SHA-2

Secure Hash Algorithms
Concepts
hash functions,SHA,DSA
Main standards
SHA-0,SHA-1,SHA-2,SHA-3

SHA-2

General
Designers	National Security Agency
First published	2001(2001)
Series	(SHA-0),SHA-1,SHA-2,SHA-3
Certification	FIPSPUB 180-4,CRYPTREC,NESSIE
Detail
Digest sizes	224, 256, 384, or 512 bits
Structure	Merkle–Damgård constructionwithDavies–Meyer compression function
Rounds	64 or 80
Best publiccryptanalysis
A 2011 attack breakspreimage resistancefor 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 tolength 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> 2−224and 2−(512−384)= 2−128> 2−384respectively.

SHA-2(Secure Hash Algorithm2) is a set ofcryptographic hash functionsdesigned by the United StatesNational Security Agency(NSA) and first published in 2001.They are built using theMerkle–Damgård construction,from a one-way compression function itself built using theDavies–Meyer structurefrom a specialized block cipher.

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 whose digests are eight 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 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 inFederal Information Processing Standards(FIPS) PUB 180-4.

SHA-2 was first published by theNational Institute of Standards and Technology(NIST) as a U.S. federal standard. The SHA-2 family of algorithms are patented in the U.S.The United States has released the patent under aroyalty-freelicense.

As of 2011, the best public attacks breakpreimage resistancefor 52 out of 64 rounds of SHA-256 or 57 out of 80 rounds of SHA-512, andcollision resistancefor 46 out of 64 rounds of SHA-256.

Hash standard

One iteration in a SHA-2 family compression function. The blue components perform the following operations:
$\operatorname {Ch} (E,F,G)=(E\land F)\oplus (\neg E\land G)$
$\operatorname {Ma} (A,B,C)=(A\land B)\oplus (A\land C)\oplus (B\land C)$
$\Sigma _{0}(A)=(A\!\ggg \!2)\oplus (A\!\ggg \!13)\oplus (A\!\ggg \!22)$
$\Sigma _{1}(E)=(E\!\ggg \!6)\oplus (E\!\ggg \!11)\oplus (E\!\ggg \!25)$
The bitwise rotation uses different constants for SHA-512. The given numbers are for SHA-256.
The red$\color {red}\boxplus$is addition modulo 2³²for SHA-256, or 2⁶⁴for SHA-512.

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 newSecure 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-keyTriple 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 recommendedsecurity 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 onpaddingthe 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.

TheNIST hash function competitionselected a new hash function,SHA-3,in 2012.The SHA-3 algorithm is not derived from SHA-2.

Applications

Further information:Cryptographic hash function § Applications

The SHA-2 hash function is implemented in some widely used security applications and protocols, includingTLSandSSL,PGP,SSH,S/MIME,andIPsec.The inherent computational demand of SHA-2 algorithms has driven the proposal of more efficient solutions, such as those based on application-specific integrated circuits (ASICs) hardware accelerators.

SHA-256 is used for authenticatingDebiansoftware packagesand in theDKIMmessage signing standard; SHA-512 is part of a system to authenticate archival video from theInternational Criminal Tribunal of the Rwandan genocide.SHA-256 and SHA-512 are proposed for use inDNSSEC.Unix and Linux vendors are moving to using 256- and 512-bit SHA-2 for secure password hashing.

Severalcryptocurrencies,includingBitcoin,use SHA-256 for verifying transactions and calculatingproof of workorproof of stake.The rise ofASICSHA-2 accelerator chips has led to the use ofscrypt-based proof-of-work schemes.

SHA-1 and SHA-2 are theSecure Hash Algorithmsrequired by law for use in certainU.S. Governmentapplications, 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 agenciesshouldstop 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 ought to, but not explicitly must, stop uses of SHA-1 after 2010was 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 olderand a lack of perceived urgency since SHA-1 collisions had not yet been found. TheGoogle Chrometeam 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 announcedthatInternet ExplorerandEdgewould stop honoring public SHA-1-signed TLS certificates from February 2017.Mozilladisabled SHA-1 in early January 2016, but had to re-enable it temporarily via aFirefoxupdate, after problems with web-based user interfaces of some router models andsecurity appliances.

Cryptanalysis and validation

For a hash function for whichLis the number ofbitsin themessage digest,finding a message that corresponds to a given message digest can always be done using abrute forcesearch in 2^Levaluations. This is called apreimage attackand may or may not be practical depending onLand the particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as acollision,requires on average only 2^L/2evaluations using abirthday attack.

Some of the applications that use cryptographic hashes, such as password storage, are only minimally affected by acollision 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 theshadowfile) 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 onweak 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 forgedSSLcertificates using anMD5collision 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.

