The SHA hash functions are five 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. Hash algorithms compute a fixed-length digital representation (known as a message digest) of an input data sequence (the message) of any length. They are called “secure” when (in the words of the standard), “it is computationally infeasible to: Shanghai Hongqiao International Airport (IATA: SHA, ICAO: ZSSS) (Simplified Chinese: 上海虹桥国际机场, Traditional Chinese: 上海虹橋國際機場, Pinyin: ShànghÇŽi Hóngqiáo Guójì JÄ«cháng, Translation: Rainbow Bridge International Airport) is one of the two airports in Shanghai, Peoples Republic of China. ... In cryptography, a cryptographic hash function is a hash function with certain additional security properties to make it suitable for use as a primitive in various information security applications, such as authentication and message integrity. ... “NSA” redirects here. ... NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerce’s Technology Administration. ... Federal Information Processing Standards (FIPS) are publicly announced standards developed by the U.S. Federal government for use by all (non-military) government agencies and by government contractors. ...

1. find a message that corresponds to a given message digest, or
2. find two different messages that produce the same message digest.

Any change to a message will, with a very high probability, result in a different message digest.”

The five algorithms are denoted SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512. The latter four variants are sometimes collectively referred to as SHA-2. SHA-1 produces a message digest that is 160 bits long; the number in the other four algorithms' names denote the bit length of the digest they produce.

SHA-1 is employed in several widely used security applications and protocols, including TLS and SSL, PGP, SSH, S/MIME, and IPsec. It was considered to be the successor to MD5, an earlier, widely-used hash function. Transport Layer Security (TLS) and its predecessor, Secure Sockets Layer (SSL), are cryptographic protocols that provide secure communications on the Internet for such things as web browsing, e-mail, Internet faxing, instant messaging and other data transfers. ... Pretty Good Privacy is a computer program that provides cryptographic privacy and authentication. ... Secure Shell or SSH is a network protocol that allows data to be exchanged over a secure channel between two computers. ... S/MIME (Secure / Multipurpose Internet Mail Extensions) is a standard for public key encryption and signing of e-mail encapsulated in MIME. // S/MIME was originally developed by RSA Data Security Inc. ... IPsec (IP security) is a suite of protocols for securing Internet Protocol (IP) communications by authenticating and/or encrypting each IP packet in a data stream. ... In cryptography, MD5 (Message-Digest algorithm 5) is a widely used cryptographic hash function with a 128-bit hash value. ...

The security of SHA-1 has been somewhat compromised by cryptography researchers^[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 alternative hashing algorithms.^[2][3] An open competition for a new SHA-3 function was formally announced in the Federal Register on November 2, 2007. ^[4] "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)."^[5] Submissions are due October 31, 2008 and the proclamation of a winner and publication of the new standard are scheduled to take place in 2012. The Federal Register contains most routine publications and public notices of United States government agencies. ... The Advanced Encryption Standard (AES), the block cipher ratified as a standard by National Institute of Standards and Technology (NIST), was chosen using a process markedly more open and transparent than its predecessor, the ageing Data Encryption Standard (DES). ... In cryptography, the Advanced Encryption Standard (AES), also known as Rijndael, is a block cipher adopted as an encryption standard by the U.S. government. ...

SHA-0 and SHA-1

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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; _n denotes a left bit rotation by n places; n varies for each operation. denotes addition modulo 2³². K_t is a constant.

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 the 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 the NSA, to correct a flaw in the original algorithm which reduced its cryptographic security. However, the NSA did not provide any further explanation or identify what flaw was corrected. Weaknesses have subsequently been reported in 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. Image File history File links This is a lossless scalable vector image. ... Image File history File links SHA-1. ... Image File history File links SHA-1. ... a LaTeX lll File links The following pages link to this file: MD5 ... a LaTeX boxplus File links The following pages link to this file: International Data Encryption Algorithm MD5 Categories: User-created public domain images ... Federal Information Processing Standards (FIPS) are publicly announced standards developed by the U.S. Federal government for use by all (non-military) government agencies and by government contractors. ... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... NSA can stand for: National Security Agency of the USA The British Librarys National Sound Archive This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... In cryptography, a one-way compression function is a function that transforms two fixed length inputs to an output of the same size as one of the inputs. ...

