Editing SHA-1 (section)

===Attacks===
In early 2005, [[Vincent Rijmen]] and [[Elisabeth 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 2<sup>80</sup> operations.<ref>{{cite journal |url=http://eprint.iacr.org/2005/010|title=Update on SHA-1 |journal=Cryptology ePrint Archive |year=2005|last1=Rijmen|first1=Vincent|last2=Oswald|first2=Elisabeth}}</ref>

In February 2005, an attack by [[Xiaoyun Wang]], Yiqun Lisa Yin, and Hongbo Yu was announced.<ref name="autogenerated1" /> The attacks can find collisions in the full version of SHA-1, requiring fewer than 2<sup>69</sup> operations. (A [[brute-force search]] would require 2<sup>80</sup> operations.)

The authors write: "In particular, our analysis is built upon the original differential attack on SHA-0, the near collision attack on SHA-0, the multiblock collision techniques, as well as the message modification techniques used in the collision search attack on MD5. Breaking SHA-1 would not be possible without these powerful analytical techniques."<ref>[http://theory.csail.mit.edu/~yiqun/shanote.pdf Collision Search Attacks on SHA1] {{Webarchive|url=https://web.archive.org/web/20050219180957/http://theory.csail.mit.edu/~yiqun/shanote.pdf |date=2005-02-19 }}, [[Massachusetts Institute of Technology]]</ref> The authors have presented a collision for 58-round SHA-1, found with 2<sup>33</sup> 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."<ref>{{cite web|url=https://www.zdnet.com/article/fixing-a-hole-in-security/|title=Fixing a hole in security|first=Robert |last=Lemos|work=ZDNet}}</ref>

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 2<sup>63</sup>.<ref name=":3">{{Cite web |title=New Cryptanalytic Results Against SHA-1 – Schneier on Security |url=https://www.schneier.com/blog/archives/2005/08/new_cryptanalyt.html |website=www.schneier.com}}</ref> On 18 December 2007 the details of this result were explained and verified by Martin Cochran.<ref>{{cite journal| url = http://eprint.iacr.org/2007/474| title = Notes on the Wang et al. 2<sup>63</sup> SHA-1 Differential Path| year = 2007| last1 = Cochran| first1 = Martin| journal = Cryptology ePrint Archive}}</ref>

Christophe De Cannière and Christian Rechberger further improved the attack on SHA-1 in "Finding SHA-1 Characteristics: General Results and Applications,"<ref>{{Cite book |first1=Christophe |title=Advances in Cryptology – ASIACRYPT 2006 |volume=4284 |pages=1–20 |last1=De Cannière |first2=Christian |last2=Rechberger |date=2006-11-15 |chapter=Finding SHA-1 Characteristics: General Results and Applications |doi=10.1007/11935230_1 |series=Lecture Notes in Computer Science |isbn=978-3-540-49475-1 }}</ref> receiving the Best Paper Award at [[ASIACRYPT]] 2006. A two-block collision for 64-round SHA-1 was presented, found using unoptimized methods with 2<sup>35</sup> compression function evaluations. Since this attack requires the equivalent of about 2<sup>35</sup> evaluations, it is considered to be a significant theoretical break.<ref>{{cite web
 | url = http://www.iaik.tugraz.at/content/research/krypto/sha1/SHA1Collision_Description.php
 | title = IAIK Krypto Group&nbsp;— Description of SHA-1 Collision Search Project
 | access-date = 2009-06-30
 | archive-url = https://web.archive.org/web/20130115071715/http://www.iaik.tugraz.at/content/research/krypto/sha1/SHA1Collision_Description.php
 | archive-date = 2013-01-15
 | url-status = dead
 }}</ref> Their attack was extended further to 73 rounds (of 80) in 2010 by Grechnikov.<ref>{{cite web
 | url = http://eprint.iacr.org/2010/413
 | title = Collisions for 72-step and 73-step SHA-1: Improvements in the Method of Characteristics
 | access-date = 2010-07-24
}}</ref> In order to find an actual collision in the full 80 rounds of the hash function, however, tremendous amounts of computer time are required. To that end, a collision search for SHA-1 using the volunteer computing platform [[BOINC]] began August 8, 2007, organized by the [[Graz University of Technology]]. The effort was abandoned May 12, 2009 due to lack of progress.<ref>{{cite web
 |url         = http://boinc.iaik.tugraz.at/sha1_coll_search/
 |title       = SHA-1 Collision Search Graz
 |access-date  = 2009-06-30
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20090225115007/http://boinc.iaik.tugraz.at/sha1_coll_search/
 |archive-date = 2009-02-25
}}</ref>

