SHA-2

{{Short description|Set of cryptographic hash functions}} {{Infobox cryptographic hash function | name = SHA-2 | image = SHA-2.svg | caption =  | designers = National Security Agency | publish date = {{Start date and age|2001}} | series = (SHA-0), SHA-1, SHA-2, SHA-3 | derived from = | derived to = | related to = | certification = FIPS PUB 180-4, CRYPTREC, NESSIE  | digest size = 224, 256, 384, or 512 bits | structure = Merkle–Damgård construction with Davies–Meyer compression function | rounds = 64 or 80 | 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.<ref name=preimage-khov/> Pseudo-collision attack against up to 46 rounds of SHA-256.<ref name=collision-lamberger/> }} {{SHA-box}} '''SHA-2''' ('''Secure Hash Algorithm 2''') is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001.<ref>{{cite web |last1=Penard |first1=Wouter |last2=van Werkhoven |first2=Tim |title=On the Secure Hash Algorithm family |url=https://www.staff.science.uu.nl/~werkh108/docs/study/Y5_07_08/infocry/project/Cryp08.pdf |url-status=dead |archive-url=https://web.archive.org/web/20160330153520/https://www.staff.science.uu.nl/~werkh108/docs/study/Y5_07_08/infocry/project/Cryp08.pdf |archive-date=2016-03-30 |website=staff.science.uu.nl}}</ref><ref name=":0" /> They are built using the Merkle–Damgård construction, from a one-way compression function itself built using the Davies–Meyer structure from a specialized block cipher.

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:<ref name=":1">{{cite web |title=IPR Details: The United States of America as represented by the National Security Agency's general license statement |url=https://datatracker.ietf.org/ipr/858/ |website=IETF Datatracker |access-date=2008-02-17 |id=858 |archive-date=2016-06-16 |archive-url=https://web.archive.org/web/20160616212010/https://datatracker.ietf.org/ipr/858/ |url-status=live }}</ref> '''SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256'''. SHA-256 and SHA-512 are hash functions whose digests are eight 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 truncated versions of SHA-256 and SHA-512 respectively, 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 first published by the National Institute of Standards and Technology (NIST) as a U.S. federal standard. The SHA-2 family of algorithms are patented in the U.S.<ref>{{cite patent|country=US|number=6829355|pubdate=2004-12-07|title=Device for and method of one-way cryptographic hashing|assign1=National Security Agency|inventor1-last=Lilly|inventor1-first=Glenn M.}}</ref> The United States has released the patent under a royalty-free license.<ref name=":1" />

As of 2011 the best public attacks break preimage resistance for 52 out of 64 rounds of SHA-256 or 57 out of 80 rounds of SHA-512, and collision resistance for 46 out of 64 rounds of SHA-256.<ref name=preimage-khov/><ref name=collision-lamberger/>{{update inline|date=January 2026}}

==Hash standard== thumbnail|upright=1.6|One iteration in a SHA-2 family compression function. The blue components perform the following operations:     <math>\operatorname{Ch}(E,F,G) = (E \land F) \oplus (\neg E \land G)</math>     <math>\operatorname{Ma}(A,B,C) = (A \land B) \oplus (A \land C) \oplus (B \land C)</math>     <math>\Sigma_0(A) = (A\!\ggg\!2) \oplus (A\!\ggg\!13) \oplus (A\!\ggg\!22)</math>     <math>\Sigma_1(E) = (E\!\ggg\!6) \oplus (E\!\ggg\!11) \oplus (E\!\ggg\!25)</math> The bitwise rotation uses different constants for SHA-512. The given numbers are for SHA-256. The red <math>\color{red}\boxplus</math> is addition modulo 232 for SHA-256, or 264 for SHA-512.

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.<ref name=":0">Federal Register Notice 02-21599, [https://federalregister.gov/a/02-21599 Announcing Approval of FIPS Publication 180-2] {{Webarchive|url=https://web.archive.org/web/20220314024321/https://www.federalregister.gov/a/02-21599 |date=2022-03-14 }}</ref>

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.<ref>{{cite web|url=https://csrc.nist.gov/publications/fips/fips180-2/fips180-2withchangenotice.pdf|title=FIPS 180-2 with Change Notice 1|website=csrc.nist.gov|access-date=2022-02-15|archive-date=2017-08-09|archive-url=https://web.archive.org/web/20170809001643/http://csrc.nist.gov/publications/fips/fips180-2/fips180-2withchangenotice.pdf|url-status=live}}</ref> 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.<ref>Federal Register Notice E8-24743, [https://federalregister.gov/a/E8-24743 Announcing Approval of FIPS Publication 180-3]</ref><ref name="sp800107">{{Cite report |url=https://csrc.nist.gov/Pubs/sp/800/107/r1/Final |title=Recommendation for Applications Using Approved Hash Algorithms |last=Dang |first=Quynh |date=2012-08-24 |publisher=National Institute of Standards and Technology |issue=NIST Special Publication (SP) 800-107 Rev. 1 |language=en |access-date=2023-08-28 |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000235/https://csrc.nist.gov/Pubs/sp/800/107/r1/Final |url-status=live }}</ref><ref name="sp80057">{{Cite report |url=https://csrc.nist.gov/Pubs/sp/800/57/pt1/r3/Final |title=Recommendation for Key Management, Part 1: General (Revision 3) |last1=Barker |first1=Elaine |last2=Barker |first2=William |date=2012-07-10 |publisher=National Institute of Standards and Technology |issue=NIST Special Publication (SP) 800-57 Part 1 Rev. 3 (Withdrawn) |language=en |last3=Burr |first3=William |last4=Polk |first4=W. |last5=Smid |first5=Miles |access-date=2023-08-28 |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000234/https://csrc.nist.gov/Pubs/sp/800/57/pt1/r3/Final |url-status=live }}</ref> Detailed test data and example message digests were also removed from the standard, and provided as separate documents.<ref>{{cite web| url=https://csrc.nist.gov/groups/ST/toolkit/examples.html#aHashing| title=NIST.gov – Computer Security Division – Computer Security Resource Center| date=29 December 2016| access-date=15 February 2022| archive-date=9 September 2017| archive-url=https://web.archive.org/web/20170909052333/http://csrc.nist.gov/groups/ST/toolkit/examples.html#aHashing| url-status=live}}</ref>

