Editing Advanced Encryption Standard (section)

=== Known attacks ===
For cryptographers, a [[cryptanalysis|cryptographic]] "break" is anything faster than a [[brute-force attack]]{{px2}}{{mdash}}{{spaces|2|hair}}i.e., performing one trial decryption for each possible key in sequence {{crossreference|(see {{slink|Cryptanalysis|Computational resources required}})}}. A break can thus include results that are infeasible with current technology. Despite being impractical, theoretical breaks can sometimes provide insight into vulnerability patterns. The largest successful publicly known brute-force attack against a widely implemented block-cipher encryption algorithm was against a 64-bit [[RC5]] key by [[distributed.net]] in 2006.<ref name=ZD20060430>{{cite web |url=https://www.zdnet.com/article/is-encryption-really-crackable/ |title=Is encryption really crackable? |first1=George |last1=Ou |publisher=Ziff-Davis |date=April 30, 2006 |archive-url=https://web.archive.org/web/20100808173034/http://www.zdnet.com/blog/ou/is-encryption-really-crackable/204 |archive-date=August 8, 2010 |access-date=August 7, 2010 |url-status=live}}</ref>

The key space increases by a factor of 2 for each additional bit of key length, and if every possible value of the key is equiprobable; this translates into a doubling of the average brute-force key search time with every additional bit of key length. This implies that the effort of a brute-force search increases exponentially with key length. Key length in itself does not imply security against attacks, since there are ciphers with very long keys that have been found to be vulnerable.

AES has a fairly simple algebraic framework.<ref>{{cite web |url=http://www.isg.rhul.ac.uk/~sean/ |title=Sean Murphy |publisher=University of London |access-date=2008-11-02 |url-status=live |archive-url=https://web.archive.org/web/20090131145521/http://www.isg.rhul.ac.uk/~sean/ |archive-date=2009-01-31}}</ref> In 2002, a theoretical attack, named the "[[XSL attack]]", was announced by [[Nicolas Courtois]] and [[Josef Pieprzyk]], purporting to show a weakness in the AES algorithm, partially due to the low complexity of its nonlinear components.<ref>{{cite web |url=http://www.schneier.com/crypto-gram-0209.html |title=AES News, Crypto-Gram Newsletter, September 15, 2002 |author=Bruce Schneier |access-date=2007-07-27 |archive-url=https://web.archive.org/web/20070707105715/http://www.schneier.com/crypto-gram-0209.html |archive-date=7 July 2007 |url-status=live}}</ref> Since then, other papers have shown that the attack, as originally presented, is unworkable; see [[XSL attack#Application to block ciphers|XSL attack on block ciphers]].

During the AES selection process, developers of competing algorithms wrote of Rijndael's algorithm "we are concerned about [its] use ... in security-critical applications."<ref name="rijndael-algebraic">
{{cite conference |author=Niels Ferguson |author-link=Niels Ferguson |author2=Richard Schroeppel |author2-link=Richard Schroeppel |author3=Doug Whiting |title=A simple algebraic representation of Rijndael |book-title=Proceedings of Selected Areas in Cryptography, 2001, Lecture Notes in Computer Science |pages=103–111 |publisher=[[Springer-Verlag]] |date=2001 |url=http://www.macfergus.com/pub/rdalgeq.html |format=PDF/[[PostScript]] |access-date=2006-10-06 |archive-url=https://web.archive.org/web/20061104080748/http://www.macfergus.com/pub/rdalgeq.html |archive-date=4 November 2006 |citeseerx=10.1.1.28.4921}}</ref> In October 2000, however, at the end of the AES selection process, [[Bruce Schneier]], a developer of the competing algorithm [[Twofish]], wrote that while he thought successful academic attacks on Rijndael would be developed someday, he "did not believe that anyone will ever discover an attack that will allow someone to read Rijndael traffic."<ref>Bruce Schneier, [http://www.schneier.com/crypto-gram-0010.html AES Announced] {{webarchive|url=https://web.archive.org/web/20090201005720/http://www.schneier.com/crypto-gram-0010.html |date=2009-02-01 }}, October 15, 2000</ref>

