Editing Data Encryption Standard (section)

== Security and cryptanalysis ==
Although more information has been published on the cryptanalysis of DES than any other block cipher, the most practical attack to date is still a brute-force approach. Various minor cryptanalytic properties are known, and three theoretical attacks are possible which, while having a theoretical complexity less than a brute-force attack, require an unrealistic number of [[known plaintext|known]] or [[chosen plaintext]]s to carry out, and are not a concern in practice.

=== Brute-force attack ===
For any [[cipher]], the most basic method of attack is [[brute-force attack|brute force]]—trying every possible key in turn. The [[key length|length of the key]] determines the number of possible keys, and hence the feasibility of this approach. For DES, questions were raised about the adequacy of its key size early on, even before it was adopted as a standard, and it was the small key size, rather than theoretical cryptanalysis, which dictated a need for a replacement [[algorithm]]. As a result of discussions involving external consultants including the NSA, the key size was reduced from 256 bits to 56 bits to fit on a single chip.<ref name="stallings-2006">Stallings, W. ''Cryptography and network security: principles and practice''. Prentice Hall, 2006. p. 73</ref>

[[File:Board300.jpg|thumb|The [[Electronic Frontier Foundation|EFF]]'s US$250,000 [[EFF DES cracker|DES cracking machine]] contained 1,856 custom chips and could brute-force a DES key in a matter of days—the photo shows a DES Cracker circuit board fitted with several Deep Crack chips.]]

In academia, various proposals for a DES-cracking machine were advanced. In 1977, Diffie and Hellman proposed a machine costing an estimated US$20 million which could find a DES key in a single day.<ref name="dh-exh"/><ref>{{Cite web | url=http://hamburgsteak.sandwich.net/writ/bruting_des.html | title=Bruting DES}}</ref> By 1993, Wiener had proposed a key-search machine costing US$1 million which would find a key within 7 hours. However, none of these early proposals were ever implemented—or, at least, no implementations were publicly acknowledged. The vulnerability of DES was practically demonstrated in the late 1990s.<ref>{{Citation|last1=van Oorschot|first1=Paul C.|title=A Known-Plaintext Attack on Two-Key Triple Encryption|date=1991|work=Advances in Cryptology – EUROCRYPT ’90|volume=473|pages=318–325|editor-last=Damgård|editor-first=Ivan Bjerre|place=Berlin, Heidelberg|publisher=Springer Berlin Heidelberg|doi=10.1007/3-540-46877-3_29|isbn=978-3-540-53587-4|last2=Wiener|first2=Michael J.|doi-access=free}}</ref> In 1997, [[RSA Security]] sponsored a series of contests, offering a $10,000 prize to the first team that broke a message encrypted with DES for the contest. That contest was won by the [[DESCHALL Project]], led by Rocke Verser, [[Matt Curtin]], and Justin Dolske, using idle cycles of thousands of computers across the Internet. The feasibility of cracking DES quickly was demonstrated in 1998 when a custom DES-cracker was built by the [[Electronic Frontier Foundation]] (EFF), a cyberspace civil rights group, at the cost of approximately US$250,000 (see [[EFF DES cracker]]). Their motivation was to show that DES was breakable in practice as well as in theory: "''There are many people who will not believe a truth until they can see it with their own eyes. Showing them a physical machine that can crack DES in a few days is the only way to convince some people that they really cannot trust their security to DES.''" The machine brute-forced a key in a little more than 2 days' worth of searching.