In January 2011, NIST published SP800-131A, which specified a move from the then-current minimum of 80-bit security (provided by SHA-1) allowable for federal government use until the end of 2013, to 112-bit security (provided by SHA-2) being both the minimum requirement (starting in 2014) and the recommended security level (starting from the publication date in 2011).<ref>{{Cite report |url=https://csrc.nist.gov/Pubs/sp/800/131/a/Final |title=Transitions: Recommendation for Transitioning the Use of Cryptographic Algorithms and Key Lengths |last1=Barker |first1=Elaine |last2=Roginsky |first2=Allen |date=2011-01-13 |publisher=National Institute of Standards and Technology |issue=NIST Special Publication (SP) 800-131A (Withdrawn) |language=en |access-date=2023-08-28 |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000236/https://csrc.nist.gov/Pubs/sp/800/131/a/Final |url-status=live }}</ref>

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.<ref>Federal Register Notice 2012-5400, [https://federalregister.gov/a/2012-5400 Announcing Approval of FIPS Publication 180-4].</ref>

In July 2012, NIST revised SP800-57, which provides guidance for cryptographic key management. The publication disallowed 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.<ref name=sp80057/> In August 2012, NIST revised SP800-107 in the same manner.<ref name=sp800107/>

In March 2023, NIST announced its decision to revise FIPS 180-4.<ref>NIST, [https://csrc.nist.gov/news/2023/decision-to-revise-fips-180-4 Decision to Revise FIPS 180-4, Secure Hash Standard (SHS)]</ref> FIPS 180-5 will remove the SHA-1 specification, add guidance from SP 800-107, and include editorial updates.

The NIST hash function competition selected a new hash function, SHA-3, in 2012.<ref name="nist.gov">{{cite journal| url=https://www.nist.gov/itl/csd/sha-100212.cfm| title=NIST Selects Winner of Secure Hash Algorithm (SHA-3) Competition| journal=NIST| date=2 October 2012| access-date=24 February 2015| archive-date=2 April 2015| archive-url=https://web.archive.org/web/20150402081721/http://www.nist.gov/itl/csd/sha-100212.cfm| url-status=live}}</ref> The SHA-3 algorithm is not derived from SHA-2.

==Applications== {{Further|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. The inherent computational demand of SHA-2 algorithms has driven the proposal of more efficient solutions, such as those based on application-specific integrated circuits (ASICs) hardware accelerators.<ref name="franck">{{cite journal |last1=Franck |first1=Lucas Daudt |last2=Ginja |first2=Gabriel Augusto |last3=Carmo |first3=João Paulo |last4=Afonso |first4=Jose A. |last5=Luppe |first5=Maximiliam |year=2024 |title=Custom ASIC Design for SHA-256 Using Open-Source Tools |journal=Computers |volume=13 |issue=1 |pages=9 |doi=10.3390/computers13010009 |hdl=1822/89307 |doi-access=free |hdl-access=free}}</ref>

SHA-256 is used for authenticating Debian software packages<ref>{{cite web |url=https://www.debian.org/CD/verify |title=Verifying authenticity of Debian images |access-date=2024-02-19 |archive-date=2024-02-19 |archive-url=https://web.archive.org/web/20240219133631/https://www.debian.org/CD/verify |url-status=live }}</ref> 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.<ref>{{Cite news |last=Markoff |first=John |date=2009-01-27 |title=A Tool to Verify Digital Records, Even as Technology Shifts |language=en-US |work=The New York Times |url=https://www.nytimes.com/2009/01/27/science/27arch.html |access-date=2023-08-27 |issn=0362-4331 |archive-date=2023-09-19 |archive-url=https://web.archive.org/web/20230919011821/https://www.nytimes.com/2009/01/27/science/27arch.html |url-status=live }}</ref> SHA-256 and SHA-512 are used in DNSSEC.<ref>{{Cite report |url=https://www.ietf.org/archive/id/draft-hardaker-dnsop-must-not-sha1-00.html |title=Remove SHA-1 from active use within DNSSEC |last=Hardaker |first=Wes |date=2022-08-12 |publisher=Internet Engineering Task Force |issue=draft-hardaker-dnsop-must-not-sha1-00}}</ref> Linux distributions usually use 512-bit SHA-2 for secure password hashing.<ref>{{Cite web |title=Security/Features - Debian Wiki |url=https://wiki.debian.org/Security/Features |access-date=2025-01-13 |website=wiki.debian.org}}</ref><ref>{{Cite web |title=SHA hashes – Arch Wiki |url=https://wiki.archlinux.org/title/SHA_hashes |access-date=2025-01-13 |website=wiki.archlinux.org}}</ref>