SHA-1 (as well as SHA-0) produces a 160-bit digest from a message with a maximum length of (2⁶⁴ − 1) bits and 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. Message in its most general meaning is an object of communication. ... Election People This box:      Professor Ronald Lorin Rivest (born 1947, Schenectady, New York) is a cryptographer. ... “MIT” redirects here. ... MD4 is a message digest algorithm (the fourth in a series) designed by Professor Ronald Rivest of MIT in 1990. ... In cryptography, MD5 (Message-Digest algorithm 5) is a widely used cryptographic hash function with a 128-bit hash value. ...

Cryptanalysis

For an ideal hash function, violating the first criterion listed above, finding a message that corresponds to a given message digest, can always be done using a brute force search in 2^L evaluations, where L is the number of bits in the message digest. This is called a preimage attack. The second criterion, finding two different messages that produce the same message digest, known as a collision, requires only 2^L/2 evaluations using a birthday attack. For the later 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 considered to have 80-bit strength. In cryptography, a preimage attack on a cryptographic hash differs from a collision attack. ... A birthday attack is a type of cryptographic attack which exploits the mathematics behind the birthday paradox, making use of a space-time tradeoff. ...

Cryptographers have produced collision pairs for SHA-0 and have found algorithms that should produce SHA-1 collisions in far fewer than the intended 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, and 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.

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 where this is possible.

Cryptanalysis of SHA-0

At CRYPTO 98, two French researchers 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. CRYPTO 2003 conference reception. ... In computer science, a hash collision is a situation that occurs when two distinct inputs into a hash function produce identical outputs. ...

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. Eli Biham is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion Israeli Institute of Technology Computer Science department. ...

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. is the 224th day of the year (225th in leap years) in the Gregorian calendar. ... Year 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... For other uses, see Supercomputer (disambiguation). ... Itanium 2 logo The Itanium 2 is an IA-64 64-bit microprocessor developed jointly by Hewlett-Packard (HP) and Intel, and introduced on July 8, 2002. ...

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. ^[6][7] is the 229th day of the year (230th in leap years) in the Gregorian calendar. ... Year 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Xiaoyun Wang (born 1966) is a researcher and professor in the Department of Mathematics and System Science, Shandong University, Shandong, China. ... In cryptography, MD5 (Message-Digest algorithm 5) is a widely used cryptographic hash function with a 128-bit hash value. ...

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 ^[8][9]

Cryptanalysis of SHA-1

In light of the results on SHA-0, some experts suggested that plans for the use of SHA-1 in new cryptosystems should be 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.^[10] There are two different meanings of the word cryptosystem. ...

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 complexity of fewer than 2⁸⁰ operations. ^[11] Together with Joan Daemen, Vincent Rijmen designed the Rijndael block cipher, which was selected as the Advanced Encryption Standard in 2000. ...

In February 2005, an attack by Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu was announced. ^[12] 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.) Xiaoyun Wang (born 1966) is a researcher and professor in the Department of Mathematics and System Science, Shandong University, Shandong, China. ... In computer science, a brute-force search consists of systematically enumerating every possible solution of a problem until a solution is found, or all possible solutions have been exhausted. ...

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" ^[13]. 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."^[14]

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.^[15] is the 229th day of the year (230th in leap years) in the Gregorian calendar. ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ...

Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications"^[16], receiving the Best Paper Award at ASIACRYPT 2006. A two-block collison for 64-round SHA-1 was presented, found using unoptimized methods with 2³⁵ compression function evaluations. Asiacrypt (also ASIACRYPT) is an important international conference for cryptography research. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ...

