Integral cryptanalysis

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Type of cryptanalytic attack

title: "Integral cryptanalysis" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["cryptographic-attacks"] description: "Type of cryptanalytic attack" topic_path: "general/cryptographic-attacks" source: "https://en.wikipedia.org/wiki/Integral_cryptanalysis" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Type of cryptanalytic attack ::

In cryptography, integral cryptanalysis is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. It was originally designed by Lars Knudsen as a dedicated attack against Square, so it is commonly known as the Square attack. It was also extended to a few other ciphers related to Square: CRYPTON, Rijndael, and SHARK. Stefan Lucks generalized the attack to what he called a saturation attack and used it to attack Twofish, which is not at all similar to Square, having a radically different Feistel network structure. Forms of integral cryptanalysis have since been applied to a variety of ciphers, including Hierocrypt, IDEA, Camellia, Skipjack, MISTY1, MISTY2, SAFER++, KHAZAD, and FOX (now called IDEA NXT).

Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant, and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation. This contrast between the differences of pairs of texts and the sums of larger sets of texts inspired the name "integral cryptanalysis", borrowing the terminology of calculus.

References

  • {{ cite conference | author = Joan Daemen, Lars Knudsen, Vincent Rijmen | title = The Block Cipher Square | conference = 4th International Workshop on Fast Software Encryption (FSE '97), Volume 1267 of Lecture Notes in Computer Science | pages = 149–165 | publisher = Springer-Verlag | date = January 1997 | location = Haifa | url = http://www.cosic.esat.kuleuven.be/publications/article-309.pdf | access-date = 2007-02-15 }}
  • {{ cite conference | author = Carl D'Halluin, Gert Bijnens, Vincent Rijmen, Bart Preneel | title = Attack on Six Rounds of Crypton | conference = 6th International Workshop on Fast Software Encryption (FSE '99) | pages = 46–59 | publisher = Springer-Verlag | date = March 1999 | location = Rome | url = http://citeseer.ist.psu.edu/479905.html | format = PDF/PostScript | access-date = 2007-03-03 }}
  • {{ cite conference | author = N. Ferguson, J. Kelsey, S. Lucks, B. Schneier, M. Stay, D. Wagner, D. Whiting | title = Improved Cryptanalysis of Rijndael | conference = 7th International Workshop on Fast Software Encryption (FSE 2000) | pages = 213–230 | publisher = Springer-Verlag | date = April 2000 | location = New York City | url = http://www.schneier.com/paper-rijndael.html | format = PDF/PostScript | access-date = 2007-03-06 }}
  • {{ cite conference | author = Stefan Lucks | title = The Saturation Attack - a Bait for Twofish | conference = 8th International Workshop on Fast Software Encryption (FSE '01) | pages = 1–15 | publisher = Springer-Verlag | date = September 14, 2000 | location = Yokohama | url = http://eprint.iacr.org/2000/046 | format = PDF/PostScript | access-date = 2006-11-30 }}
  • {{ cite conference | author = Paulo S. L. M. Barreto, Vincent Rijmen, Jorge Nakahara, Jr., Bart Preneel, Joos Vandewalle, Hae Yong Kim | title = Improved SQUARE Attacks against Reduced-Round HIEROCRYPT | conference = 8th International Workshop on Fast Software Encryption (FSE '01) | pages = 165–173 | publisher = Springer-Verlag | date = April 2001 | location = Yokohama | url = http://www.cosic.esat.kuleuven.be/publications/article-83.pdf | access-date = 2007-03-03 }}
  • {{ cite journal |author1=Jorge Nakahara, Jr. |author2=Paulo S.L.M. Barreto |author3=Bart Preneel |author4=Joos Vandewalle |author5=Hae Y. Kim | title = SQUARE Attacks on Reduced-Round PES and IDEA Block Ciphers | year = 2001 | url = http://citeseer.ist.psu.edu/548521.html | format = PDF/PostScript | access-date = 2007-03-03 }}
  • {{cite conference | author1 = Yongjin Yeom | author2 = Sangwoo Park | author3 = Iljun Kim | title = On the Security of CAMELLIA against the Square Attack | conference = 9th International Workshop on Fast Software Encryption (FSE '02) | pages = 89–99 | publisher = Springer-Verlag | date = February 2002 | location = Leuven | url = http://maths.utime.cn:81/Crypt1998-2003/bibs/2365/23650089.htm | format = PDF | access-date = 2007-03-03
  • {{cite conference | author1 = Kyungdeok Hwang | author2 = Wonil Lee | author3 = Sungjae Lee | author4 = Sangjin Lee | author5 = Jongin Lim | title = Saturation Attacks on Reduced Round Skipjack | conference = 9th International Workshop on Fast Software Encryption (FSE '02) | pages = 100–111 | publisher = Springer-Verlag | date = February 2002 | location = Leuven | url = http://maths.utime.cn:81/Crypt1998-2003/bibs/2365/23650100.htm | format = PDF | access-date = 2007-03-03 | archive-url = https://web.archive.org/web/20070525204822/http://maths.utime.cn:81/Crypt1998-2003/bibs/2365/23650100.htm | archive-date = 2007-05-25 | url-status = dead
  • {{ cite conference |author1=Lars Knudsen |author2=David Wagner | title = Integral cryptanalysis | conference = 9th International Workshop on Fast Software Encryption (FSE '02) | pages = 112–127 | publisher = Springer-Verlag | date = December 11, 2001 | location = Leuven | url = https://www.iacr.org/archive/fse2002/23650114/23650114.pdf | format = PDF/PostScript | access-date = 2006-11-30 }}
  • {{ cite journal | author = Gilles Piret, Jean-Jacques Quisquater | title = Integral Cryptanalysis on reduced-round Safer++ | date = February 16, 2003 | url = http://citeseer.ist.psu.edu/559604.html | format = PDF/PostScript | access-date = 2007-03-03 }}
  • {{cite conference | author = Frédéric Muller | title = A New Attack against Khazad | conference = Advances in Cryptology – ASIACRYPT 2003 | pages = 347–358 | publisher = Springer-Verlag | date = December 2003 | location = Taipei | url = http://www.mathmagic.cn/Crypt1998-2003/bibs/2894/28940347.htm | archive-url = https://archive.today/20070723200754/http://www.mathmagic.cn/Crypt1998-2003/bibs/2894/28940347.htm | url-status = dead | archive-date = 2007-07-23 | format = PDF | access-date = 2007-03-03
  • {{ cite journal |author1=Wu Wenling |author2=Zhang Wentao |author3=Feng Dengguo | title = Improved Integral Cryptanalysis of FOX Block Cipher | date = August 25, 2005 | url = http://eprint.iacr.org/2005/292.pdf | access-date = 2007-03-03 }}

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