SHA_hash_functions by zzzmarcus


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SHA hash functions

SHA hash functions
The SHA hash functions are a set of cryptographic hash functions designed by the National Security Agency (NSA) and published by the NIST as a U.S. Federal Information Processing Standard. SHA stands for Secure Hash Algorithm. The three SHA algorithms are structured differently and are distinguished as SHA-0, SHA-1, and SHA-2. The SHA-2 family uses an identical algorithm with a variable digest size which is distinguished as SHA-224, SHA-256, SHA-384, and SHA-512. SHA-1 is the best established of the existing SHA hash functions, and is employed in several widely used security applications and protocols. In 2005, security flaws were identified in SHA-1, namely that a possible mathematical weakness might exist, indicating that a stronger hash function would be desirable.[1] Although no attacks have yet been reported on the SHA-2 variants, they are algorithmically similar to SHA-1 and so efforts are underway to develop improved alternatives.[2][3] A new hash standard, SHA-3, is currently under development — the function will be selected via an open competition running between 2008 and 2012. both SHA-0 and SHA-1. SHA-1 appears to provide greater resistance to attacks, supporting the NSA’s assertion that the change increased the security. SHA-1 (as well as SHA-0) produces a 160-bit digest from a message with a maximum length of (264 − 1) bits. SHA-1 is based on principles similar to those used by Ronald L. Rivest of MIT in the design of the MD4 and MD5 message digest algorithms, but has a more conservative design.

SHA-2 family

One iteration in a SHA-2 family compression function. NIST published four additional hash functions in the SHA family, named after their digest lengths (in bits): SHA-224, SHA-256, SHA-384, and SHA-512. The algorithms are collectively known as SHA-2. The algorithms were first published in 2001 in the draft FIPS PUB 180-2, at which time review and comment were accepted. FIPS PUB 180-2, which also includes SHA-1, was released as an official standard in 2002. 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. These variants are patented in US patent 6829355. The United States has released the patent under a royalty free license.[4] SHA-256 and SHA-512 are novel hash functions computed with 32- and 64-bit words, respectively. They use different shift

The hash functions
SHA-0 and SHA-1
The original specification of the algorithm was published in 1993 as the Secure Hash Standard, FIPS PUB 180, by US government standards agency NIST (National Institute of Standards and Technology). This version is now often referred to as SHA-0. It was withdrawn by NSA shortly after publication and was superseded by the revised version, published in 1995 in FIPS PUB 180-1 and commonly referred to as SHA-1. SHA-1 differs from SHA-0 only by a single bitwise rotation in the message schedule of its compression function; this was done, according to NSA, to correct a flaw in the original algorithm which reduced its cryptographic security. However, NSA did not provide any further explanation or identify the flaw that was corrected. Weaknesses have subsequently been reported in


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Algorithm and variant Output Internal Block size state size (bits) size (bits) (bits) 160 160 160 160 512 512

SHA hash functions
Max Word Rounds Operations message size size (bits) (bits) 264 − 1 264 − 1 32 32 80 80 +,and,or,xor,rot +,and,or,xor,rot Collisions found


Yes None (252[10] attack)

SHA-2 SHA-256/ 256/ 224 224 SHA-512/ 512/ 384 384

256 512

512 1024

264 − 1


64 80

+,and,or,xor,shr,rot None +,and,or,xor,shr,rot None

2128 − 1 64

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. These hash functions are not as widely used as SHA-1, though they appear to provide much better security. This is partly because protocols like SSL do not make it easy to introduce new hash functions without breaking backwards compatibility. SHA-256 is used to authenticate Debian Linux software packages[5] 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.[6] Currently, the best public attacks on SHA-2 break 24 of the 64 or 80 rounds.[7]

of a data block; see Merkle-Damgård construction for more details.

For more details on this topic, see Cryptographic hash function#Applications. SHA-1 is the most widely employed of the SHA family. It forms part of several widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, and IPsec. Those applications can also use MD5; both MD5 and SHA-1 are descended from MD4. SHA-1 hashing is also used in distributed revision control systems such as Git, Mercurial, and Monotone to identify revisions, and detect data corruption or tampering. SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 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).[11] A prime motivation for the publication of the Secure Hash Algorithm was the Digital Signature Standard, in which it is incorporated. The SHA hash functions have been used as the basis for the SHACAL block ciphers.