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.<ref>{{cite web|url=http://www.heise-online.co.uk/security/SHA-1-hash-function-under-pressure--/news/77244|title=heise online – IT-News, Nachrichten und Hintergründe|work=heise online|date=27 August 2023 }}</ref><ref>{{Cite web|url=https://www.iacr.org/conferences/crypto2006/rumpsched.html|title=Crypto 2006 Rump Schedule|website=www.iacr.org}}</ref>

In 2008, an attack methodology by Stéphane Manuel reported hash collisions with an estimated theoretical complexity of 2<sup>51</sup> to 2<sup>57</sup> operations.<ref>{{Cite web | first=Stéphane |last=Manuel | title=Classification and Generation of Disturbance Vectors for Collision Attacks against SHA-1 |website=Cryptology ePrint Archive |url=http://eprint.iacr.org/2008/469.pdf | access-date = 2011-05-19 }}</ref> However he later retracted that claim after finding that local collision paths were not actually independent, and finally quoting for the most efficient a collision vector that was already known before this work.<ref>{{Cite journal | first=Stéphane | last=Manuel | title=Classification and Generation of Disturbance Vectors for Collision Attacks against SHA-1 | journal=Designs, Codes and Cryptography | volume=59 | issue=1–3 | pages=247–263 | doi=10.1007/s10623-010-9458-9 | year=2011 | s2cid=47179704 }} ''the most efficient disturbance vector is Codeword2 first reported by Jutla and Patthak''</ref>

Cameron McDonald, Philip Hawkes and Josef Pieprzyk presented a hash collision attack with claimed complexity 2<sup>52</sup> at the Rump Session of Eurocrypt 2009.<ref>{{cite web| url = http://eurocrypt2009rump.cr.yp.to/837a0a8086fa6ca714249409ddfae43d.pdf| title = SHA-1 collisions now 2^52 }}</ref> However, the accompanying paper, "Differential Path for SHA-1 with complexity [[Big O notation|''O'']](2<sup>52</sup>)" has been withdrawn due to the authors' discovery that their estimate was incorrect.<ref>{{cite journal |url=http://eprint.iacr.org/2009/259|title=Differential Path for SHA-1 with complexity O(<sup>252</sup>) |journal=Cryptology ePrint Archive |year=2009|last1=McDonald|first1=Cameron|last2=Hawkes|first2=Philip|last3=Pieprzyk|first3=Josef}} (withdrawn)</ref>

One attack against SHA-1 was Marc Stevens<ref name="Cryptanalysis of MD5 & SHA-1">{{cite web| url = http://2012.sharcs.org/slides/stevens.pdf| title = Cryptanalysis of MD5 & SHA-1}}</ref> with an estimated cost of $2.77M (2012) to break a single hash value by renting CPU power from cloud servers.<ref>{{Cite web |title=When Will We See Collisions for SHA-1? – Schneier on Security |url=https://www.schneier.com/blog/archives/2012/10/when_will_we_se.html |website=www.schneier.com}}</ref> Stevens developed this attack in a project called HashClash,<ref>{{Cite web |title=Google Code Archive – Long-term storage for Google Code Project Hosting. |url=https://code.google.com/archive/p/hashclash |website=code.google.com}}</ref> implementing a differential path attack. On 8 November 2010, he claimed he had a fully working near-collision attack against full SHA-1 working with an estimated complexity equivalent to 2<sup>57.5</sup> SHA-1 compressions. He estimated this attack could be extended to a full collision with a complexity around 2<sup>61</sup>.

