# SHA-2

(Redirected from SHA384)
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 with Davies–Meyer compression function
Rounds 64 or 80
Best public cryptanalysis

A 2011 attack breaks preimage resistance for 57 out of 80 rounds of SHA-512, and 52 out of 64 rounds for SHA-256.[1]

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

SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the National Security Agency (NSA).[3] SHA stands for Secure Hash Algorithm. 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.

SHA-2 includes significant changes from its predecessor, SHA-1. The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256.

SHA-256 and SHA-512 are novel hash functions computed with 32-bit and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are simply truncated versions of 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 Federal Information Processing Standards (FIPS) PUB 180-4. SHA-2 was published in 2001 by the National Institute of Standards and Technology (NIST) a U.S. federal standard (FIPS). The SHA-2 family of algorithms are patented in US patent 6829355.[5] The United States has released the patent under a royalty-free license.[6]

In 2005, an algorithm emerged for finding SHA-1 collisions in about 2,000-times fewer steps than was previously thought possible.[7] Although (as of 2015) no example of a SHA-1 collision has been published yet, the security margin left by SHA-1 is weaker than intended, and its use is therefore no longer recommended for applications that depend on collision resistance, such as digital signatures. 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 for 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:
${\displaystyle \operatorname {Ch} (E,F,G)=(E\land F)\oplus (\neg E\land G)}$
${\displaystyle \operatorname {Ma} (A,B,C)=(A\land B)\oplus (A\land C)\oplus (B\land C)}$
${\displaystyle \Sigma _{0}(A)=(A\!\ggg \!2)\oplus (A\!\ggg \!13)\oplus (A\!\ggg \!22)}$
${\displaystyle \Sigma _{1}(E)=(E\!\ggg \!6)\oplus (E\!\ggg \!11)\oplus (E\!\ggg \!25)}$
The bitwise rotation uses different constants for SHA-512. The given numbers are for SHA-256. The red ${\displaystyle \color {red}\boxplus }$ 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.[8]

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.[9] 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.[10][11][12] Detailed test data and example message digests were also removed from the standard, and provided as separate documents.[13]

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.[14]

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.[15]

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.[12] In August 2012, NIST revised SP800-107 in the same manner.[11]

The NIST hash function competition selected a new hash function, SHA-3, in 2012.[16] The SHA-3 algorithm is not derived from SHA-2.

## Applications

For more details on this topic, see Cryptographic hash function § 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 GNU/Linux software packages[17] 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.[18] SHA-256 and SHA-512 are proposed for use in DNSSEC.[19] Unix and Linux vendors are moving to using 256- and 512-bit SHA-2 for secure password hashing.[20]

Several cryptocurrencies like Bitcoin use SHA-256 for verifying transactions and calculating proof-of-work or proof-of-stake. The rise of ASIC SHA-2 accelerator chips has led to the use of scrypt-based proof-of-work schemes.

SHA-1 and SHA-2 are the secure hash algorithms required by law for use in certain U.S. Government applications, including use within other cryptographic algorithms and protocols, for the protection of sensitive unclassified information. FIPS PUB 180-1 also encouraged adoption and use of SHA-1 by private and commercial organizations. SHA-1 is being retired for most government uses; the U.S. National Institute of Standards and Technology says, "Federal agencies should stop using SHA-1 for...applications that require collision resistance as soon as practical, and must use the SHA-2 family of hash functions for these applications after 2010" (emphasis in original).[21] NIST's directive that U.S. government agencies must stop uses of SHA-1 after 2010[22] was hoped to accelerate migration away from SHA-1.

The SHA-2 functions were not quickly adopted, despite better security than SHA-1. Reasons might include lack of support for SHA-2 on systems running Windows XP SP2 or older[23] and a lack of perceived urgency since SHA-1 collisions have 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.[24][25][26]

## 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.

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.[27]

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.[28]

Published in Year Attack method Attack Variant Rounds Complexity
New Collision Attacks Against
Up To 24-step SHA-2
[29]
2008 Deterministic Collision SHA-256 24/64 228.5
SHA-512 24/80 232.5
Preimages for step-reduced SHA-2[30] 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
[31]
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
33/64 246
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
Improving Local Collisions: New
Attacks on Reduced SHA-256
[32]
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
[33]
2014 Heuristic differential Pseudo-collision SHA-512 38/80 240.5
Analysis of SHA-512/224 and SHA-512/256[34] 2016 Differential Collision SHA-256 28/64 practical
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 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).

## Test vectors

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 this sentence changes 111 out of 224 bits in the hash:

```SHA224("The quick brown fox jumps over the lazy dog")
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 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 message schedule array w has 80 64-bit words instead of 64 32-bit words,
• to extend the message schedule array w, the loop is from 16 to 79 instead of from 16 to 63,
• the round constants are based on the first 80 primes 2..409,
• the word size used for calculations is 64 bits long,
• the appended length of the message (before pre-processing), in bits, is a 128-bit big-endian integer, and
• the shift and rotate amounts used are different.
```SHA-512 initial hash values (in big-endian):

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

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.

The SHA-512/t IV generation function evaluates a modified SHA-512 on the ASCII string "SHA-512/t", substituted with the decimal representation of t. The modified SHA-512 is the same as SHA-512 except its initial values `h0` through `h7` have each been XORed with the hexadecimal constant `0xa5a5a5a5a5a5a5a5`.