SHA-3 (in development)
An open competition for a new SHA-3 function was formally announced in the Federal Register on November 2, 2007.[8] "NIST is initiating an effort to develop one or more additional hash algorithms through a public competition, similar to the development process for the Advanced Encryption Standard (AES)."[9] Submissions were due October 31, 2008 and the proclamation of a winner and publication of the new standard are scheduled to take place in 2012.

Comparison of SHA functions
In the table below, internal state means the “internal hash sum” after each compression


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SHA hash functions
One iteration within the SHA-1 compression function. A, B, C, D and E are 32-bit words of the state; F is a nonlinear function that varies;

denotes a left bit rotation by n places; n varies for each operation. Wt is the expanded message word of round t, Kt is the round constant of round t.

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. For the latter reason the strength of a hash function is usually compared to a symmetric cipher of half the message digest length. Thus SHA-1 was originally thought to have 80-bit strength. Cryptographers have produced collision pairs for SHA-0 and have found algorithms that should produce SHA-1 collisions in far fewer than the originally expected 280 evaluations. In terms of practical security, a major concern about these new attacks is that they might pave the way to more efficient ones. Whether this is the case has yet to be seen, but a migration to stronger hashes is believed to be prudent. 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

denotes addition modulo 232. 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 can’t 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 an MD5 collision.[12]


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SHA hash functions
reconsidered. After the CRYPTO 2004 results were published, NIST announced that they planned to phase out the use of SHA-1 by 2010 in favor of the SHA-2 variants.[17] In early 2005, Rijmen and Oswald published an attack on a reduced version of SHA-1—53 out of 80 rounds—which finds collisions with a computational effort of fewer than 280 operations.[18] In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced.[15] The attacks can find collisions in the full version of SHA-1, requiring fewer than 269 operations. (A brute-force search would require 280 operations.) The authors write: "In particular, our analysis is built upon the original differential attack on SHA0 [sic], the near collision attack on SHA0, the multiblock collision techniques, as well as the message modification techniques used in the collision search attack on MD5. Breaking SHA1 would not be possible without these powerful analytical techniques."[19] The authors have presented a collision for 58-round SHA-1, found with 233 hash operations. The paper with the full attack description was published in August 2005 at the CRYPTO conference. In an interview, Yin states that, "Roughly, we exploit the following two weaknesses: One is that the file preprocessing step is not complicated enough; another is that certain math operations in the first 20 rounds have unexpected security problems."[20] On 17 August 2005, an improvement on the SHA-1 attack was announced on behalf of Xiaoyun Wang, Andrew Yao and Frances Yao at the CRYPTO 2005 rump session, lowering the complexity required for finding a collision in SHA-1 to 263.[21] On 18 December 2007 the details of this result were explained and verified by Martin Cochran.[22] Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications,"[23] receiving the Best Paper Award at ASIACRYPT 2006. A two-block collision for 64-round SHA-1 was presented, found using unoptimized methods with 235 compression function evaluations. As this attack requires the equivalent of about 235 evaluations, it is considered to be a significant theoretical break.[24] In order to find an actual collision in the full 80 rounds of the hash function, however, massive

At CRYPTO 98, two French researchers, Florent Chabaud and Antoine Joux, presented an attack on SHA-0 (Chabaud and Joux, 1998): collisions can be found with complexity 261, fewer than the 280 for an ideal hash function of the same size. In 2004, Biham and Chen found near-collisions for SHA-0—two messages that hash to nearly the same value; in this case, 142 out of the 160 bits are equal. They also found full collisions of SHA-0 reduced to 62 out of its 80 rounds. Subsequently, on 12 August 2004, a collision for the full SHA-0 algorithm was announced by Joux, Carribault, Lemuet, and Jalby. This was done by using a generalization of the Chabaud and Joux attack. Finding the collision had complexity 251 and took about 80,000 CPU hours on a supercomputer with 256 Itanium 2 processors. (Equivalent to 13 days of full-time use of the computer.) On 17 August 2004, at the Rump Session of CRYPTO 2004, preliminary results were announced by Wang, Feng, Lai, and Yu, about an attack on MD5, SHA-0 and other hash functions. The complexity of their attack on SHA-0 is 240, significantly better than the attack by Joux et al. [13][14] In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced which could find collisions in SHA-0 in 239 operations.[15][16]


