# SHA-2

(Redirected from Sha-2)
SHA-2
General
Designers National Security Agency
First published 2001
Series (SHA-0), SHA-1, SHA-2, SHA-3
Certification FIPS PUB 180-4, CRYPTREC, NESSIE
Detail
Digest sizes 224, 256, 384, or 512 bits
Structure Merkle–Damgård construction
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.[1]

Pseudo collision attack against up to 46 rounds of SHA-256.[2]

SHA-2 is a set of cryptographic hash functions (SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256) designed by the U.S. National Security Agency (NSA) and published in 2001 by the NIST as a U.S. Federal Information Processing Standard (FIPS). SHA stands for Secure Hash Algorithm. SHA-2 includes a significant number of changes from its predecessor, SHA-1. SHA-2 currently consists of a set of six hash functions with digests that are 224, 256, 384 or 512 bits.

SHA-256 and SHA-512 are novel hash functions computed with 32 and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are simply truncated versions of the first two, computed with different initial values. SHA-512/224 and SHA-512/256 are also truncated versions of SHA-512, but the initial values are generated using the method described in FIPS PUB 180-4. The SHA-2 family of algorithms are patented in US 6829355 . The United States has released the patent under a royalty-free license.[3]

In 2005, security flaws were identified in SHA-1, namely that a mathematical weakness might exist, indicating that a stronger hash function would be desirable.[4] Although SHA-2 bears some similarity to the SHA-1 algorithm, these attacks have not been successfully extended to SHA-2.

Currently, the best public attacks break preimage resistance 52 rounds of SHA-256 or 57 rounds of SHA-512, and collision resistance for 46 rounds of SHA-256, as shown in the "Cryptanalysis and Validation" section below.[1][2]

## Hash standard

One iteration in a SHA-2 family compression function. The blue components perform the following operations:
$\operatorname{Ch}(E,F,G) = (E \and F) \oplus (\neg E \and G)$ $\operatorname{Ma}(A,B,C) = (A \and B) \oplus (A \and C) \oplus (B \and C)$ $\Sigma_0(A) = (A\!\ggg\!2) \oplus (A\!\ggg\!13) \oplus (A\!\ggg\!22)$ $\Sigma_1(E) = (E\!\ggg\!6) \oplus (E\!\ggg\!11) \oplus (E\!\ggg\!25)$
The bitwise rotation uses different constants for SHA-512. The given numbers are for SHA-256. The red $\color{red}\boxplus$ is addition modulo 232.

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.[5]

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.[6] 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.[7][8][9] Detailed test data and example message digests were also removed from the standard, and provided as separate documents.[10]

In January 2011, NIST published SP800-131A, which specified a move from the current minimum security of 80-bits (provided by SHA-1) allowable 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.[11]

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.[12]

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 112-bits after 2013. The previous revision from 2007 specified the cutoff to be the end of 2010.[9] In August 2012, NIST revised SP800-107 in the same manner.[8]

The NIST hash function competition selected a new hash function, SHA-3, in 2012.[13] The SHA-3 algorithm is not derived from SHA-2.

## 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 (bits) Internal state size (bits) Block size (bits) Max message size (bits) Word size (bits) Rounds Bitwise operations Collisions found Example Performance (MiB/s)[14]
MD5 (as reference) 128 128 512 264 − 1 32 64 and,or,xor,rot Yes 335
SHA-0 160 160 512 264 − 1 32 80 and,or,xor,rot Yes -
SHA-1 160 160 512 264 − 1 32 80 and,or,xor,rot Theoretical attack (261)[15] 192
SHA-2 SHA-224
SHA-256
224
256
256 512 264 − 1 32 64 and,or,xor,shr,rot None 139
SHA-384
SHA-512
SHA-512/224
SHA-512/256
384
512
224
256
512 1024 2128 − 1 64 80 and,or,xor,shr,rot None 154
SHA-3 224/256/384/512 1600
(5×5 array of 64-bit words)
1152/1088/832/576 64 24 and,xor,not,rot None

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.

The performance numbers above were for a single-threaded implementation on an AMD Opteron 8354 running at 2.2 GHz under Linux in 64-bit mode, and serve only as a rough point for general comparison. More detailed performance measurements on modern processor architectures are given in the table below.

CPU Architecture Frequency Algorithm Word size (bits) Cycles/Byte x86 MiB/s x86 Cycles/Byte x86-64 MiB/s x86-64
Intel Ivy Bridge 3.5 GHz SHA-256 32-bit 16.80 199 13.05 256
SHA-512 64-bit 43.66 76 8.48 394
AMD Piledriver 3.8 GHz SHA-256 32-bit 22.87 158 18.47 196
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. 32-bit implementations of SHA-512 are significantly slower than their 64-bit counterparts. Variants of both algorithms with different output sizes will perform similarly, since the message expansion and compression functions are identical, and only the initial hash values and output sizes are different. The best implementations of MD5 and SHA-1 perform between 4.5 and 6 cycles per byte on modern processors.