Several cryptocurrencies, including Bitcoin, use SHA-256 for verifying transactions and calculating proof of work<ref>{{Cite web |title=Bitcoin Does Not Waste Energy |url=https://surplusbitcoin.com/ |url-status=dead |archive-url=https://web.archive.org/web/20220528202245/https://surplusbitcoin.com/ |archive-date=2022-05-28 |access-date=2020-04-20 |website=Surplus Bitcoin |language=en-US}}</ref> or proof of stake.<ref>{{Cite news|url=https://www.mycryptopedia.com/sha-256-related-bitcoin/|title=What Is SHA-256 And How Is It Related to Bitcoin? - Mycryptopedia|date=2017-09-21|work=Mycryptopedia|access-date=2018-09-17|language=en-US|archive-date=2018-09-17|archive-url=https://web.archive.org/web/20180917215259/https://www.mycryptopedia.com/sha-256-related-bitcoin/|url-status=live}}</ref> The rise of ASIC SHA-2 accelerator chips has led to the use of scrypt-based proof-of-work schemes.

In both 4G and 5G mobile networks, HMAC-SHA-256 is utilized as a key derivation function (KDF) to generate cryptographic keys essential for securing communications. This process is defined in the 3rd Generation Partnership Project (3GPP) Technical Specifications TS 33.401<ref>3GPP TS 33.401, [https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=2296 Security architecture and procedures for E-UTRAN]</ref> and TS 33.501,<ref>3GPP TS 33.501, [https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3169 Security architecture and procedures for 5G systems]</ref> which outline the security architecture and procedures for these networks.

SHA-1, SHA-2, and SHA-3 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, "NIST recommends that federal agencies transition away from SHA-1 for all applications as soon as possible. Federal agencies should use SHA-2 or SHA-3 as an alternative to SHA-1.".<ref>{{Cite web |last=Computer Security Division |first=Information Technology Laboratory |date=2017-01-04 |title=NIST Policy on Hash Functions – Hash Functions {{!}} CSRC {{!}} CSRC |url=https://csrc.nist.gov/projects/hash-functions/nist-policy-on-hash-functions |access-date=2023-08-27 |website=CSRC {{!}} NIST |language=EN-US |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000235/https://csrc.nist.gov/projects/hash-functions/nist-policy-on-hash-functions |url-status=live }}</ref> NIST's directive that U.S. government agencies ought to, but not explicitly must, stop uses of SHA-1 after 2010<ref>{{cite web| url=https://csrc.nist.gov/groups/ST/toolkit/secure_hashing.html| title=Secure Hashing| work=NIST| access-date=2010-11-25| archive-url=https://web.archive.org/web/20110625054822/https://csrc.nist.gov/groups/ST/toolkit/secure_hashing.html| archive-date=2011-06-25| url-status=dead}}</ref> was hoped to accelerate migration away from SHA-1.