SHA-1 HMAC Generation. In light of the results for SHA-0, some experts suggested that plans for the use of SHA-1 in new cryptosystems should be


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amounts of computer time would be required. To that end, a collision search for SHA-1 using the distributed computing platform BOINC is currently in progress, organized by the Graz University of Technology.[25] At the Rump Session of CRYPTO 2006, Christian Rechberger and Christophe De Cannière claimed to have discovered a collision attack on SHA-1 that would allow an attacker to select at least parts of the message.[26][27] Cameron McDonald, Philip Hawkes and Josef Pieprzyk presented a hash collision attack with complexity 252 at the Rump session of Eurocrypt 2009[28].

SHA hash functions
cog produces a hash with different values for 81 of the 160 bits:

SHA1("The quick brown fox jumps over the lazy = de9f2c7f d25e1b3a fad3e85a 0bd17d9b 100db4b

SHA-1 pseudocode
Pseudocode for the SHA-1 algorithm follows:

Note 1: All variables are unsigned 32 bits and Note 2: All constants in this pseudo code are Within each word, the most significant bit is Initialize variables: h0 = 0x67452301 h1 = 0xEFCDAB89 h2 = 0x98BADCFE h3 = 0x10325476 h4 = 0xC3D2E1F0

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 October 2006, there are more than 500 validated implementations of SHA-1, with fewer than ten of them capable of handling messages with a length in bits not a multiple of eight (see SHS Validation List). It is also important to note that some implementations available on the Internet do not digest the NIST validation vectors correctly, although they may correctly process the examples listed in the SHA-1 standard.

Pre-processing: append the bit ’1’ to the message append k bits ’0’, where k is the minimum numb length (in bits) is congruent to 448 (mod append length of message (before pre-processin

Process the message in successive 512-bit chun break message into 512-bit chunks for each chunk break chunk into sixteen 32-bit big-endian

Extend the sixteen 32-bit words into eight for i from 16 to 79 w[i] = (w[i-3] xor w[i-8] xor w[i-14] x Initialize hash value for this chunk: a = h0 b = h1 c = h2 d = h3 e = h4

Examples and pseudocode

Main loop: for i from 0 to 79 if 0 ≤ i ≤ 19 then Example hashes f = (b and c) or ((not b) and d) The following is an example of SHA-1 digests. k = 0x5A827999 ASCII encoding is assumed for all messages. else if 20 ≤ i ≤ 39 f = b xor c xor d SHA1("The quick brown fox jumps over the lazy dog") k = 0x6ED9EBA1 = 2fd4e1c6 7a2d28fc ed849ee1 bb76e739 1b93eb12 else if 40 ≤ i ≤ 59 f = (b and c) or (b and d) or (c an Even a small change in the message will, k = 0x8F1BBCDC with overwhelming probability, result in a else if 60 ≤ i ≤ 79 completely different hash due to the avaf = b xor c xor d lanche effect. For example, changing dog to


