SHA-2

SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA).[3]
Cryptographic hash functions are mathematical operations run on digital data; by comparing the computed "hash" (the output from execution of the Secure Hash
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 Algorithm
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 theircollision 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
Concepts
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 hash functions · SHA ·
values are generated using the method described in Federal Information Processing Standards(FIPS) PUB 180-4. SHA-2 was published in 2001 by the
DSA
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.[5] The United States has released the patent under a royalty-free license.
[6] Main standards
Currently, the best public attacks break preimage resistance for 52 out of 64 rounds of SHA-256 or 57 out of 80 rounds of SHA-512, and collision SHA-0 · SHA-1 · SHA-2 ·
resistance for 46 out of 64 rounds of SHA-256.[1][2] SHA-3
SHA-256 and SHA-512, and, to a lesser degree, SHA-224 and SHA-384 are prone to length extension attacks,[7] 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
[8]
and SHA-256. This also happens to be faster than SHA-224 and SHA-256 on x86-64, since SHA-512 works on 64 bit instead of 32 bit words. SHA-2
General
Designers National Security
Agency
Contents First 2001
Hash standard published
Applications Series (SHA-0), SHA-1,
Cryptanalysis and validation SHA-2, SHA-3
Official validation
Certification FIPS PUB 180-4,
Test vectors CRYPTREC, NESSIE
Pseudocode
Detail
Comparison of SHA functions
Digest sizes 224, 256, 384, or 512
See also
bits
References
Additional reading Structure Merkle–Damgård
construction with
External links
Davies–Meyer
compression function
Rounds 64 or 80
Hash standard
Best public cryptanalysis
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. A 2011 attack breaks preimage
resistance for 57 out of 80 rounds of
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, SHA-512, and 52 out of 64 rounds for
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 SHA-256.[1] Pseudo-collision attack
.[9]
the original SHA-1 algorithm, with updated technical notation consistent with that describing the inner workings of the SHA-2 family against up to 46 rounds of SHA-256.[2]

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 SHA-256 and SHA-512 are prone to
two-key Triple DES.[10] In October 2008, the standard was updated in FIPS PUB 180-3, including SHA-224 from the change notice, but otherwise length extension attacks. By
making no fundamental changes to the standard. The primary motivation for updating the standard was relocating security information about the hash guessing the hidden part of the
state, length extension attacks on
algorithms and recommendations for their use to Special Publications 800-107 and 800-57.[11][12][13] Detailed test data and example message digests
SHA-224 and SHA-384 succeed
[14]
were also removed from the standard, and provided as separate documents. with probability 2−(256−224) = 2−32 >
2−224 and 2−(512−384) = 2−128 > 2−384
In January 2011, NIST published SP800-131A, which specified a move from the current minimum security of 80-bits (provided by SHA-1) allowable respectively.
for federal government use until the end of 2013, with 112-bit security (provided by SHA-2) 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 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
[16]
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 disallows creation of digital signatures with a hash security lower than
12-bits
1 after
f to be the end of 2010.[13] In August 2012, NIST revised SP800-107 in the same manner
2013. The previous revision from 2007 specified the cutof .[12]

The NIST hash function competitionselected a new hash function,SHA-3, in 2012.[17] The SHA-3 algorithm is not derived from SHA-2.

Applications
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[18] 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.[19] SHA-256 and SHA-512 are proposed for use in DNSSEC.[20] Unix and Linux vendors are
[21]
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 ofscrypt-based proof-of-work schemes.

SHA-1 and SHA-2 are the Secure Hash Algorithmsrequired 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).[22] NIST's
directive that U.S. government agencies must stop uses of SHA-1 after 2010[23] was hoped to accelerate migration
away from SHA-1. One iteration in a SHA-2 family compression function. The blue
components perform the following operations:
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[24] 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.[25][26][27]
Similarly, Microsoft announced[28] that Internet Explorer and Edge would stop honouring public SHA-1-signed TLS The bitwise rotation uses different constants for SHA-512. The given
numbers are for SHA-256.
certificates from February 2017. Mozilla disabled SHA-1 in early January 2016, but had to re-enable it temporarily
The red is addition modulo 232 for SHA-256, or 264 for SHA-512.
via a Firefox update, after problems with web-based user interfaces of some router models and security
appliances.[29]

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 acollision, 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 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 forged SSL certificates using
[30]
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.[31]

Published in Year Attack method Attack Variant Rounds Complexity

New Collision Attacks Against SHA-256 24/64 228.5

2008 Deterministic Collision
Up To 24-step SHA-2[32] SHA-512 24/80 232.5

42/64 2251.7
SHA-256
43/64 2254.9
Preimages for step-reduced SHA-2[33] 2009 Meet-in-the-middle Preimage
42/80 2502.3
SHA-512
46/80 2511.5

Advanced meet-in-the-middle SHA-256 42/64 2248.4

2010 Meet-in-the-middle Preimage
preimage attacks[34] SHA-512 42/80 2494.6

Higher-Order Differential Attack 46/64 2178

2011 Differential Pseudo-collision SHA-256
on Reduced SHA-256[2] 33/64 246

SHA-256 45/64 2255.5

Preimage
Bicliques for Preimages: Attacks on SHA-512 50/80 2511.5
2011 Biclique
Skein-512 and the SHA-2 family[1] SHA-256 52/64 2255
Pseudo-preimage
SHA-512 57/80 2511

Improving Local Collisions: New Collision SHA-256 31/64 265.5

2013 Differential
Attacks on Reduced SHA-256[35] Pseudo-collision SHA-256 38/64 237
Branching Heuristics in Differential Collision
2014 Heuristic differential Pseudo-collision SHA-512 38/80 240.5
Search with Applications to SHA-512[36]
SHA-256 28/64 practical
Collision
Analysis of SHA-512/224 and SHA-512/256[37] 2016 Differential SHA-512 27/80 practical
Pseudo-collision SHA-512 39/80 practical

Official validation
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 forertain
c 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.[38]

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 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
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 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: 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:
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:

 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 thech and maj values can be optimized the same wayas described for SHA-1.