As this attack requires the equivalent of about 2³⁵ evaluations, it is considered to be a theoretical break^[17]. To find an actual collision, however, a massive distributed computing effort is required. To that end, a collision search for SHA-1 using the distributed computing platform BOINC is currently being made^[18]. The Berkeley Open Infrastructure for Network Computing (BOINC) is a distributed computing infrastructure intended to be useful to fields beyond SETI. It is being developed by a team based at the University of California, Berkeley led by the project director of SETI@home, David Anderson. ...

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. ^[19][20]

SHA-2

A round of the SHA-2

NIST has published four additional hash functions in the SHA family, each with longer digests, collectively known as SHA-2. The individual variants are named after their digest lengths (in bits): SHA-224, SHA-256, SHA-384, and SHA-512. The latter three 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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In cryptography, Triple DES (also 3DES) is a block cipher formed from the Data Encryption Standard (DES) cipher. ...

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.

These new hash functions have not received as much scrutiny by the public cryptographic community as SHA-1 has, and so their cryptographic security is not yet as well-established. Gilbert and Handschuh (2003) have studied the newer variants and found no weaknesses.

SHA sizes

In the table below, internal state means the “internal hash sum” after each compression of a data block; see Merkle-Damgård construction for more details. In cryptography, the Merkle-DamgÃ¥rd hash function is a generic construction of a cryptographic hash function. ...

In computer science, a hash collision is a situation that occurs when two distinct inputs into a hash function produce identical outputs. ...

Applications

For more details on this topic, see Cryptographic hash function#Applications.

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. In cryptography, a cryptographic hash function is a hash function with certain additional security properties to make it suitable for use as a primitive in various information security applications, such as authentication and message integrity. ...

A prime motivation for the publication of the Secure Hash Algorithm was the Digital Signature Standard, in which it is incorporated. The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. ...

The SHA hash functions have been used as the basis for the SHACAL block ciphers. SHACAL-1 and SHACAL-2 are block ciphers based on cryptographic hash function from the SHA family. ... Encryption Decryption In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ...

Example hashes

Main article: Examples of SHA digests

The following is an example of SHA-1 digests. ASCII encoding is assumed for all messages. The following are some examples of SHA digests. ... Image:ASCII fullsvg There are 95 printable ASCII characters, numbered 32 to 126. ...

 SHA1("The quick brown fox jumps over the lazy dog") = 2fd4e1c6 7a2d28fc ed849ee1 bb76e739 1b93eb12 

Even a small change in the message will, with overwhelming probability, result in a completely different hash due to the avalanche effect. For example, changing dog to cog: A quick brown fox illustrates the best-known English pangram by jumping over a lazy dog. ... This article is about cryptography; for other meanings, see snowball effect. ...

 SHA1("The quick brown fox jumps over the lazy cog") = de9f2c7f d25e1b3a fad3e85a 0bd17d9b 100db4b3 

Other SHA examples can be found in examples of SHA digests The following are some examples of SHA digests. ...

Official validation

Main article: CMVP

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. The Cryptographic Module Validation Program (CMVP) is an Information Technology (IT) security accrediation program for cryptographic modules produced by private sector vendors who seek to have their products certified for use in government departments and regulated industries (such as financial and health_care institutions) that collect, store, transfer, share and disseminate... The Cryptographic Module Validation Program (CMVP) is an Information Technology (IT) security accrediation program for cryptographic modules produced by private sector vendors who seek to have their products certified for use in government departments and regulated industries (such as financial and health_care institutions) that collect, store, transfer, share and disseminate... NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerce’s Technology Administration. ... The CSE badge The Communications Security Establishment or CSE is an intelligence agency of the Canadian government, charged with the duty of keeping track of foreign signals intelligence. ...

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. 2006 is a common year starting on Sunday of the Gregorian calendar. ...

SHA-1 algorithm

Pseudocode for the SHA-1 algorithm follows: Pseudocode (derived from pseudo and code) is a compact and informal high-level description of a computer programming algorithm that uses the structural conventions of programming languages, but omits detailed subroutines, variable declarations or language-specific syntax. ...