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k = 0xCA62C1D6

SHA hash functions

Initialize table of round constants (first 32 bits of the fractional parts of the temp = (a leftrotate 5) + f + e k[0..63] := + k + w[i] e = d 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5d d = c 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7 c = b leftrotate 30 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca b = a 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597 a = temp 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c5 Add this chunk’s hash to result so far: 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0b h0 = h0 + a 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70 h1 = h1 + b h2 = h2 + c Pre-processing: h3 = h3 + d append the bit ’1’ to the message h4 = h4 + e append k bits ’0’, where k is the minimum numb length (in bits) is congruent to 448 (mod Produce the final hash value (big-endian): append length of message (before pre-processin digest = hash = h0 append h1 append h2 append h3 append h4 Process the message in successive 512-bit chun Instead of the formulation from the original break message into 512-bit chunks FIPS PUB 180-1 shown, the following equifor each chunk valent expressions may be used to compute f break chunk into sixteen 32-bit big-endian in the main loop above: Extend the sixteen 32-bit words into sixty (0 ≤ i ≤ 19): f = d xor (b and (c xor d)) for i from 16 to 63 (alternative 1) (0 ≤ i ≤ 19): f = (b and c) xor ((not b) and d)s0 := (w[i-15] rightrotate 7) xor (w[i(alternative 2) (0 ≤ i ≤ 19): f = (b and c) + ((not b) and d) s1 := (w[i-2] rightrotate 17) xor (w[i(alternative 3) (0 ≤ i ≤ 19): f = vec_sel(d, c, b) (alternative 4) w[i] := w[i-16] + s0 + w[i-7] + s1 (40 (40 (40 (40 ≤ ≤ ≤ ≤ i i i i ≤ ≤ ≤ ≤ 59): 59): 59): 59): f f f f = = = = (b (b (b (b and and and and c) c) c) c) or (d and (b orInitialize hash value for this chunk: c)) (alternative 1) or (d and (b xor := h0 (alternative 2) a c)) + (d and (b xor c)) h1 (alternative 3) b := xor (b and d) xor:= h2 (c and d) (alternative 4) c d e f g h := := := := := h3 h4 h5 h6 h7

SHA-256 (a SHA-2 variant) 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.

Main loop: for i from 0 to 63 s0 := (a rightrotate calculating Note 1: All variables are unsigned 32 bits and wrap modulo 232 when 2) xor (a rightrot maj := (a and Note 2: All constants in this pseudo code are in big endian b) xor (a and c) xor (b a t2 := s0 + maj s1 := (e rightrotate 6) xor (e rightrot Initialize variables ch := (e and f) xor ((not primes 2..1 (first 32 bits of the fractional parts of the square roots of the first 8e) and g) t1 := h + s1 + ch + k[i] + w[i] h0 := 0x6a09e667 h1 := 0xbb67ae85 h := g h2 := 0x3c6ef372 g := f h3 := 0xa54ff53a f := e h4 := 0x510e527f e := d + t1 h5 := 0x9b05688c d := c h6 := 0x1f83d9ab c := b h7 := 0x5be0cd19 b := a a := t1 + t2


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SHA hash functions

chunk’s hash to result so far: + a [1] Schneier on Security: Cryptanalysis of + b SHA-1 + c [2] Schneier on Security: NIST Hash + d Workshop Liveblogging (5) + e [3] Hash cracked - heise Security + f [4] Licensing Declaration for US patent + g 6829355.. + h 858/. Retrieved on 2008-02-17. [5] Debian codebase in Google Code Produce the final hash value (big-endian): John Markoff, A Tool to Verify Digital [6] digest = hash = h0 append h1 append h2 append h3 append as Technology Shifts, New append h7 Records, Even h4 append h5 append h6 York Times, January 26, 2009 The ch and maj functions can be optimized [7] Somitra Kumar Sanadhya and Palash the same way as described for SHA-1. Sarkar, New Collision attacks Against Up SHA-224 is identical to SHA-256, except To 24-step SHA-2 that: [8] • the initial variable values h0 through h7 documents/FR_Notice_Nov07.pdf [9] Bounce to index.html are different, and [10] • the output is constructed by omitting h7. users/dkg/weblog/48, A new 252 attack Here the initial values for the variables (in SHA-1. Retrieved on 2009-05-08. on big endian): h0 := 0xc1059ed8 [11] National Institute on Standards and h1 := 0x367cd507 Technology Computer Security Resource h2 := 0x3070dd17 Center, NIST’S POLICY ON HASH h3 := 0xf70e5939 FUNCTIONS, accessed March 29, 2009. h4 := 0xffc00b31 [12] Alexander Sotirov, Marc Stevens, Jacob h5 := 0x68581511 Appelbaum, Arjen Lenstra, David h6 := 0x64f98fa7 Molnar, Dag Arne Osvik, Benne de h7 := 0xbefa4fa4 Weger, MD5 considered harmful today: Creating a rogue CA certificate, accessed SHA-512 is identical in structure, but: March 29, 2009 • all numbers are 64 bits long, [13] Freedom to Tinker » Blog Archive » • there are 80 rounds instead of 64, Report from Crypto 2004 • the initial values and additive constants [14] are extended to 64 bits, and groups?selm=fgrieu-05A994.05060218082004%40in • the shift and rotate amounts used are [15] ^ Schneier on Security: SHA-1 Broken different. [16] SHA-384 is identical to SHA-512, except that: sha0-crypto-author-new.pdf • the initial values h0 through h7 are [17] different, and hash_standards_comments.pdf • the output is constructed by omitting h6 [18] Cryptology ePrint Archive and h7. [19] shanote.pdf [20] Fixing a hole in security | Tech News on ZDNet • sha1sum [21] Schneier on Security: New Cryptanalytic • Digital timestamping Results Against SHA-1 • Hash collision [22] Cryptology ePrint Archive • Hashcash [23] SpringerLink Home - Main • RIPEMD-160 (Patent free) [24] IAIK Krypto Group - Description of • Secure Hash Standard SHA-1 Collision Search Project • Tiger [25] SHA-1 Collision Search Graz • WHIRLPOOL (Patent free) [26] SHA-1 hash function under pressure heise Security