The SHA-2 functions were not quickly adopted initially, despite better security than SHA-1. Reasons might include lack of support for SHA-2 on systems running Windows XP SP2 or older<ref>{{cite web |url=https://download.microsoft.com/download/6/8/7/687484ed-8174-496d-8db9-f02b40c12982/Overview%20of%20Windows%20XP%20Service%20Pack%203.pdf |title=Overview of Windows XP Service Pack 3 |publisher=Microsoft Corporation |archive-url=https://web.archive.org/web/20080530175317/https://download.microsoft.com/download/6/8/7/687484ed-8174-496d-8db9-f02b40c12982/Overview%20of%20Windows%20XP%20Service%20Pack%203.pdf |archive-date=May 30, 2008 |url-status=dead |df=mdy-all }}</ref> and a lack of perceived urgency since SHA-1 collisions had 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.<ref>{{Cite web |title=Gradually Sunsetting SHA-1 |url=https://blog.chromium.org/2014/09/gradually-sunsetting-sha-1.html |access-date=2023-08-27 |website=Chromium Blog |language=en |archive-date=2023-08-07 |archive-url=https://web.archive.org/web/20230807123806/https://blog.chromium.org/2014/09/gradually-sunsetting-sha-1.html |url-status=live }}</ref><ref>{{cite web |author=Mill |first=Eric |title=SHAAAAAAAAAAAAA |url=https://shaaaaaaaaaaaaa.com/ |url-status=live |archive-url=https://web.archive.org/web/20170301035323/https://shaaaaaaaaaaaaa.com/ |archive-date=2017-03-01 |access-date=2015-08-26 |work=SHAAAAAAAAAAAAA.com}}</ref><ref>{{Cite web |date=2015-04-08 |title=The unofficial Chrome SHA1 deprecation FAQ |url=https://words.filippo.io/the-unofficial-chrome-sha1-faq/ |access-date=2023-08-27 |website=Filippo Valsorda |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000235/https://words.filippo.io/the-unofficial-chrome-sha1-faq/ |url-status=live }}</ref> Similarly, Microsoft announced<ref>{{Cite web|url=https://blogs.windows.com/msedgedev/2016/04/29/sha1-deprecation-roadmap|title=An update to our SHA-1 deprecation roadmap – Microsoft Edge Dev Blog|website=blogs.windows.com|date=29 April 2016|access-date=2016-11-28|archive-date=2016-11-28|archive-url=https://web.archive.org/web/20161128200047/https://blogs.windows.com/msedgedev/2016/04/29/sha1-deprecation-roadmap/|url-status=live}}</ref> that Internet Explorer and [[Microsoft Edge Legacy|Edge [Legacy]]] would stop honoring public SHA-1-signed TLS certificates from February 2017. Mozilla disabled SHA-1 in Firefox during early January 2016, but had to re-enable it temporarily via an update, after problems with web-based user interfaces of some router models and security appliances.<ref>{{Cite web |date=2016-01-08 |title=Firefox: Mozilla schaltet SHA-1 ab … und direkt wieder an |url=https://www.heise.de/news/Firefox-Mozilla-schaltet-SHA-1-ab-und-direkt-wieder-an-3066832.html |access-date=2025-01-18 |website=heise.de |language=de |archive-date=2023-08-28 |archive-url=https://web.archive.org/web/20230828000234/https://www.heise.de/news/Firefox-Mozilla-schaltet-SHA-1-ab-und-direkt-wieder-an-3066832.html |url-status=live }}</ref>

==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 2''L'' 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 2''L''/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 <code>shadow</code> 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 an MD5 collision which would be accepted by widely used web browsers.<ref>Alexander Sotirov, Marc Stevens, Jacob Appelbaum, Arjen Lenstra, David Molnar, Dag Arne Osvik, Benne de Weger, [https://www.win.tue.nl/hashclash/rogue-ca/ MD5 considered harmful today: Creating a rogue CA certificate]. {{Webarchive|url=https://web.archive.org/web/20220323052759/https://www.win.tue.nl/hashclash/rogue-ca/|date=2022-03-23}}, accessed March 29, 2009.</ref>

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.<ref>Ji Li, Takanori Isobe and Kyoji Shibutani, Sony China Research Laboratory and Sony Corporation, [https://fse2012.inria.fr/SLIDES/67.pdf Converting Meet-in-the-Middle Preimage Attack into Pseudo Collision Attack: Application to SHA-2 ]. {{Webarchive|url=https://web.archive.org/web/20220224204936/http://fse2012.inria.fr/SLIDES/67.pdf|date=2022-02-24}}.</ref>

{| class="wikitable sortable" |- ! Published in ! Year ! Attack method ! Attack ! Variant ! Rounds ! Complexity

|- | rowspan="2" | ''New Collision Attacks Against Up To 24-step SHA-2''<ref>{{citation |last1=Sanadhya |first1=Somitra Kumar |title=New collision attacks against up to 24-step SHA-2 |volume=5365 |pages=91–103 |year=2008 |url=https://link.springer.com/chapter/10.1007/978-3-540-89754-5_8 |access-date=2024-02-12 |archive-url=https://web.archive.org/web/20220121011031/https://link.springer.com/chapter/10.1007%2F978-3-540-89754-5_8 |archive-date=2022-01-21 |url-status=live |series=Lecture Notes in Computer Science |publisher=Springer-Verlag |doi=10.1007/978-3-540-89754-5_8 |isbn=978-3-540-89753-8 |last2=Sarkar |first2=Palash |url-access=subscription}}.</ref><ref>{{cite journal|last1=Sanadhya|first1=Somitra Kumar|last2=Sarkar|first2=Palash|title=A combinatorial analysis of recent attacks on step reduced SHA-2 family|journal=Cryptography and Communications|year=2009|volume=1 |issue=2 |pages=135–173 |url=https://link.springer.com/article/10.1007/s12095-009-0011-5|doi=10.1007/s12095-009-0011-5|access-date=2024-02-12|archive-date=2023-08-02|archive-url=https://web.archive.org/web/20230802133147/https://link.springer.com/article/10.1007/s12095-009-0011-5|url-status=live|url-access=subscription}}</ref> || rowspan="2" | 2008 || rowspan="2" | Differential || rowspan="2" | Collision || SHA-256 || 24/64 || 215.5 |- | SHA-512 || 24/80 || 222.5

|- | rowspan="4" | ''Preimages for step-reduced SHA-2''<ref name="preimage-merged">{{Cite book |last1=Aoki |first1=Kazumaro |title=Advances in Cryptology – ASIACRYPT 2009 |last2=Guo |first2=Jian |last3=Matusiewicz |first3=Krystian |last4=Sasaki |first4=Yu |last5=Wang |first5=Lei |publisher=Springer Berlin Heidelberg |year=2009 |isbn=978-3-642-10366-7 |series=Lecture Notes in Computer Science |volume=5912 |pages=578–597 |chapter=Preimages for Step-Reduced SHA-2 |doi=10.1007/978-3-642-10366-7_34 |issn=0302-9743 |name-list-style=amp}}</ref>|| rowspan="4" | 2009 || rowspan="4" | Meet-in-the-middle || rowspan="4" | Preimage || rowspan="2" | SHA-256 || 42/64 || 2251.7 |- | 43/64 || 2254.9 |- | rowspan="2" | SHA-512 || 42/80 || 2502.3 |- | 46/80 || 2511.5