The next confirmed DES cracker was the COPACOBANA machine built in 2006 by teams of the [[Ruhr University|Universities of Bochum]] and [[University of Kiel|Kiel]], both in [[Germany]]. Unlike the EFF machine, COPACOBANA consists of commercially available, reconfigurable integrated circuits. 120 of these [[field-programmable gate array]]s (FPGAs) of type XILINX Spartan-3 1000 run in parallel. They are grouped in 20 DIMM modules, each containing 6 FPGAs. The use of reconfigurable hardware makes the machine applicable to other code breaking tasks as well.<ref>{{cite web
 | title = Getting Started, COPACOBANA — Cost-optimized Parallel Code-Breaker
 | url = http://www.copacobana.org/paper/copacobana_gettingstarted.pdf
 | date = December 12, 2006
 | access-date = March 6, 2012
}}</ref>  One of the more interesting aspects of COPACOBANA is its cost factor. One machine can be built for approximately $10,000.<ref>{{cite book
 | author = Reinhard Wobst
 | title = Cryptology Unlocked
 | url = https://archive.org/details/Cryptology_Unlocked
 | date = October 16, 2007
 | publisher = John Wiley & Sons
| isbn = 9780470060643
 }}</ref> The cost decrease by roughly a factor of 25 over the EFF machine is an example of the continuous improvement of [[digital hardware]]—see [[Moore's law]]. Adjusting for inflation over 8 years yields an even higher improvement of about 30x. Since 2007, [[SciEngines GmbH]], a spin-off company of the two project partners of COPACOBANA has enhanced and developed successors of COPACOBANA. In 2008 their COPACOBANA RIVYERA reduced the time to break DES to less than one day, using 128 Spartan-3 5000's. SciEngines RIVYERA held the record in brute-force breaking DES, having utilized 128 Spartan-3 5000 FPGAs.<ref>[http://www.sciengines.com/company/news-a-events/74-des-in-1-day.html Break DES in less than a single day] {{Webarchive|url=https://web.archive.org/web/20170828035212/http://www.sciengines.com/company/news-a-events/74-des-in-1-day.html |date=2017-08-28 }} [Press release of Firm, demonstrated on 2009 Workshop]</ref> Their 256 Spartan-6 LX150 model has further lowered this time.

In 2012, David Hulton and [[Moxie Marlinspike]] announced a system with 48 Xilinx Virtex-6 LX240T FPGAs, each FPGA containing 40 fully pipelined DES cores running at 400&nbsp;MHz, for a total capacity of  768 gigakeys/sec. The system can exhaustively search the entire 56-bit DES key space in about 26 hours and this service is offered for a fee online.<ref>{{cite web| url = http://crack.sh| title = The World's fastest DES cracker}}</ref><ref>''Think Complex Passwords Will Save You?,'' David Hulton, Ian Foster, BSidesLV 2017</ref> However, the service has been offline since the year 2024, supposedly for maintenance but probably permanently switched off. <ref>{{cite web| url =https://crack.sh/get-cracking/| title = DES Cracker is currently down for maintenance}}</ref>

=== Attacks faster than brute force ===
There are three attacks known that can break the full 16 rounds of DES with less complexity than a brute-force search: [[differential cryptanalysis]] (DC),<ref name=":0" /> [[linear cryptanalysis]] (LC),<ref name=":1" /> and [[Davies' attack]].<ref name=":2" /> However, the attacks are theoretical and are generally considered infeasible to mount in practice;<ref>{{Cite journal|last=Alanazi|first=Hamdan O.|display-authors=et al|date=2010|title=New Comparative Study Between DES, 3DES and AES within Nine Factors|arxiv=1003.4085|journal=Journal of Computing|volume=2|issue=3|bibcode=2010arXiv1003.4085A}}</ref> these types of attack are sometimes termed certificational weaknesses.