### C++ Implementation

```#include <cstring> // memcpy, memset
#define ROL(v, c) (((v) << (c)) | ((v) >> ((sizeof(v) * 8) - (c))))
#define ROR(v, c) (((v) >> (c)) | ((v) << ((sizeof(v) * 8) - (c))))

// len usually does not include null terminator; o1 is the most significant dword, 07 the least
void __cdecl SHA256(const char *src, unsigned int len, unsigned int *o0, unsigned int *o1, unsigned int *o2, unsigned int *o3, unsigned int *o4, unsigned int *o5, unsigned int *o6, unsigned int *o7)
{
unsigned int h0 = 1779033703;
unsigned int h1 = -1150833019;
unsigned int h2 = 1013904242;
unsigned int h3 = -1521486534;
unsigned int h4 = 1359893119;
unsigned int h5 = -1694144372;
unsigned int h6 = 528734635;
unsigned int h7 = 1541459225;

const int k[64] = {
1116352408, 1899447441, -1245643825, -373957723,
961987163, 1508970993, -1841331548, -1424204075,
-670586216, 310598401, 607225278, 1426881987,
1925078388, -2132889090, -1680079193, -1046744716,
-459576895, -272742522, 264347078, 604807628,
770255983, 1249150122, 1555081692, 1996064986,
-1740746414, -1473132947, -1341970488, -1084653625,
-958395405, -710438585, 113926993, 338241895,
666307205, 773529912, 1294757372, 1396182291,
1695183700, 1986661051, -2117940946, -1838011259,
-1564481375, -1474664885, -1035236496, -949202525,
-778901479, -694614492, -200395387, 275423344,
430227734, 506948616, 659060556, 883997877,
958139571, 1322822218, 1537002063, 1747873779,
1955562222, 2024104815, -2067236844, -1933114872,
-1866530822, -1538233109, -1090935817, -965641998 };

unsigned int width = (len + 63) & 0xFFFFFFC0;
if (!((len + 63) & 0xFFFFFFC0))
width = 64;
if ((len & 0x7F) > 0x38)
width += 64;

unsigned int *msg = new unsigned int[width << 2];
memset(msg, 0, width);
memcpy(msg, src, len);

// append 1
*((char *)msg + len) = -128;

// append length in big endian
*((char *)msg + width - 1) = 8 * len;
*((char *)msg + width - 2) = (8 * len) >> 8;
*((char *)msg + width - 3) = (8 * len) >> 16;
*((char *)msg + width - 4) = (8 * len) >> 24;

unsigned int w[64];
unsigned char lsb; int other, s1, offset;
unsigned int value, def;
unsigned int t1, t2, a, b, c, d, e, f, g, h;

unsigned int blocks = width >> 6;
if (blocks)
{
int chunk = (int)((char *)msg + 2);
do
{
unsigned int r = 0;
do // w[0] -- w[15]
{
// must be in big endian
lsb = *(char *)(chunk + 1);
other = (*(char *)chunk |
(((*(char *)(chunk - 2) << 8) |
*(char *)(chunk - 1)) << 8)) << 8;
chunk += 4;
w[r++] = lsb | other;
} while (r < 0x10);

unsigned int *set = &w[14];
r = 48;
do // w[16] -- w[63]
{
value = *set; ++set;
def = *(set - 14);
s1 = (value >> 10) ^ ROL(value, 13) ^ ROL(value, 15);
set[1] = *(set - 6) + *(set - 15) +
((def >> 3) ^ ROR(def, 7) ^ ROL(*(set - 14), 14)) + s1;
--r;
} while (r);

a = h0; b = h1; c = h2; d = h3; e = h4; f = h5; g = h6; h = h7;

offset = 0;
do // SHA-256 compression function
{
t1 = h + *(int *)((char *)k + offset) + *(unsigned int *)((char *)w + offset) +
(e & f ^ g & ~e) + (ROR(e, 6) ^ ROL(e, 7) ^ ROR(e, 11));
t2 = (a & b ^ c & (a ^ b)) + (ROR(a, 2) ^ ROL(a, 10) ^ ROR(a, 13));
h = g; g = f; f = e; e = d + t1; d = c; c = b; b = a; a = t1 + t2;

offset += 4;
} while (offset < 0x100);

h0 += a; h1 += b; h2 += c; h3 += d; h4 += e; h5 += f; h6 += g; h7 += h;

} while (!(blocks--));
}

delete[] msg;
*o0 = h0; *o1 = h1; *o2 = h2; *o3 = h3; *o4 = h4; *o5 = h5; *o6 = h6; *o7 = h7;
}
```

## Comparison of SHA functions

In the table below, internal state means 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)
Max message size
(bits)
Rounds Operations Security
(bits)
Example performance[36]
(MiB/s)
MD5 (as reference) 128 128
(4 × 32)
512 Unlimited[37] 64 And, Xor, Rot, Add (mod 232), Or <64
(collisions found)
335
SHA-0 160 160
(5 × 32)
512 264 − 1 80 And, Xor, Rot, Add (mod 232), Or <80
(collisions found)
-
SHA-1 160 160
(5 × 32)
512 264 − 1 80 <80
(theoretical attack[38])
192
SHA-2 SHA-224
SHA-256
224
256
256
(8 × 32)
512 264 − 1 64 And, Xor, Rot, Add (mod 232), Or, Shr 112
128
139
SHA-384
SHA-512
SHA-512/224
SHA-512/256
384
512
224
256
512
(8 × 64)
1024 2128 − 1 80 And, Xor, Rot, Add (mod 264), Or, Shr 192
256
112
128
154
SHA-3 SHA3-224
SHA3-256
SHA3-384
SHA3-512
224
256
384
512
1600
(5 × 5 × 64)
1152
1088
832
576
Unlimited[39] 24[40] And, Xor, Rot, Not 112
128
192
256
-
SHAKE128
SHAKE256
d (arbitrary)
d (arbitrary)
1344
1088
min(d/2, 128)
min(d/2, 256)
-

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 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 at a clock speed of 3.8 GHz.[41] 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.[42] 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.

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