|- | rowspan="2" | ''Advanced meet-in-the-middle preimage attacks''<ref name="preimage-gou">{{Cite book |last1=Guo |first1=Jian |url=https://eprint.iacr.org/2010/016.pdf |title=Advances in Cryptology – ASIACRYPT 2010 |last2=Ling |first2=San |last3=Rechberger |first3=Christian |last4=Wang |first4=Huaxiong |publisher=Springer Berlin Heidelberg |year=2010 |isbn=978-3-642-17373-8 |series=Lecture Notes in Computer Science |volume=6477 |pages=56–75 |chapter=Advanced Meet-in-the-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2 |doi=10.1007/978-3-642-17373-8_4 |issn=0302-9743 |access-date=2022-02-15 |archive-url=https://web.archive.org/web/20220303171536/https://eprint.iacr.org/2010/016.pdf |archive-date=2022-03-03 |url-status=live |name-list-style=amp}}</ref>|| rowspan="2" | 2010 || rowspan="2" | Meet-in-the-middle || rowspan="2" | Preimage || SHA-256 || 42/64 || 2248.4 |- | SHA-512 || 42/80 || 2494.6

|- | rowspan="2" | ''Higher-Order Differential Attack on Reduced SHA-256''<ref name="collision-lamberger">{{Cite journal |last1=Lamberger |first1=Mario |last2=Mendel |first2=Florian |name-list-style=amp |year=2011 |title=Higher-Order Differential Attack on Reduced SHA-256 |url=https://eprint.iacr.org/2011/037.pdf |url-status=live |journal=IACR Cryptology ePrint Archive |volume=2011 |issue=37 |archive-url=https://web.archive.org/web/20221222014546/https://eprint.iacr.org/2011/037.pdf |archive-date=2022-12-22 |access-date=2022-02-15}}</ref>|| rowspan="2" | 2011 || rowspan="2" | Differential || rowspan="2" | Pseudo-collision || rowspan="2" | SHA-256 || 46/64 || 2178 |- | 33/64 || 246

|- | rowspan="4" | ''Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family''<ref name="preimage-khov">{{Cite journal |last1=Khovratovich |first1=Dmitry |last2=Rechberger |first2=Christian |last3=Savelieva |first3=Alexandra |name-list-style=amp |year=2011 |title=Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family |url=https://eprint.iacr.org/2011/286.pdf |url-status=live |journal=IACR Cryptology ePrint Archive |volume=2011 |issue=286 |archive-url=https://web.archive.org/web/20220215055932/https://eprint.iacr.org/2011/286.pdf |archive-date=2022-02-15 |access-date=2022-02-15}}</ref>|| rowspan="4" | 2011 || rowspan="4" | Biclique || rowspan="2" | Preimage || SHA-256 || 45/64 || 2255.5 |- | SHA-512 || 50/80 || 2511.5 |- | rowspan="2" | Pseudo-preimage || SHA-256 || 52/64 || 2255 |- | SHA-512 || 57/80 || 2511

|- | rowspan="2" | ''Improving Local Collisions: New Attacks on Reduced SHA-256''<ref name="collision-mendel">{{Cite book |last1=Mendel |first1=Florian |url=https://online.tugraz.at/tug_online/voe_main2.getvolltext?pCurrPk=69018 |title=Advances in Cryptology – EUROCRYPT 2013 |last2=Nad |first2=Tomislav |last3=Schläffer |first3=Martin |publisher=Springer Berlin Heidelberg |year=2013 |isbn=978-3-642-38348-9 |series=Lecture Notes in Computer Science |volume=7881 |pages=262–278 |chapter=Improving Local Collisions: New Attacks on Reduced SHA-256 |doi=10.1007/978-3-642-38348-9_16 |issn=0302-9743 |access-date=2014-12-13 |archive-url=https://web.archive.org/web/20181106192811/https://online.tugraz.at/tug_online/voe_main2.getvolltext?pCurrPk=69018 |archive-date=2018-11-06 |url-status=live}}</ref>|| rowspan="2" | 2013 || rowspan="2" | Differential || Collision || SHA-256 || 31/64 || 265.5 |- | Pseudo-collision || SHA-256 || 38/64 || 237

|- | rowspan="1" | ''Branching Heuristics in Differential Collision Search with Applications to SHA-512''<ref name="collision-eichlseder">{{Cite journal |author=Eichlseder |first1=Maria |last2=Mendel |first2=Florian |last3=Schläffer |first3=Martin |name-list-style=and |year=2014 |title=Branching Heuristics in Differential Collision Search with Applications to SHA-512 |url=https://eprint.iacr.org/2014/302.pdf |url-status=live |journal=IACR Cryptology ePrint Archive |volume=2014 |issue=302 |archive-url=https://web.archive.org/web/20220120220202/https://eprint.iacr.org/2014/302.pdf |archive-date=2022-01-20 |access-date=2022-02-15}}</ref>|| 2014 || Heuristic differential || Pseudo-collision || SHA-512 || 38/80 || 240.5