* [[Differential cryptanalysis]] was rediscovered in the late 1980s by [[Eli Biham]] and [[Adi Shamir]]; it was known earlier to both IBM and the NSA and kept secret. To break the full 16 rounds, differential cryptanalysis requires 2<sup>47</sup> [[chosen plaintext]]s.<ref name=":0">{{Cite book|url=https://link.springer.com/978-1-4613-9314-6|title=Differential cryptanalysis of the data encryption standard|last=Biham, E. & Shamir, A|date=1993|publisher=Springer-Verlag|others=Shamir, Adi.|isbn=978-0387979304|location=New York|pages=487–496|doi=10.1007/978-1-4613-9314-6|s2cid=6361693|oclc=27173465}}</ref> DES was designed to be resistant to DC.{{Citation needed|reason=Need a source that will help the reader find how DES was designed to be DC-resistant|date=August 2022}}
* [[Linear cryptanalysis]] was discovered by [[Mitsuru Matsui]], and needs 2<sup>43</sup> [[known plaintext]]s (Matsui, 1993);<ref name=":1">{{Cite book|last=Matsui|first=Mitsuru|title=Advances in Cryptology — EUROCRYPT '93 |chapter=Linear Cryptanalysis Method for DES Cipher |date=1993-05-23|volume=765|series=Lecture Notes in Computer Science|language=en|publisher=Springer, Berlin, Heidelberg|pages=386–397|doi=10.1007/3-540-48285-7_33|isbn=978-3540482857|doi-access=free}}</ref> the method was implemented (Matsui, 1994), and was the first experimental cryptanalysis of DES to be reported. There is no evidence that DES was tailored to be resistant to this type of attack. A generalization of LC—''multiple linear cryptanalysis''—was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov and others. (2004); their analysis suggests that multiple linear approximations could be used to reduce the data requirements of the attack by at least a factor of 4 (that is, 2<sup>41</sup> instead of 2<sup>43</sup>).<ref>{{Cite book|last1=Biryukov|first1=Alex|last2=Cannière|first2=Christophe De|last3=Quisquater|first3=Michaël|title=Advances in Cryptology – CRYPTO 2004 |chapter=On Multiple Linear Approximations |date=2004-08-15|series=Lecture Notes in Computer Science|volume=3152 |language=en|publisher=Springer, Berlin, Heidelberg|pages=1–22|doi=10.1007/978-3-540-28628-8_1|isbn=9783540226680}}</ref> A similar reduction in data complexity can be obtained in a chosen-plaintext variant of linear cryptanalysis (Knudsen and Mathiassen, 2000).<ref>{{Cite book|last1=Knudsen|first1=Lars R.|last2=Mathiassen|first2=John Erik|title=Fast Software Encryption |chapter=A Chosen-Plaintext Linear Attack on DES |date=2000-04-10|series=Lecture Notes in Computer Science|volume=1978 |language=en|publisher=Springer, Berlin, Heidelberg|pages=262–272|doi=10.1007/3-540-44706-7_18|isbn=978-3540447061}}</ref> Junod (2001) performed several experiments to determine the actual time complexity of linear cryptanalysis, and reported that it was somewhat faster than predicted, requiring time equivalent to 2<sup>39</sup>–2<sup>41</sup> DES evaluations.<ref>{{Cite book|last=Junod|first=Pascal|title=Selected Areas in Cryptography |chapter=On the Complexity of Matsui's Attack |date=2001-08-16|volume=2259|series=Lecture Notes in Computer Science|language=en|publisher=Springer, Berlin, Heidelberg|pages=199–211|doi=10.1007/3-540-45537-X_16|isbn=978-3540455370}}</ref>
* ''Improved Davies' attack'': while linear and differential cryptanalysis are general techniques and can be applied to a number of schemes, Davies' attack is a specialized technique for DES, first suggested by [[Donald Davies]] in the eighties,<ref name=":2">{{Cite journal|last=Davies|first=D. W.|date=1987|title=Investigation of a potential weakness in the DES algorithm, Private communications|url=https://scholar.google.com/scholar?q=D.%20W.%20Davies%2C%20Investigation%20of%20a%20potential%20weakness%20in%20the%20DES%20algorithm%2C%20Private%20communications%2C%201987.|journal=Private Communications}}</ref> and improved by Biham and [[Alex Biryukov|Biryukov]] (1997).<ref>{{Cite journal|last1=Biham|first1=Eli|last2=Biryukov|first2=Alex|date=1997-06-01|title=An improvement of Davies' attack on DES|journal=Journal of Cryptology|language=en|volume=10|issue=3|pages=195–205|doi=10.1007/s001459900027|s2cid=4070446|issn=0933-2790|doi-access=free}}</ref> The most powerful form of the attack requires 2<sup>50</sup> [[known plaintext]]s, has a computational complexity of 2<sup>50</sup>, and has a 51% success rate.

There have also been attacks proposed against reduced-round versions of the cipher, that is, versions of DES with fewer than 16 rounds. Such analysis gives an insight into how many rounds are needed for safety, and how much of a "security margin" the full version retains.