 Note: All variables are unsigned 32 bits and wrap modulo 232 when calculating Initialize variables: h0 := 0x67452301 h1 := 0xEFCDAB89 h2 := 0x98BADCFE h3 := 0x10325476 h4 := 0xC3D2E1F0 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 (in bits) is congruent to 448 (mod 512) append length of message (before pre-processing), in bits, as 64-bit big-endian integer Process the message in successive 512-bit chunks: break message into 512-bit chunks for each chunk break chunk into sixteen 32-bit big-endian words w[i], 0 ≤ i ≤ 15 Extend the sixteen 32-bit words into eighty 32-bit words: for i from 16 to 79 w[i] := (w[i-3] xor w[i-8] xor w[i-14] xor w[i-16]) leftrotate 1 Initialize hash value for this chunk: a := h0 b := h1 c := h2 d := h3 e := h4 Main loop: for i from 0 to 79 if 0 ≤ i ≤ 19 then f := (b and c) or ((not b) and d) k := 0x5A827999 else if 20 ≤ i ≤ 39 f := b xor c xor d k := 0x6ED9EBA1 else if 40 ≤ i ≤ 59 f := (b and c) or (b and d) or (c and d) k := 0x8F1BBCDC else if 60 ≤ i ≤ 79 f := b xor c xor d k := 0xCA62C1D6 temp := (a leftrotate 5) + f + e + k + w[i] e := d d := c c := b leftrotate 30 b := a a := temp Add this chunk's hash to result so far: h0 := h0 + a h1 := h1 + b h2 := h2 + c h3 := h3 + d h4 := h4 + e Produce the final hash value (big-endian): digest = hash = h0 append h1 append h2 append h3 append h4 

Instead of the formulation from the original FIPS PUB 180-1 shown, the following equivalent expressions may be used to compute f in the main loop above: Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ... In computing, endianness is the byte (and sometimes bit) ordering in memory used to represent some kind of data. ... In combinatorial mathematics, a circular shift is a permutation of the entries in a tuple where the last element becomes the first element and all the other elements are shifted, or where the first element becomes the last element and all the other are shifted. ...

 (0 ≤ i ≤ 19): f := d xor (b and (c xor d)) (alternative 1) (0 ≤ i ≤ 19): f := (b and c) xor ((not b) and d) (alternative 2) (40 ≤ i ≤ 59): f := (b and c) or (d and (b or c)) (alternative 1) (40 ≤ i ≤ 59): f := (b and c) or (d and (b xor c)) (alternative 2) (40 ≤ i ≤ 59): f := (b and c) + (d and (b xor c)) (alternative 3) (40 ≤ i ≤ 59): f := (b and c) xor (b and d) xor (c and d) (alternative 4) 

SHA-2 algorithm

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. Pseudocode (derived from pseudo and code) is a compact and informal high-level description of a computer programming algorithm that uses the structural conventions of programming languages, but omits detailed subroutines, variable declarations or language-specific syntax. ...

 Note: All variables are unsigned 32 bits and wrap modulo 232 when calculating Initialize variables (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 table 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 (in bits) is congruent to 448 (mod 512) append length of message (before pre-processing), in bits, as 64-bit big-endian integer Process the message in successive 512-bit chunks: break message into 512-bit chunks for each chunk break chunk into sixteen 32-bit big-endian words w[0..15] Extend the sixteen 32-bit words into sixty-four 32-bit words: 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 hash value for this chunk: a := h0 b := h1 c := h2 d := h3 e := h4 f := h5 g := h6 h := h7 Main loop: for i from 0 to 63 s0 := (a rightrotate 2) xor (a rightrotate 13) xor (a rightrotate 22) maj := (a and b) xor (a and c) xor (b and c) t2 := s0 + maj s1 := (e rightrotate 6) xor (e rightrotate 11) xor (e rightrotate 25) ch := (e and f) xor ((not e) and g) t1 := h + s1 + ch + k[i] + w[i] h := g g := f f := e e := d + t1 d := c c := b b := a a := t1 + t2 Add this chunk's hash to result so far: 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 ch and maj functions can be optimized the same way as described for SHA-1. Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ...