By 2006, the best known attacks were on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys.<ref name="improved">[[John Kelsey (cryptanalyst)|John Kelsey]], [[Stefan Lucks]], [[Bruce Schneier]], [[Mike Stay]], [[David A. Wagner|David Wagner]], and [[Doug Whiting]], ''Improved Cryptanalysis of Rijndael'', [[Fast Software Encryption]], 2000 pp213–230 {{cite web |title=Academic: Improved Cryptanalysis of Rijndael - Schneier on Security |url=http://www.schneier.com/paper-rijndael.html |url-status=live |archive-url=https://web.archive.org/web/20070223215007/http://www.schneier.com/paper-rijndael.html |archive-date=2007-02-23 |access-date=2007-03-06}}</ref>

Until May 2009, the only successful published attacks against the full AES were [[side-channel attack]]s on some specific implementations. In 2009, a new [[related-key attack]] was discovered that exploits the simplicity of AES's key schedule and has a complexity of 2<sup>119</sup>. In December 2009 it was improved to 2<sup>99.5</sup>.<ref name=relkey /> This is a follow-up to an attack discovered earlier in 2009 by [[Alex Biryukov]], [[Dmitry Khovratovich]], and Ivica Nikolić, with a complexity of 2<sup>96</sup> for one out of every 2<sup>35</sup> keys.<ref>{{cite book |volume=5677 |chapter=Distinguisher and Related-Key Attack on the Full AES-256 |last1=Nikolić |first1=Ivica |title=Advances in Cryptology - CRYPTO 2009 |date=2009 |publisher=Springer Berlin / Heidelberg |isbn=978-3-642-03355-1 |pages=231–249 |doi=10.1007/978-3-642-03356-8_14 |series=Lecture Notes in Computer Science}}</ref> However, related-key attacks are not of concern in any properly designed cryptographic protocol, as a properly designed protocol (i.e., implementational software) will take care not to allow related keys, essentially by [[Related-key attack#Preventing related-key attacks|constraining]] an attacker's means of selecting keys for relatedness.

Another attack was blogged by Bruce Schneier<ref name="Bruce Schneier">{{cite web |url=http://www.schneier.com/blog/archives/2009/07/another_new_aes.html |title=Another New AES Attack |author=Bruce Schneier |date=2009-07-30 |work=Schneier on Security, A blog covering security and security technology |access-date=2010-03-11 |url-status=live |archive-url=https://web.archive.org/web/20091005183132/http://www.schneier.com/blog/archives/2009/07/another_new_aes.html |archive-date=2009-10-05}}</ref>
on July 30, 2009, and released as a [[preprint]]<ref>{{cite web |url=http://eprint.iacr.org/2009/374 |title=Key Recovery Attacks of Practical Complexity on AES Variants With Up To 10 Rounds |author=Alex Biryukov |author2=Orr Dunkelman |author3=Nathan Keller |author4=Dmitry Khovratovich |author5=Adi Shamir |date=2009-08-19 |access-date=2010-03-11 |archive-url=https://web.archive.org/web/20100128050656/http://eprint.iacr.org/2009/374 |archive-date=28 January 2010 |url-status=live}}</ref>
on August 3, 2009. This new attack, by Alex Biryukov, [[Orr Dunkelman]], [[Nathan Keller]], Dmitry Khovratovich, and [[Adi Shamir]], is against AES-256 that uses only two related keys and 2<sup>39</sup> time to recover the complete 256-bit key of a 9-round version, or 2<sup>45</sup> time for a 10-round version with a stronger type of related subkey attack, or 2<sup>70</sup> time for an 11-round version. 256-bit AES uses 14 rounds, so these attacks are not effective against full AES.

The practicality of these attacks with stronger related keys has been criticized,<ref>{{Cite book |title=On Some Symmetric Lightweight Cryptographic Designs |last=Agren |first=Martin |publisher=Dissertation, Lund University |year=2012 |pages=38–39}}</ref> for instance, by the paper on chosen-key-relations-in-the-middle attacks on AES-128 authored by Vincent Rijmen in 2010.<ref>{{cite journal |url=http://eprint.iacr.org/2010/337.pdf |title=Practical-Titled Attack on AES-128 Using Chosen-Text Relations |author=Vincent Rijmen |date=2010 |journal=IACR Cryptology ePrint Archive |url-status=live |archive-url=https://web.archive.org/web/20100702184311/http://eprint.iacr.org/2010/337.pdf |archive-date=2010-07-02}}</ref>