[[Differential-linear cryptanalysis]] was proposed by Langford and Hellman in 1994, and combines differential and linear cryptanalysis into a single attack.<ref>{{Cite book|last1=Langford|first1=Susan K.|last2=Hellman|first2=Martin E.|title=Advances in Cryptology — CRYPTO '94 |chapter=Differential-Linear Cryptanalysis |date=1994-08-21|series=Lecture Notes in Computer Science|volume=839 |language=en|publisher=Springer, Berlin, Heidelberg|pages=17–25|doi=10.1007/3-540-48658-5_3|isbn=978-3540486589}}</ref> An enhanced version of the attack can break 9-round DES with 2<sup>15.8</sup> chosen plaintexts and has a 2<sup>29.2</sup> time complexity (Biham and others, 2002).<ref>{{Cite book|last1=Biham|first1=Eli|last2=Dunkelman|first2=Orr|last3=Keller|first3=Nathan|title=Advances in Cryptology — ASIACRYPT 2002 |chapter=Enhancing Differential-Linear Cryptanalysis |date=2002-12-01|series=Lecture Notes in Computer Science|volume=2501 |language=en|publisher=Springer, Berlin, Heidelberg|pages=254–266|doi=10.1007/3-540-36178-2_16|isbn=978-3540361787}}</ref>

=== Minor cryptanalytic properties ===
DES exhibits the complementation property, namely that
:<math>E_K(P)=C \iff E_{\overline{K}}(\overline{P})=\overline{C}</math>
where <math>\overline{x}</math> is the [[bitwise complement]] of <math>x.</math> <math>E_K</math> denotes encryption with key <math>K.</math> <math>P</math> and <math>C</math> denote plaintext and ciphertext blocks respectively. The complementation property means that the work for a [[brute-force attack]] could be reduced by a factor of 2 (or a single bit) under a [[chosen-plaintext attack|chosen-plaintext]] assumption. By definition, this property also applies to TDES cipher.<ref>{{cite book |last1=Menezes |first1=Alfred J. |last2=van Oorschot |first2=Paul C. |last3=Vanstone |first3=Scott A. |date=1996 |title=Handbook of Applied Cryptography |url=https://archive.org/details/handbookofapplie0000mene/page/257 |publisher=CRC Press |page=[https://archive.org/details/handbookofapplie0000mene/page/257 257] |isbn=978-0849385230 |url-access=registration }}</ref>

DES also has four so-called ''[[Weak key#Weak keys in DES|weak keys]]''. Encryption (''E'') and decryption (''D'') under a weak key have the same effect (see [[involution (mathematics)|involution]]):
:<math>E_K(E_K(P)) = P</math> or equivalently, <math>E_K = D_K.</math>
There are also six pairs of ''semi-weak keys''. Encryption with one of the pair of semiweak keys, <math>K_1</math>, operates identically to decryption with the other, <math>K_2</math>:
:<math>E_{K_1}(E_{K_2}(P)) = P</math> or equivalently, <math>E_{K_2} = D_{K_1}.</math>
It is easy enough to avoid the weak and semiweak keys in an implementation, either by testing for them explicitly, or simply by choosing keys randomly; the odds of picking a weak or semiweak key by chance are negligible. The keys are not really any weaker than any other keys anyway, as they do not give an attack any advantage.

DES has also been proved not to be a [[group (mathematics)|group]], or more precisely, the set <math>\{E_K\}</math> (for all possible keys <math>K</math>) under [[functional composition]] is not a group, nor "close" to being a group.<ref>{{cite book| url = http://dl.acm.org/citation.cfm?id=705523| title = Campbell and Wiener, 1992| date = 16 August 1992| pages = 512–520| isbn = 9783540573401| last1 = Brickell| first1 = Ernest F.}}</ref> This was an open question for some time, and if it had been the case, it would have been possible to break DES, and multiple encryption modes such as [[Triple DES]] would not increase the security, because repeated encryption (and decryptions) under different keys would be equivalent to encryption under another, single key.<ref>{{Cite web|url=https://www.nku.edu/~christensen/3DES.pdf |archive-url=https://web.archive.org/web/20110409080716/http://www.nku.edu/~christensen/3DES.pdf |archive-date=2011-04-09 |url-status=live|title=Double DES}}</ref>