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

the initial hash values h0 through h7 are 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 := (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 h0 through h7 are different (taken from the 9th through 16thprimes), and
the output is constructed by omittingh6 and h7.

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 h0 through h7 are given by the SHA-512/t IV generation function,
the output is constructed by truncating the concatenation ofh0 through h7 at 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 functionevaluates 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 valuesh0 through h7 have each been XORed with the hexadecimal constant0xa5a5a5a5a5a5a5a5.

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.
 Comparison of SHA functions
Performance on
Capacity Skylake (median
Max against cpb)[39]
Output Internal Block message Security length
size state size size size bits extension long First
Algorithm and variant (bits) (bits) (bits) (bits) Rounds Operations (Info) attacks messages 8 bytes Published
MD5 (as reference) 128 128 512 Unlimited[40] 64 And, Xor, Rot, <64 4.99 55.00 1992
(4 × 32) Add (mod 232), (collisions 0
Or found)

SHA-0 160 160 512 264 − 1 80 And, Xor, Rot, <34 ≈ SHA-1 ≈ SHA-1 1993
(5 × 32) Add (mod 232), (collisions
Or found)
0
SHA-1 <63 3.47 52.00 1995
(collisions
found[41] )
SHA-2 SHA-224 224 256 512 264 − 1 64 And, Xor, Rot,
112 32
7.62 84.50 2004
SHA-256 256 (8 × 32) Add (mod 232), 128 0
7.63 85.25 2001
Or, Shr
SHA-384 384 512 1024 2128 − 1 80 And, Xor, Rot, 192 128 (≤ 384) 5.12 135.75
SHA-512 512 (8 × 64) Add (mod 264), 256 0 5.06 135.50
Or, Shr
SHA-512/224 224 112 288 ≈ SHA-384 ≈ SHA-384
SHA-512/256 256 128 256
SHA-3 SHA3-224 224 1600 1152 Unlimited[42] 24[43] And, Xor, Rot, 112 448 8.12 154.25 2015
SHA3-256 256 (5 × 5 × 64) 1088 Not 128 512 8.59 155.50
SHA3-384 384 832 192 768 11.06 164.00
SHA3-512 512 576 256 1024 15.88 164.00
SHAKE128 d (arbitrary) 1344 min(d/2, 128) 256 7.08 155.25
SHAKE256 d (arbitrary) 1088 min(d/2, 256) 512 8.59 155.50

In the bitwise operations column, "Rot" stands forrotate no carry, and "Shr" stands for right logical shift. All of these algorithms employmodular 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
SHA-256 32-bit 16.80 199 13.05 256
Intel Ivy Bridge 3.5 GHz
SHA-512 64-bit 43.66 76 8.48 394
SHA-256 32-bit 22.87 158 18.47 196
AMD Piledriver APU 3.8 GHz
SHA-512 64-bit 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 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.[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; real-world performance will vary due to a variety of factors.

See also
Comparison of cryptographic hash functions
Hash-based message authentication code
Hashcash
International Association for Cryptologic Research(IACR)
sha1sum (sha224sum, sha256sum, sha384sum and sha512sum) commands
Trusted timestamping

References
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2. Mario Lamberger & Florian Mendel (2011)."Higher-Order Differential Attack on (https://federalregister.gov/a/E8-24743)
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9. Federal Register Notice 02-21599,Announcing Approval of FIPS Publication 180-2 ist.gov/itl/csd/sha-100212.cfm). Retrieved 24 February 2015.
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e.com/codesearch/p?hl=en#nywQboHfkw4/apt/apt-pkg/acquire-item.cc&q=SHA256) 78-3-642-10366-7_34). Advances in Cryptology –ASIACRYPT 2009. Lecture Notes
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w.nytimes.com/2009/01/27/science/27arch.html), New York Times, January 26, 2009 642-10366-7. ISSN 0302-9743 (https://www.worldcat.org/issn/0302-9743).
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21. Ulrich Drepper, Unix crypt with SHA-256/512(http://people.redhat.com/drepper/sha-c
on MD4 and SHA-2" (http://eprint.iacr.org/2010/016.pdf) (PDF). Advances in
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echnology Computer Security Resource Center, Heidelberg. 6477: 56–75. doi:10.1007/978-3-642-17373-8_4(https://doi.org/10.100
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Retrieved 2010-11-25. New Attacks on Reduced SHA-256"(https://online.tugraz.at/tug_online/voe_main2.g
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Additional 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. Retrieved
2007-04-26.

External links
Descriptions of SHA-256, SHA-384, and SHA-512from NIST
SHA-2 Checker – SHAChecker check your 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, 1.7 MB) – Current version of the Secure Hash Standard (SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512), March
2012
Test vectors for SHA-256/384/512from the NESSIE project
Test vectors for SHA-1, SHA-2from NIST site
NIST Cryptographic Hash ProjectSHA-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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