|- | rowspan="3" | ''Analysis of SHA-512/224 and SHA-512/256''<ref>{{Cite web |last1=Dobraunig |first1=Christoph |last2=Eichlseder |first2=Maria |last3=Mendel |first3=Florian |name-list-style=amp |year=2016 |title=Analysis of SHA-512/224 and SHA-512/256 |url=https://eprint.iacr.org/2016/374.pdf |url-status=live |archive-url=https://web.archive.org/web/20170715223048/https://eprint.iacr.org/2016/374.pdf |archive-date=2017-07-15 |access-date=2016-04-15 |website=International Association for Cryptologic Research}}</ref>|| rowspan="3" | 2016 || rowspan="3" | Differential || rowspan="2" | Collision || SHA-256 || 28/64 || practical |- | SHA-512 || 27/80 || practical |- | Pseudo-collision || SHA-512 || 39/80 || practical

|- | rowspan="3" | ''New Records in Collision Attacks on SHA-2''<ref>{{cite journal | last1=Li | first1=Yingxin | last2=Liu | first2=Fukang | last3=Wang | first3=Gaoli | title=New Records in Collision Attacks on SHA-2 | journal=Cryptology ePrint Archive | date=2024 | url=https://eprint.iacr.org/2024/349 | access-date=2024-03-02 | page= | archive-date=2024-03-02 | archive-url=https://web.archive.org/web/20240302224244/https://eprint.iacr.org/2024/349 | url-status=live }}</ref> || rowspan="3" | 2024 || rowspan="3" | Differential || rowspan="2" | Collision || SHA-256 || 31/64 || 249.8 |- | SHA-512 || 31/80 || 2115.6 |- | Pseudo-collision || SHA-256 || 39/64 || practical |}

===Official validation=== {{Main|Cryptographic Module Validation Program}} 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<ref>{{cite web |title=Secure Hashing – Cryptographic Algorithm Validation Program |url=https://csrc.nist.gov/projects/cryptographic-algorithm-validation-program/secure-hashing |website=NIST CSRC |date=5 October 2016 |access-date=8 November 2025}}</ref> for certain applications.

{{As of|2013|12|post=,}} 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.<ref>{{cite web|title=SHS Validation List|url=https://csrc.nist.gov/groups/STM/cavp/documents/shs/shaval.html|website=NIST|archive-url=https://web.archive.org/web/20170617035122/https://csrc.nist.gov/groups/STM/cavp/documents/shs/shaval.html|archive-date=2017-06-17|date=2017-06-16}}</ref>

==Test vectors== Hash values of an empty string (i.e., a zero-length input text). {{color|green|SHA224("")}} 0x d14a028c2a3a2bc9476102bb288234c415a2b01f828ea62ac5b3e42f {{color|green|SHA256("")}} 0x e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855 {{color|green|SHA384("")}} 0x 38b060a751ac96384cd9327eb1b1e36a21fdb71114be07434c0cc7bf63f6e1da274edebfe76f65fbd51ad2f14898b95b {{color|green|SHA512("")}} 0x cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e {{color|green|SHA512/224("")}} 0x 6ed0dd02806fa89e25de060c19d3ac86cabb87d6a0ddd05c333b84f4 {{color|green|SHA512/256("")}} 0x c672b8d1ef56ed28ab87c3622c5114069bdd3ad7b8f9737498d0c01ecef0967a

Even a small change in the message will (with overwhelming probability) result in a different hash, due to the avalanche effect. For example, adding a period to the end of the following sentence changes approximately half (111 out of 224) of the bits in the hash, equivalent to picking a new hash at random: {{color|green|SHA224("The quick brown fox jumps over the lazy dog")}} 0x 730e109bd7a8a32b1cb9d9a09aa2325d2430587ddbc0c38bad911525 {{color|green|SHA224("The quick brown fox jumps over the lazy dog{{highlight|.}}")}} 0x 619cba8e8e05826e9b8c519c0a5c68f4fb653e8a3d8aa04bb2c8cd4c

==Pseudocode== Pseudocode for the SHA-256 algorithm follows. Note the great increase in mixing between bits of the <code>w[16..63]</code> words compared to SHA-1.