AtFSE2012, researchers atSonygave a presentation suggesting pseudo-collision attacks could be extended to 52 rounds on SHA-256 and 57 rounds on SHA-512 by building upon thebicliquepseudo-preimage attack.

Published in	Year	Attack method	Attack	Variant	Rounds	Complexity
New Collision Attacks Against Up To 24-step SHA-2	2008	Differential	Collision	SHA-256	24/64	215.5
				SHA-512	24/80	222.5
Preimages for step-reduced SHA-2	2009	Meet-in-the-middle	Preimage	SHA-256	42/64	2251.7
					43/64	2254.9
				SHA-512	42/80	2502.3
					46/80	2511.5
Advanced meet-in-the-middle preimage attacks	2010	Meet-in-the-middle	Preimage	SHA-256	42/64	2248.4
				SHA-512	42/80	2494.6
Higher-Order Differential Attack on Reduced SHA-256	2011	Differential	Pseudo-collision	SHA-256	46/64	2178
					33/64	246
Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family	2011	Biclique	Preimage	SHA-256	45/64	2255.5
				SHA-512	50/80	2511.5
			Pseudo-preimage	SHA-256	52/64	2255
				SHA-512	57/80	2511
Improving Local Collisions: New Attacks on Reduced SHA-256	2013	Differential	Collision	SHA-256	31/64	265.5
			Pseudo-collision	SHA-256	38/64	237
Branching Heuristics in Differential Collision Search with Applications to SHA-512	2014	Heuristic differential	Pseudo-collision	SHA-512	38/80	240.5
Analysis of SHA-512/224 and SHA-512/256	2016	Differential	Collision	SHA-256	28/64	practical
				SHA-512	27/80	practical
			Pseudo-collision	SHA-512	39/80	practical
New Records in Collision Attacks on SHA-2	2023	Differential	Collision	SHA-256	31/64	249.8
				SHA-512	31/80	2115.6
			Pseudo-collision	SHA-256	39/64	practical

Official validation

Main article:Cryptographic Module Validation Program

Implementations of all FIPS-approved security functions can be officially validated through theCMVP program,jointly run by theNational Institute of Standards and Technology(NIST) and theCommunications 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 lawfor certain applications.

As of December 2013,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.

Test vectors

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 different hash, due to theavalanche effect.For example, adding a period to the end of the following sentence changes approximately half (111 out of 224) of the bits in the hash, equivalent to picking a new hash at random:

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

Pseudocodefor the SHA-256 algorithm follows. Note the great increase in mi xing between bits of thew[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 thefractional partsof 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 thefractional partsof 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
such that the bits in the message are: <original message of length L> 1 <K zeros> <L as 64 bit integer>, (the number of bits will be a multiple of 512)

Process the message in successive 512-bit chunks:
break message into 512-bit chunks
foreach 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:
forifrom16 to 63
s0:= (w[i-15]rightrotate7)xor(w[i-15]rightrotate18)xor(w[i-15]rightshift3)
s1:= (w[i-2]rightrotate17)xor(w[i-2]rightrotate19)xor(w[i-2]rightshift10)
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:
forifrom0 to 63
S1:= (erightrotate6)xor(erightrotate11)xor(erightrotate25)
ch:= (eandf)xor((note)andg)
temp1:= h+S1+ch+k[i]+w[i]
S0:= (arightrotate2)xor(arightrotate13)xor(arightrotate22)
maj:= (aandb)xor(aandc)xor(bandc)
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:= h0appendh1appendh2appendh3appendh4appendh5appendh6appendh7

The computation of thechandmajvalues can be optimized the same wayas described for SHA-1.

SHA-224 is identical to SHA-256, except that:

• the initial hash valuesh0throughh7are different, and
• the output is constructed by omittingh7.

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), inbits,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:= (arightrotate28)xor(arightrotate34)xor(arightrotate39)
S1:= (erightrotate14)xor(erightrotate18)xor(erightrotate41)

s0:= (w[i-15]rightrotate1)xor(w[i-15]rightrotate8)xor(w[i-15]rightshift7)
s1:= (w[i-2]rightrotate19)xor(w[i-2]rightrotate61)xor(w[i-2]rightshift6)

SHA-384 is identical to SHA-512, except that:

• the initial hash valuesh0throughh7are different (taken from the 9th through 16th primes), and
• the output is constructed by omittingh6andh7.

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 valuesh0throughh7are given by theSHA-512/t IV generation function,
• the output is constructed by truncating the concatenation ofh0throughh7attbits,
• tequal to 384 is not allowed, instead SHA-384 should be used as specified, and
• tvalues 224 and 256 are especially mentioned as approved.