====The SHAppening====
On 8 October 2015, Marc Stevens, Pierre Karpman, and Thomas Peyrin published a freestart collision attack on SHA-1's compression function that requires only 2<sup>57</sup> SHA-1 evaluations. This does not directly translate into a collision on the full SHA-1 hash function (where an attacker is ''not'' able to freely choose the initial internal state), but undermines the security claims for SHA-1. In particular, it was the first time that an attack on full SHA-1 had been ''demonstrated''; all earlier attacks were too expensive for their authors to carry them out. The authors named this significant breakthrough in the [[cryptanalysis]] of SHA-1 ''The SHAppening''.<ref name="shappening" />

The method was based on their earlier work, as well as the auxiliary paths (or boomerangs) speed-up technique from Joux and Peyrin, and using high performance/cost efficient GPU cards from [[Nvidia]]. The collision was found on a 16-node cluster with a total of 64 graphics cards. The authors estimated that a similar collision could be found by buying US$2,000 of GPU time on [[Amazon Elastic Compute Cloud|EC2]].<ref name="shappening" />

The authors estimated that the cost of renting enough of EC2 CPU/GPU time to generate a full collision for SHA-1 at the time of publication was between US$75K and $120K, and noted that was well within the budget of criminal organizations, not to mention national [[intelligence agency|intelligence agencies]]. As such, the authors recommended that SHA-1 be deprecated as quickly as possible.<ref name="shappening">{{cite web |url=https://sites.google.com/site/itstheshappening/ |title=The SHAppening: freestart collisions for SHA-1 |access-date=2015-10-09 |first1=Marc |last1=Stevens |first2=Pierre |last2=Karpman |first3=Thomas |last3=Peyrin}}</ref>

==== SHAttered – first public collision ====
On 23 February 2017, the [[Centrum Wiskunde & Informatica|CWI (Centrum Wiskunde & Informatica)]] and Google announced the ''SHAttered'' attack, in which they generated two different PDF files with the same SHA-1 hash in roughly 2<sup>63.1</sup> SHA-1 evaluations. This attack is about 100,000 times faster than brute forcing a SHA-1 collision with a [[birthday attack]], which was estimated to take 2<sup>80</sup> SHA-1 evaluations. The attack required "the equivalent processing power of 6,500 years of single-CPU computations and 110 years of single-GPU computations".<ref name="sha1-shattered"/>

==== Birthday-Near-Collision Attack – first practical chosen-prefix attack ====
On 24 April 2019 a paper by Gaëtan Leurent and Thomas Peyrin presented at Eurocrypt 2019 described an enhancement to the previously best [[Collision attack#Chosen-prefix collision attack|chosen-prefix attack]] in [[Merkle–Damgård construction|Merkle–Damgård]]–like digest functions based on [[One-way compression function#Davies–Meyer|Davies–Meyer]] block ciphers. With these improvements, this method is capable of finding chosen-prefix collisions in approximately 2<sup>68</sup> SHA-1 evaluations. This is approximately 1 billion times faster (and now usable for many targeted attacks, thanks to the possibility of choosing a prefix, for example malicious code or faked identities in signed certificates) than the previous attack's 2<sup>77.1</sup> evaluations (but without chosen prefix, which was impractical for most targeted attacks because the found collisions were almost random)<ref name="stevens-attacks"/> and is fast enough to be practical for resourceful attackers, requiring approximately $100,000 of cloud processing. This method is also capable of finding chosen-prefix collisions in the [[MD5]] function, but at a complexity of 2<sup>46.3</sup> does not surpass the prior best available method at a theoretical level (2<sup>39</sup>), though potentially at a practical level (≤2<sup>49</sup>).<ref name="leurent-peyrin-sha1">{{cite conference |chapter-url=https://hal.inria.fr/hal-02424900/file/SHA1_EC19.pdf |last1=Leurent |first1=Gaëtan |last2=Peyrin |first2=Thomas |title=Advances in Cryptology – EUROCRYPT 2019 |chapter=From Collisions to Chosen-Prefix Collisions Application to Full SHA-1 | conference= 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19–23, 2019 |date=2019 |url=https://eprint.iacr.org/2019/459.pdf | publisher= Springer |series=Lecture Notes in Computer Science |volume=11478 |pages=527–555 |doi=10.1007/978-3-030-17659-4_18 |isbn=978-3-030-17658-7 |s2cid=153311244 | editor1= Yuval Ishai| editor2= Vincent Rijmen}}</ref> This attack has a memory requirement of 500+ GB.

On 5 January 2020 the authors published an improved attack called "shambles".<ref name="leurent-peyrin-sha1-shambles"/> In this paper they demonstrate a chosen-prefix collision attack with a complexity of 2<sup>63.4</sup>, that at the time of publication would cost US$45K per generated collision.