In November 2009, the first [[known-key distinguishing attack]] against a reduced 8-round version of AES-128 was released as a preprint.<ref>{{cite journal |url=http://eprint.iacr.org/2009/531 |title=Super-Sbox Cryptanalysis: Improved Attacks for AES-like permutations |author=Henri Gilbert |author2=Thomas Peyrin |date=2009-11-09 |journal=IACR Cryptology ePrint Archive |access-date=2010-03-11 |url-status=live |archive-url=https://web.archive.org/web/20100604095754/http://eprint.iacr.org/2009/531 |archive-date=2010-06-04}}</ref>
This known-key distinguishing attack is an improvement of the rebound, or the start-from-the-middle attack, against AES-like permutations, which view two consecutive rounds of permutation as the application of a so-called Super-S-box. It works on the 8-round version of AES-128, with a time complexity of 2<sup>48</sup>, and a memory complexity of 2<sup>32</sup>.  128-bit AES uses 10 rounds, so this attack is not effective against full AES-128.

The first [[key-recovery attack]]s on full AES were by Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger, and were published in 2011.<ref>{{Cite book |chapter=Biclique Cryptanalysis of the Full AES |title=Advances in Cryptology – ASIACRYPT 2011 |last1=Bogdanov |first1=Andrey |volume=7073 |pages=344–371 |last2=Khovratovich |first2=Dmitry |last3=Rechberger |first3=Christian |doi=10.1007/978-3-642-25385-0_19 |series=Lecture Notes in Computer Science |date=2011 |editor-first1=Dong Hoon |editor-last1=Lee |editor-first2=Xiaoyun |editor-last2=Wang |isbn=978-3-642-25385-0}}</ref> The attack is a [[biclique attack]] and is faster than brute force by a factor of about four. It requires 2<sup>126.2</sup> operations to recover an AES-128 key. For AES-192 and AES-256, 2<sup>190.2</sup> and 2<sup>254.6</sup> operations are needed, respectively. This result has been further improved to 2<sup>126.0</sup> for AES-128, 2<sup>189.9</sup> for AES-192, and 2<sup>254.3</sup> for AES-256 by Biaoshuai Tao and Hongjun Wu in a 2015 paper,<ref name=":0">{{cite book |first1=Biaoshuai |last1=Tao |title=Information Security and Privacy |volume=9144 |pages=39–56 |first2=Hongjun |last2=Wu |chapter=Improving the Biclique Cryptanalysis of AES |date=2015 |doi=10.1007/978-3-319-19962-7_3 |series=Lecture Notes in Computer Science |isbn=978-3-319-19962-7 |editor-first1=Ernest |editor-last1=Foo |editor-first2=Douglas |editor-last2=Stebila}}</ref> which are the current best results in key recovery attack against AES.

This is a very small gain, as a 126-bit key (instead of 128 bits) would still take billions of years to brute force on current and foreseeable hardware. Also, the authors calculate the best attack using their technique on AES with a 128-bit key requires storing 2<sup>88</sup> bits of data. That works out to about 38 trillion terabytes of data, which was more than all the data stored on all the computers on the planet in 2016.<ref>{{cite web |author=Jeffrey Goldberg |title=AES Encryption isn't Cracked |url=https://blog.agilebits.com/2011/08/18/aes-encryption-isnt-cracked/ |access-date=30 December 2014 |url-status=dead |archive-url=https://web.archive.org/web/20150108165723/https://blog.agilebits.com/2011/08/18/aes-encryption-isnt-cracked/ |archive-date=8 January 2015 |date=2011-08-18}}</ref> A paper in 2015 later improved the space complexity to 2<sup>56</sup> bits,<ref name=":0"/> which is 9007 terabytes (while still keeping a time complexity of approximately 2<sup>126</sup>).

According to the [[Edward Snowden#Surveillance disclosures|Snowden documents]], the NSA is doing research on whether a cryptographic attack based on [[Kendall tau rank correlation coefficient|tau statistic]] may help to break AES.<ref>{{cite news |url=http://www.spiegel.de/international/germany/inside-the-nsa-s-war-on-internet-security-a-1010361.html |title=Prying Eyes: Inside the NSA's War on Internet Security |location=Hamburg, Germany |date=28 December 2014 |work=[[Der Spiegel (website)|Spiegel Online]] |access-date=4 September 2015 |url-status=live |archive-url=https://web.archive.org/web/20150124202809/http://www.spiegel.de/international/germany/inside-the-nsa-s-war-on-internet-security-a-1010361.html |archive-date=24 January 2015}}</ref>

At present, there is no known practical attack that would allow someone without knowledge of the key to read data encrypted by AES when correctly implemented.{{cn|date=September 2024}}