Add this h0 := h0 h1 := h1 h2 := h2 h3 := h3 h4 := h4 h5 := h5 h6 := h6 h7 := h7


See also


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SHA hash functions

[27] Crypto 2006 Rump Schedule • CSRC Cryptographic Toolkit – Official [28] SHA-1 collisions now 2^52 NIST site for the Secure Hash Standard • Florent Chabaud, Antoine Joux: • FIPS 180-2: Secure Hash Standard Differential Collisions in SHA-0. CRYPTO (SHS) (PDF, 236 kB) – Current version 1998. pp56–71 of the Secure Hash Standard (SHA-1, • Eli Biham, Rafi Chen, Near-Collisions of SHA-224, SHA-256, SHA-384, and SHA-0, Cryptology ePrint Archive, Report SHA-512), 1 August 2002, amended 25 2004/146, 2004 (appeared on CRYPTO February 2004 2004) [1] • NIST Cryptographic Hash Project SHA-3 • Xiaoyun Wang, Hongbo Yu and Yiqun Lisa competition Yin, Efficient Collision Search Attacks on • RFC 3174 (with sample C implementation) SHA-0, CRYPTO 2005 [2] • Xiaoyun Wang, Yiqun Lisa Yin and Hongbo Cryptanalysis Yu, Finding Collisions in the Full SHA-1, • Interview with Yiqun Lisa Yin concerning CRYPTO 2005 [3] the attack on SHA-1 • Henri Gilbert, Helena Handschuh: • Lenstra’s Summary of impact of the Security Analysis of SHA-256 and Sisters. February 2005 cryptanalytic results Selected Areas in Cryptography 2003: • Explanation of the successful attacks on pp175–193 SHA-1 (3 pages, 2006) • "Proposed Revision of Federal Information • Cryptography Research - Hash Collision Processing Standard (FIPS) 180, Secure Q&A Hash Standard". Federal Register 59 (131): 35317–35318. 1994-07-11. Implementations • The OpenSSL Project – The widely used waisgate.cgi?WAISdocID=5963452267+0+0+0&WAISaction=retrieve. OpenSSL crypto library includes free, Retrieved on 2007-04-26. open-source implementations of SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512 • Crypto++ Crypto++ Library is a free C++ class library of cryptographic schemes. Standards: SHA-0, SHA-1, • Bouncy Castle The Bouncy Castle Library SHA-2, SHA-3... is a free Java and C# class library that • Specifications for a Secure Hash Standard contains implementations of the SHA-1, (SHS) – Draft for proposed SHS (SHA-0) SHA-224, SHA-256, SHA-384 and • Secure Hash Standard (SHS) – Proposed SHA-512 algorithms as well as other SHS (SHA-0) algorithms like Whirlpool, Tiger, RIPEMD, GOST-3411, MD2, MD4 and MD5.

External links

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