{{color|green|''Note 1: All variables are 32 bit unsigned integers and addition is calculated modulo 232''}} {{color|green|''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''}} {{color|green|''Note 3: The compression function uses 8 working variables, a through h''}} {{color|green|''Note 4: Big-endian convention is used when expressing the constants in this pseudocode,''}} {{color|green|''and when parsing message block data from bytes to words, for example,''}} {{color|green|''the first word of the input message "abc" after padding is 0x61626380''}} {{color|green|''Initialize hash values:''}} {{color|green|(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 {{color|green|''Initialize array of round constants:''}} {{color|green|(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 {{color|green|''Pre-processing (Padding):''}} begin with the original message of length L bits append a single '1' bit append K '0' bits, where K is the minimum number >= 0 such that (L + 1 + K + 64) is a multiple of 512 append L as a 64-bit big-endian integer, making the total post-processed length a multiple of 512 bits such that the bits in the message are: {{angbr|original message of length L}} 1 {{angbr|K zeros}} {{angbr|L as 64 bit integer}} , (the number of bits will be a multiple of 512) {{color|green|''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 {{color|green|''(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 {{color|green|''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 {{color|green|''Initialize working variables to current hash value:''}} a := h0 b := h1 c := h2 d := h3 e := h4 f := h5 g := h6 h := h7 {{color|green|''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 {{not a typo|a}} := temp1 '''+''' temp2 {{color|green|''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 {{color|green|''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 <code>ch</code> and <code>maj</code> 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 <code>h0</code> through <code>h7</code> are different, and * the output is constructed by omitting <code>h7</code>. {{color|green|SHA-224 initial hash values (in big endian):}} {{color|green|(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. {{pre|style=font-size:90%|1=<nowiki/> {{color|green|SHA-512 initial hash values (in big-endian):}} {{color|green|}} h[0..7] := 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179 {{color|green|SHA-512 round constants:}} {{color|green|}} k[0..79] := 0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118, 0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694, 0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65, 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, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178, 0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b, 0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c, 0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817 {{color|green|SHA-512 Sum & Sigma:}} {{color|green|}} S0 := (a '''rightrotate''' 28) '''xor''' (a '''rightrotate''' 34) '''xor''' (a '''rightrotate''' 39) S1 := (e '''rightrotate''' 14) '''xor''' (e '''rightrotate''' 18) '''xor''' (e '''rightrotate''' 41) {{color|green|}} 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 <code>h0</code> through <code>h7</code> are different (taken from the 9th through 16th primes), and * the output is constructed by omitting <code>h6</code> and <code>h7</code>. {{pre|style=font-size:90%|1=<nowiki/> {{color|green|SHA-384 initial hash values (in big-endian):}} {{color|green|}} 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 <code>h0</code> through <code>h7</code> are given by the ''SHA-512/t IV generation function'', * the output is constructed by truncating the concatenation of <code>h0</code> through <code>h7</code> 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. {{pre|style=font-size:90%|1=<nowiki/> {{color|green|SHA-512/224 initial hash values (in big-endian):}} {{color|green|}} h[0..7] := 0x8c3d37c819544da2, 0x73e1996689dcd4d6, 0x1dfab7ae32ff9c82, 0x679dd514582f9fcf, 0x0f6d2b697bd44da8, 0x77e36f7304C48942, 0x3f9d85a86a1d36C8, 0x1112e6ad91d692a1 {{color|green|SHA-512/256 initial hash values (in big-endian):}} {{color|green|}} h[0..7] := 0x22312194fc2bf72c, 0x9f555fa3c84c64c2, 0x2393b86b6f53b151, 0x963877195940eabd, 0x96283ee2a88effe3, 0xbe5e1e2553863992, 0x2b0199fc2c85b8aa, 0x0eb72ddC81c52ca2 }} 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 <code>h0</code> through <code>h7</code> have each been XORed with the hexadecimal constant <code>0xa5a5a5a5a5a5a5a5</code>.

Sample C implementation for SHA-2 family of hash functions can be found in {{IETF RFC|6234|link=no}}.

==Comparison of SHA functions== In the table below, ''internal state'' means the "internal hash sum" after each compression of a data block. {{Further|Merkle–Damgård construction}}

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.

More detailed performance measurements on modern processor architectures are given in the table below.

{| class="wikitable sortable" |- ! CPU architecture ! Frequency ! Algorithm ! Word size (bits) ! Cycles/byte x86 ! MiB/s x86 ! Cycles/byte x86-64 ! MiB/s x86-64 |- style="text-align:center;" | rowspan="2" | Intel Ivy Bridge ||- rowspan="2" | 3.5 GHz || SHA-256 || 32 || 16.80 || 199 || 13.05 || 256 |- style="text-align:center;" | SHA-512 || 64 || 43.66 || 76 || 8.48 || 394 |- style="text-align:center;" | rowspan="2" | AMD Piledriver APU ||- rowspan="2" | 3.8 GHz || SHA-256 || 32 || 22.87 || 158 || 18.47 || 196 |- style="text-align:center;" | SHA-512 || 64 || 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 APU at a clock speed of 3.8 GHz.<ref>SUPERCOP Benchmarks [https://bench.cr.yp.to/results-hash.html Measurements of hash functions, indexed by machine].</ref> 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.<ref>{{cite web|url=https://bench.cr.yp.to/supercop.html|title=SUPERCOP|access-date=24 February 2015|archive-date=15 February 2015|archive-url=https://web.archive.org/web/20150215055126/http://bench.cr.yp.to/supercop.html|url-status=live}}</ref> 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.

