Secure Hash Algorithms

The Secure Hash Algorithms are a family of cryptographic hash functions published by the National Institute of Standards and Technology (NIST) as a U.S. Federal Information Processing Standard (FIPS), including:

SHA-0: A retronym applied to the original version of the 160-bit hash function published in 1993 under the name "SHA". It was withdrawn shortly after publication due to an undisclosed "significant flaw" and replaced by the slightly revised version SHA-1.
SHA-1: A 160-bit hash function which resembles the earlier MD5 algorithm. This was designed by the National Security Agency (NSA) to be part of the Digital Signature Algorithm. Cryptographic weaknesses were discovered in SHA-1, and the standard was no longer approved for most cryptographic uses after 2010.
SHA-2: A family of two similar hash functions, with different block sizes, known as SHA-256 and SHA-512. They differ in the word size; SHA-256 uses 32-bit words where SHA-512 uses 64-bit words. There are also truncated versions of each standard, known as SHA-224, SHA-384, SHA-512/224 and SHA-512/256. These were also designed by the NSA.
SHA-3: A hash function formerly called Keccak, chosen in 2012 after a public competition among non-NSA designers. It supports the same hash lengths as SHA-2, and its internal structure differs significantly from the rest of the SHA family.

The corresponding standards are FIPS PUB 180 (original SHA), FIPS PUB 180-1 (SHA-1), FIPS PUB 180-2 (SHA-1, SHA-256, SHA-384, and SHA-512). NIST has updated Draft FIPS Publication 202, SHA-3 Standard separate from the Secure Hash Standard (SHS).

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
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Algorithm and variant		Output size (bits)	Internal state size (bits)	Block size (bits)	Rounds	Operations	Security against collision attacks (bits)	Security against length extension attacks (bits)	Performance on Skylake (median cpb)^[1]		First published
Algorithm and variant		Output size (bits)	Internal state size (bits)	Block size (bits)	Rounds	Operations	Security against collision attacks (bits)	Security against length extension attacks (bits)	Long messages	8 bytes	First published
MD5 (as reference)		128	128 (4 × 32)	512	4 (16 operations in each round)	And, Xor, Or, Rot, Add (mod 2³²)	≤ 18 (collisions found)^[2]	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		160	160 (5 × 32)	512	80	And, Xor, Or, Rot, Add (mod 2³²)	< 63 (collisions found)^[3]	0	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^[4]	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^[5]	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
SHA-3	SHAKE128 SHAKE256	d (arbitrary) d (arbitrary)	1600 (5 × 5 × 64)	1344 1088	24^[5]	And, Xor, Rot, Not	min(d/2, 128) min(d/2, 256)	256 512	7.08 8.59	155.25 155.50	2015

Validation

All SHA-family algorithms, as FIPS-approved security functions, are subject to official validation by the CMVP (Cryptographic Module Validation Program), a joint program run by the American National Institute of Standards and Technology (NIST) and the Canadian Communications Security Establishment (CSE).

References

^ "Measurements table". bench.cr.yp.to.
^ Tao, Xie; Liu, Fanbao; Feng, Dengguo (2013). Fast Collision Attack on MD5 (PDF). Cryptology ePrint Archive (Technical report). IACR.
^
Stevens, Marc; Bursztein, Elie; Karpman, Pierre; Albertini, Ange; Markov, Yarik. The first collision for full SHA-1 (PDF) (Technical report). Google Research.
- Marc Stevens; Elie Bursztein; Pierre Karpman; Ange Albertini; Yarik Markov; Alex Petit Bianco; Clement Baisse (February 23, 2017). "Announcing the first SHA1 collision". Google Security Blog.
^ Without truncation, the full internal state of the hash function is known, regardless of collision resistance. If the output is truncated, the removed part of the state must be searched for and found before the hash function can be resumed, allowing the attack to proceed.
^ "The Keccak sponge function family". Retrieved 2016-01-27.

[1] "Measurements table". bench.cr.yp.to.

[2] Tao, Xie; Liu, Fanbao; Feng, Dengguo (2013). Fast Collision Attack on MD5 (PDF). Cryptology ePrint Archive (Technical report). IACR.

[3] Stevens, Marc; Bursztein, Elie; Karpman, Pierre; Albertini, Ange; Markov, Yarik. The first collision for full SHA-1 (PDF) (Technical report). Google Research.
Marc Stevens; Elie Bursztein; Pierre Karpman; Ange Albertini; Yarik Markov; Alex Petit Bianco; Clement Baisse (February 23, 2017). "Announcing the first SHA1 collision". Google Security Blog.

[4] Marc Stevens; Elie Bursztein; Pierre Karpman; Ange Albertini; Yarik Markov; Alex Petit Bianco; Clement Baisse (February 23, 2017). "Announcing the first SHA1 collision". Google Security Blog.

[4] Without truncation, the full internal state of the hash function is known, regardless of collision resistance. If the output is truncated, the removed part of the state must be searched for and found before the hash function can be resumed, allowing the attack to proceed.

[5] "The Keccak sponge function family". Retrieved 2016-01-27.

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