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

• the initial variable values h0 through h7 are different, and
• the output is constructed by omitting h7.

SHA-512 is identical in structure, but:

• all numbers are 64 bits long,
• there are 80 rounds instead of 64,
• the initial values and additive constants are extended to 64 bits, and
• the shift and rotate amounts used are different.

SHA-384 is identical to SHA-512, except that:

• the initial values h0 through h7 are different, and
• the output is constructed by omitting h6 and h7.

See also

• Digital timestamping
• Hashcash
• RIPEMD-160
• WHIRLPOOL

Digital timestamping is the process of securely keeping track of the creation and modification time of a document. ... Hashcash is a proof-of-work system designed to limit email spam and denial of service attacks. ... RIPEMD-160 (RACE Integrity Primitives Evaluation Message Digest) is a 160-bit message digest algorithm (and cryptographic hash function) developed in Europe by Hans Dobbertin, Antoon Bosselaers and Bart Preneel, and first published in 1996. ... This article is about the water movement. ...

References

Crypto is an English prefix that means hidden or secret. The term crypto is also employed as shorthand for the following: Cryptography, the practice of the use of encryption. ... Eli Biham is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion Israeli Institute of Technology Computer Science department. ... Xiaoyun Wang (born 1966) is a researcher and professor in the Department of Mathematics and System Science, Shandong University, Shandong, China. ... Xiaoyun Wang (born 1966) is a researcher and professor in the Department of Mathematics and System Science, Shandong University, Shandong, China. ... Selected Areas in Cryptography (SAC) is a series of international cryptography workshops held annually in Canada, every August since 1994. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 116th day of the year (117th in leap years) in the Gregorian calendar. ...

External links

Online Hash Calculators

• http://www.johnmaguire.us/tools/hashcalc/index.php – Allows for the encoding of zero-length strings.

Standards: SHA-0, SHA-1, SHA-2, SHA-3...

• Specifications for a Secure Hash Standard (SHS) – Draft for proposed SHS standard (SHA-0)
• Secure Hash Standard (SHS) – Proposed SHS standard (SHA-0)
• RFC 3174, “US Secure Hash Algorithm 1 (SHA-1)”
• RFC 4634, “US Secure Hash Algorithms (SHA and HMAC-SHA)”
• CSRC Cryptographic Toolkit – Official NIST site for the Secure Hash Standard
  • FIPS 180-2: Secure Hash Standard (SHS) (PDF, 236 kB) – Current version of the Secure Hash Standard (SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512), 1 August 2002, amended 25 February 2004
• NIST Cryptographic Hash Project SHA-3 competition

NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerce’s Technology Administration. ... “PDF” redirects here. ...

Cryptanalysis

• Interview with Yiqun Lisa Yin concerning the attack on SHA-1
• Lenstra's Summary of impact of the February 2005 cryptanalytic results
• Explanation of the successful attacks on SHA-1 (3 pages, 2006)

Implementations

• The OpenSSL Project – The widely used OpenSSL crypto library includes free, 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.

Free software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions only to ensure that further recipients can also do these things. ... Open source refers to projects that are open to the public and which draw on other projects that are freely available to the general public. ...

Tutorials and example code

• Comparison of SHA function in different languages
• A SHA-1 implementation in C by Christophe Devine
• SHA-1 implementations in C and C++, including Win32 and Linux binaries by Paul E. Jones (RFC Co-Author)
• A SHA-2 implementation in C by Olivier Gay
• A SHA implementation in C by Brian Gladman
• SHA-2 implementation in Delphi by eCat (Note: This version may give incorrect results for SHA-256.)
• A Visual Basic SHA-1 implementation by John Taylor
• SHA-1 implementation in JavaScript by Chris Veness
• Sha1sum and social networks + a java applet to calculate the sum of an email

Test Vectors

The NESSIE project test vectors for SHA-1, SHA-256, SHA-384, and SHA-512. For other uses, see nessie (disambiguation). ...

SHA1 reverse lookup databases

• SHA1search - reverses MD5 and SHA1 hashes (330 000+ strings)