== Implementations == Cryptography libraries that support SHA-2:

* Botan * Bouncy Castle * Cryptlib * Crypto++ * Libgcrypt * Mbed TLS<ref>{{Cite web |url=https://tls.mbed.org/supported-ssl-ciphersuites |title=''Supported SSL / TLS ciphersuites'' |access-date=2019-10-19 |archive-date=2019-05-12 |archive-url=https://web.archive.org/web/20190512061037/https://tls.mbed.org/supported-ssl-ciphersuites |url-status=live }}</ref><ref>{{Cite web |url=https://github.com/ARMmbed/mbedtls/blob/master/ChangeLog |title=''Mbed TLS Changelog'', 7 July 2007 |website=GitHub |access-date=19 October 2019 |archive-date=4 February 2019 |archive-url=https://web.archive.org/web/20190204101359/https://github.com/ARMmbed/mbedtls/blob/master/ChangeLog |url-status=live }}</ref> * libsodium * Nettle * LibreSSL * OpenSSL * GnuTLS * wolfSSL

Hardware acceleration is provided by the following processor extensions:

* Intel SHA extensions: Available on some Intel and AMD x86 processors. * VIA PadLock * ARMv8 Cryptography Extensions<ref>{{cite web |title=ARM Cortex-A53 MPCore Processor Technical Reference Manual Cryptography Extension |url=https://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.ddi0500e/CJHDEBAF.html |access-date=2022-02-15 |archive-date=2020-06-01 |archive-url=https://web.archive.org/web/20200601095542/http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.ddi0500e/CJHDEBAF.html |url-status=live }}</ref> * IBM z/Architecture: Available since 2005 as part of the Message-Security-Assist Extensions 1 (SHA-256) and 2 (SHA-512)<ref>IBM z/Architecture Principles of Operation, publication number SA22-7832. See KIMD and KLMD instructions in Chapter 7.</ref> * IBM Power ISA since v.2.07

==See also== {{Wikifunctions|Z10124|SHA-256}} {{Wikifunctions|Z10132|SHA-384}} {{Wikifunctions|Z10067|SHA-512}} * Comparison of cryptographic hash functions * Comparison of cryptography libraries * Hash function security summary * Hashcash * HMAC * International Association for Cryptologic Research (IACR) * Trusted timestamping

==References== {{Reflist|colwidth=30em}}

==Further reading== {{Refbegin}} * Henri Gilbert, Helena Handschuh: Security Analysis of SHA-256 and Sisters. Selected Areas in Cryptography 2003: pp. 175–193. * {{cite journal |title=Proposed Revision of Federal Information Processing Standard (FIPS) 180, Secure Hash Standard |journal=Federal Register |date=1994-07-11 |volume=59 |issue=131 |pages=35317–35318 |url=https://www.federalregister.gov/documents/1994/07/11/94-16666/proposed-revision-of-federal-information-processing-standard-fips-180-secure-hash-standard |access-date=2007-04-26 |archive-date=2020-07-28 |archive-url=https://web.archive.org/web/20200728142609/https://www.federalregister.gov/documents/1994/07/11/94-16666/proposed-revision-of-federal-information-processing-standard-fips-180-secure-hash-standard |url-status=live}} {{Refend}}

==External links== * [https://web.archive.org/web/20130526224224/https://csrc.nist.gov/groups/STM/cavp/documents/shs/sha256-384-512.pdf Descriptions of SHA-256, SHA-384, and SHA-512] from NIST * [https://shachecker.com SHA-2 Checker] – SHAChecker to check one's SSL compatibility for SHA-2 * [https://fe-tool.com/hash/sha256 SHA-256 Calculator] – SHA-256 Calculator * [https://web.archive.org/web/20141008212020/https://w2.eff.org/Privacy/Digital_signature/?f=fips_sha_shs.standard.txt Specifications for a Secure Hash Standard (SHS)] – Draft for proposed SHS (SHA-0) * [https://web.archive.org/web/20141008212429/https://w2.eff.org/Privacy/Digital_signature/?f=fips_sha_shs.info.txt Secure Hash Standard (SHS)] – Proposed SHS (SHA-0) * [https://web.archive.org/web/20110625054822/https://csrc.nist.gov/groups/ST/toolkit/secure_hashing.html CSRC Cryptographic Toolkit] – Official NIST site for the Secure Hash Standard * [https://web.archive.org/web/20161126003357/https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf FIPS PUB 180-4: Secure Hash Standard (SHS)] (PDF, 834 KB) – Current version of the Secure Hash Standard (SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512), August 2015 * [https://www.cosic.esat.kuleuven.be/nessie/testvectors/hash/sha/index.html Test vectors for SHA-256/384/512] from the NESSIE project * [https://csrc.nist.gov/groups/STM/cavp/index.html#03 Test vectors for SHA-1, SHA-2] from NIST site * [https://web.archive.org/web/20100505162618/https://csrc.nist.gov/groups/ST/hash/index.html NIST Cryptographic Hash Project] – SHA-3 competition * {{IETF RFC|3874|link=no}}: "A 224-bit One-way Hash Function: SHA-224" * {{IETF RFC|6234|link=no}}: "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)"; contains sample C implementation * [https://sha256algorithm.com/ SHA-256 algorithm demonstration]

{{DEFAULTSORT:Sha-2}} Category:Cryptographic hash functions Category:Articles with example pseudocode Category:Checksum algorithms Category:National Security Agency cryptography Category:Public-domain software with source code Category:National Institute of Standards and Technology