TheSHA-512/t IV generation functionevaluates amodified SHA-512on the ASCII string "SHA-512/t",substituted with the decimal representation oft.Themodified SHA-512is the same as SHA-512 except its initial valuesh0throughh7have each beenXORedwith the hexadecimal constant0xa5a5a5a5a5a5a5a5.

Sample C implementation for SHA-2 family of hash functions can be found inRFC6234.

Comparison of SHA functions

In the table below,internal statemeans the "internal hash sum" after each compression of a data block.

Further information:Merkle–Damgård construction

Comparison of SHA functions

Algorithm and variant		Output size (bits)	Internal state size (bits)	Block size (bits)	Rounds	Operations	Security againstcollision attacks (bits)	Security againstlength extension attacks (bits)	Performance onSkylake(mediancpb)		First published
									Long messages	8 bytes
MD5(as reference)		128	128 (4 × 32)	512	4 (16 operationsin each round)	And, Xor, Or, Rot,Add (mod 232)	≤ 18 (collisions found)	0	4.99	55.00	1992
SHA-0		160	160 (5 × 32)	512	80	And, Xor, Or, Rot,Add (mod 232)	< 34 (collisions found)	0	≈ SHA-1	≈ SHA-1	1993
SHA-1							< 63 (collisions found)		3.47	52.00	1995
SHA-2	SHA-224 SHA-256	224 256	256 (8 × 32)	512	64	And, Xor, Or, Rot, Shr,Add (mod 232)	112 128	32 0	7.62 7.63	84.50 85.25	2004 2001
	SHA-384	384	512 (8 × 64)	1024	80	And, Xor, Or, Rot, Shr,Add (mod 264)	192	128	5.12	135.75	2001
	SHA-512	512					256	0	5.06	135.50	2001
	SHA-512/224 SHA-512/256	224 256					112 128	288 256	≈ SHA-384	≈ SHA-384	2012
SHA-3	SHA3-224 SHA3-256 SHA3-384 SHA3-512	224 256 384 512	1600 (5 × 5 × 64)	1152 1088 832 576	24	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 forrotate no carry,and "Shr" stands forright logical shift.All of these algorithms employmodular additionin 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/bytex86	MiB/s x86	Cycles/bytex86-64	MiB/s x86-64
Intel Ivy Bridge	3.5 GHz	SHA-256	32	16.80	199	13.05	256
		SHA-512	64	43.66	76	8.48	394
AMD PiledriverAPU	3.8 GHz	SHA-256	32	22.87	158	18.47	196
		SHA-512	64	88.36	41	12.43	292

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 theUniversity of Illinois at Chicagoon 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.

Implementations

Below is a list of cryptography libraries that support SHA-2:

• Botan
• Bouncy Castle
• Cryptlib
• Crypto++
• Libgcrypt
• Mbed TLS
• libsodium
• Nettle
• LibreSSL
• OpenSSL
• GnuTLS
• wolfSSL

Hardware acceleration is provided by the following processor extensions:

• Intel SHA extensions:Available on some Intel and AMD x86 processors.
• VIA PadLock
• ARMv8 Cryptography Extensions
• IBMz/Architecture:Available since 2005 as part of the Message-Security-Assist Extensions 1 (SHA-256) and 2 (SHA-512)
• IBMPower ISAsince v.2.07

See also

• Comparison of cryptographic hash functions
• Comparison of cryptography libraries
• Hash function security summary
• Hashcash
• HMAC
• International Association for Cryptologic Research(IACR)
• Trusted timestamping

Further reading

• Henri Gilbert, Helena Handschuh: Security Analysis of SHA-256 and Sisters.Selected Areas in Cryptography2003: pp175–193
• "Proposed Revision of Federal Information Processing Standard (FIPS) 180, Secure Hash Standard".Federal Register.59(131): 35317–35318. 1994-07-11.Archivedfrom the original on 2020-07-28.Retrieved2007-04-26.

External links

• Descriptions of SHA-256, SHA-384, and SHA-512fromNIST
• SHA-2 Checker– SHAChecker to check one's SSL compatibility for SHA-2
• SHA-256 Calculator– SHA-256 Calculator
• SHA-256 Hash Generator– SHA256 Generator – Also serves other critical secure hash algorithms
• Specifications for a Secure Hash Standard (SHS)– Draft for proposed SHS (SHA-0)
• Secure Hash Standard (SHS)– Proposed SHS (SHA-0)
• CSRC Cryptographic Toolkit– OfficialNISTsite 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-256/384/512from theNESSIEproject
• Test vectors for SHA-1, SHA-2fromNISTsite
• NIST Cryptographic Hash Project– SHA-3 competition
• RFC3874:"A 224-bit One-way Hash Function: SHA-224"
• RFC6234:"US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)"; contains sample C implementation
• SHA-256 algorithm demonstration