Testing was performed by the University of Illinois at Chicago on their hydra8 system running an Intel Xeon E3-1275 V2 at a clock speed of 3.5 GHz, and on their hydra9 system running an AMD A10-5800K at a clock speed of 3.8 GHz.[16] The referenced cycles per byte speeds above are the median performance of an algorithm digesting a 4096 byte message using the SUPERCOP cryptographic benchmarking software.[17] 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.

## Applications

The SHA-2 hash function is implemented in some widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, Bitcoin and IPsec.

Several cryptocurrencies use SHA-2 as part of their proof-of-work scheme. Bitcoin was the first to do this by using Hashcash with a double round of SHA-256 at its core. The rise of ASIC SHA-2 accelerator chips used in cryptocurrency mining has led to the use of scrypt based proof-of-work schemes for many alternative cryptocurrencies. SHA-256 is used to authenticate Debian GNU/Linux 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 moving to using 256- and 512-bit SHA-2 for secure password hashing.[21]

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).[22] NIST's directive that U.S. government agencies must stop uses of SHA-1 after 2010[23] and the completion of SHA-3[13] may accelerate migration away from SHA-1.

The SHA-2 functions are not as widely used as SHA-1, despite their better security. Reasons might include lack of support for SHA-2 on systems running Windows XP SP2 or older,[24] or a lack of perceived urgency since SHA-1 collisions have not yet been found.

## Cryptanalysis and validation

For a hash function for which L is the number of bits in the message digest, finding a message that corresponds to a given message digest can always be done using a brute force search in 2L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as a collision, requires on average only 2L/2 evaluations using a birthday attack.

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 a MD5 collision.[25]

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.[26]

Published in Year Attack Method Attack Variant Rounds Complexity
New Collision attacks Against
Up To 24-step SHA-2 [27]
2008 Deterministic Collision SHA-256 24/64 228.5
SHA-512 24/80 232.5
Preimages for step-reduced SHA-2 [28] 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
preimage attacks [29]
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 [2]
2011 Differential Pseudo Collision SHA-256 46/64 2178
46/64 246
Bicliques for Preimages: Attacks on
Skein-512 and the SHA-2 family [1]
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

### 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, in any way, the formal CMVP validation, which is required by law for 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 (see SHS Validation List).

## Examples of SHA-2 variants

Hash values of empty string.

```SHA224("")
0x d14a028c2a3a2bc9476102bb288234c415a2b01f828ea62ac5b3e42f
SHA256("")
0x e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855
SHA384("")
SHA512("")
0x cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e
SHA512/224("")
0x 6ed0dd02806fa89e25de060c19d3ac86cabb87d6a0ddd05c333b84f4
SHA512/256("")
```

Even a small change in the message will (with overwhelming probability) result in a mostly different hash, due to the avalanche effect. For example, adding a period to the end of the sentence:

```SHA224("The quick brown fox jumps over the lazy dog")
SHA224("The quick brown fox jumps over the lazy dog.")
0x 619cba8e8e05826e9b8c519c0a5c68f4fb653e8a3d8aa04bb2c8cd4c

SHA256("The quick brown fox jumps over the lazy dog")
0x d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592
SHA256("The quick brown fox jumps over the lazy dog.")
0x ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c

SHA384("The quick brown fox jumps over the lazy dog")
0x ca737f1014a48f4c0b6dd43cb177b0afd9e5169367544c494011e3317dbf9a509cb1e5dc1e85a941bbee3d7f2afbc9b1
SHA384("The quick brown fox jumps over the lazy dog.")
0x ed892481d8272ca6df370bf706e4d7bc1b5739fa2177aae6c50e946678718fc67a7af2819a021c2fc34e91bdb63409d7

SHA512("The quick brown fox jumps over the lazy dog")
0x 07e547d9586f6a73f73fbac0435ed76951218fb7d0c8d788a309d785436bbb642e93a252a954f23912547d1e8a3b5ed6e1bfd7097821233fa0538f3db854fee6
SHA512("The quick brown fox jumps over the lazy dog.")
0x 91ea1245f20d46ae9a037a989f54f1f790f0a47607eeb8a14d12890cea77a1bbc6c7ed9cf205e67b7f2b8fd4c7dfd3a7a8617e45f3c463d481c7e586c39ac1ed

SHA512/224("The quick brown fox jumps over the lazy dog")
0x 944cd2847fb54558d4775db0485a50003111c8e5daa63fe722c6aa37
SHA512/224("The quick brown fox jumps over the lazy dog.")
0x 6d6a9279495ec4061769752e7ff9c68b6b0b3c5a281b7917ce0572de

SHA512/256("The quick brown fox jumps over the lazy dog")
SHA512/256("The quick brown fox jumps over the lazy dog.")
0x 1546741840f8a492b959d9b8b2344b9b0eb51b004bba35c0aebaac86d45264c3
```

## 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 232
Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63
Note 3: The compression function uses 8 working variables, a through h
Note 4: Big-endian convention is used when expressing the constants in this pseudocode,
and when parsing message block data from bytes to words, for example,
the first word of the input message "abc" after padding is 0x61626380

