA512 except that:
h0
through h7
are given by the SHA512/t IV generation function,h0
through h7
at t bits,The SHA512/t IV generation function evaluates a modified SHA512 on the ASCII string "SHA512/t", substituted with the decimal representation of t. The modified SHA512 is the same as SHA512 except its initial values h0
through h7
have each been XORed with the hexadecimal constant 0xa5a5a5a5a5a5a5a5
.
Sample C implementation for SHA2 family of hash functions can be found in RFC 6234.
In the table below, internal state means the "internal hash sum" after each compression of a data block.
Algorithm and variant  Output size (bits) 
Internal state size (bits) 
Block size (bits) 
Max message size (bits) 
Rounds  Operations  Security bits (Info) 
Capacity against length extension attacks 
Performance on Skylake (median cpb)^{[39]}  First Published  

long messages  8 bytes  
MD5 (as reference)  128  128 (4 × 32) 
512  Unlimited^{[40]}  64  And, Xor, Rot, Add (mod 2^{32}), Or  <64 (collisions found) 
0  4.99  55.00  1992  
SHA0  160  160 (5 × 32) 
512  2^{64} − 1  80  And, Xor, Rot, Add (mod 2^{32}), Or  <34 (collisions found) 
0  ≈ SHA1  ≈ SHA1  1993  
SHA1  <63 (collisions found^{[41]}) 
3.47  52.00  1995  
SHA2  SHA224 SHA256 
224 256 
256 (8 × 32) 
512  2^{64} − 1  64  And, Xor, Rot, Add (mod 2^{32}), Or, Shr  112 128 
32 0 
7.62 7.63 
84.50 85.25 
2004 2001 
SHA384 SHA512 
384 512 
512 (8 × 64) 
1024  2^{128} − 1  80  And, Xor, Rot, Add (mod 2^{64}), Or, Shr  192 256 
128 (≤ 384) 0 
5.12 5.06 
135.75 135.50 

SHA512/224 SHA512/256 
224 256 
112 128 
288 256 
≈ SHA384  ≈ SHA384  
SHA3  SHA3224 SHA3256 SHA3384 SHA3512 
224 256 384 512 
1600 (5 × 5 × 64) 
1152 1088 832 576 
Unlimited^{[42]}  24^{[43]}  And, Xor, Rot, Not  112 128 192 256 
448 512 768 1024 
8.12 8.59 11.06 15.88 
154.25 155.50 164.00 164.00 
2015 
SHAKE128 SHAKE256 
d (arbitrary) d (arbitrary) 
1344 1088 
min(d/2, 128) min(d/2, 256) 
256 512 
7.08 8.59 
155.25 155.50 
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 SHA3.
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 x8664  MiB/s x8664 

Intel Ivy Bridge  3.5 GHz  SHA256  32bit  16.80  199  13.05  256 
SHA512  64bit  43.66  76  8.48  394  
AMD Piledriver APU  3.8 GHz  SHA256  32bit  22.87  158  18.47  196 
SHA512  64bit  88.36  41  12.43  292 
The performance numbers labeled 'x86' were running using 32bit code on 64bit processors, whereas the 'x8664' numbers are native 64bit code. While SHA256 is designed for 32bit calculations, it does benefit from code optimized for 64bit processors on the x86 architecture. 32bit implementations of SHA512 are significantly slower than their 64bit 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 SHA1 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 E31275 V2 at a clock speed of 3.5 GHz, and on their hydra9 system running an AMD A105800K APU at a clock speed of 3.8 GHz.^{[44]} 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.^{[45]} The MiB/s performance is extrapolated from the CPU clockspeed on a single core; realworld performance will vary due to a variety of factors.
sha1sum
(sha224sum
, sha256sum
, sha384sum
and sha512sum
) commandsIn the unlikely event that b is greater than 2^64, then only the loworder 64 bits of b are used.