Initialize hash values:
(first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):
h0 := 0x6a09e667
h1 := 0xbb67ae85
h2 := 0x3c6ef372
h3 := 0xa54ff53a
h4 := 0x510e527f
h5 := 0x9b05688c
h6 := 0x1f83d9ab
h7 := 0x5be0cd19

Initialize array of round constants:
(first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):
k[0..63] :=
0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2

Pre-processing:
append the bit '1' to the message
append k bits '0', where k is the minimum number >= 0 such that the resulting message
length (modulo 512 in bits) is 448.
append length of message (without the '1' bit or padding), in bits, as 64-bit big-endian integer
(this will make the entire post-processed length a multiple of 512 bits)

Process the message in successive 512-bit chunks:
break message into 512-bit chunks
for each chunk
create a 64-entry message schedule array w[0..63] of 32-bit words
(The initial values in w[0..63] don't matter, so many implementations zero them here)
copy chunk into first 16 words w[0..15] of the message schedule array

Extend the first 16 words into the remaining 48 words w[16..63] of the message schedule array:
for i from 16 to 63
s0 := (w[i-15] rightrotate 7) xor (w[i-15] rightrotate 18) xor (w[i-15] rightshift 3)
s1 := (w[i-2] rightrotate 17) xor (w[i-2] rightrotate 19) xor (w[i-2] rightshift 10)
w[i] := w[i-16] + s0 + w[i-7] + s1

Initialize working variables to current hash value:
a := h0
b := h1
c := h2
d := h3
e := h4
f := h5
g := h6
h := h7

Compression function main loop:
for i from 0 to 63
S1 := (e rightrotate 6) xor (e rightrotate 11) xor (e rightrotate 25)
ch := (e and f) xor ((not e) and g)
temp1 := h + S1 + ch + k[i] + w[i]
S0 := (a rightrotate 2) xor (a rightrotate 13) xor (a rightrotate 22)
maj := (a and b) xor (a and c) xor (b and c)
temp2 := S0 + maj

h := g
g := f
f := e
e := d + temp1
d := c
c := b
b := a
a := temp1 + temp2

Add the compressed chunk to the current hash value:
h0 := h0 + a
h1 := h1 + b
h2 := h2 + c
h3 := h3 + d
h4 := h4 + e
h5 := h5 + f
h6 := h6 + g
h7 := h7 + h

Produce the final hash value (big-endian):
digest := hash := h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7
```

The computation of the `ch` and `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 `h0` through `h7` are different, and
• the output is constructed by omitting `h7`.
```SHA-224 initial hash values (in big endian):
(The second 32 bits of the fractional parts of the square roots of the 9th through 16th primes 23..53)
h[0..7] :=
0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939, 0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4
```

SHA-512 is identical in structure to SHA-256, but:

• the message is broken into 1024-bit chunks,
• the initial hash values and round constants are extended to 64 bits,
• there are 80 rounds instead of 64,
• the round constants are based on the first 80 primes 2..409,
• the word size used for calculations is 64 bits long,
• the appended length of the message (before pre-processing), in bits, is a 128-bit big-endian integer, and
• the shift and rotate amounts used are different.
```SHA-512 initial hash values (in big-endian):

h[0..7] := 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,

SHA-512 round constants:

k[0..79] := [ 0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538,
0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118, 0xd807aa98a3030242, 0x12835b0145706fbe,
0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235,
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,
0x113f9804bef90dae, 0x1b710b35131c471b, 0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc,

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 16th primes), and
• the output is constructed by omitting `h6` 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 of `h0` 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.

## Notes

1. ^ a b c Dmitry Khovratovich, Christian Rechberger and Alexandra Savelieva (2011). "Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family". IACR Cryptology ePrint Archive. 2011:286.
2. ^ a b c Mario Lamberger and Florian Mendel (2011). "Higher-Order Differential Attack on Reduced SHA-256". IACR Cryptology ePrint Archive. 2011:37.
3. ^ Licensing Declaration for US patent 6829355.. Retrieved 2008-02-17.
4. ^ "Schneier on Security: Cryptanalysis of SHA-1". Schneier.com. Retrieved 2011-11-08.
5. ^ Federal Register Notice 02-21599, Announcing Approval of FIPS Publication 180-2
6. ^ FIPS 180-2 with Change Notice 1
7. ^ Federal Register Notice E8-24743, Announcing Approval of FIPS Publication 180-3
8. ^ a b
9. ^ a b FIPS SP 800-57 Recommendation for Key Management: Part 1: General
10. ^ NIST Algorithm Examples, Secure Hashing
11. ^
12. ^ Federal Register Notice 2012-5400, Announcing Approval of FIPS Publication 180-4
13. ^ a b NIST Selects Winner of Secure Hash Algorithm (SHA-3) Competition
14. ^ "Crypto++ 5.6.0 Benchmarks". Retrieved 2013-06-13.
15. ^ "Cryptanalysis of MD5 & SHA-1" (PDF). Retrieved 2013-04-25.
16. ^ SUPERCOP Benchmarks Measurements of hash functions, indexed by machine
17. ^ SUPERCOP Benchmarking Toolkit