- Integral cryptanalysis
In

cryptography ,**integral cryptanalysis**is a cryptanalytic attack that is particularly applicable toblock cipher s based onsubstitution-permutation network s. It was originally designed byLars Knudsen as a dedicated attack against Square, so is commonly known as the**Square attack**. It was also extended to a few other ciphers related to Square:CRYPTON ,Rijndael , andSHARK .Stefan Lucks generalized the attack to what he called a "saturation attack" and used it to attackTwofish , which is not at all similar to Square, having a radically differentFeistel network structure. Forms of integral cryptanalysis have since been applied to a variety of ciphers, includingHierocrypt , IDEA, Camellia, Skipjack,MISTY1 ,MISTY2 ,SAFER++ ,KHAZAD , and "FOX" (now calledIDEA NXT ).Unlike

differential cryptanalysis , which uses pairs of chosen plaintexts with a fixedXOR difference, integral cryptanalysis usesset s or evenmultiset s 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 ofcalculus .**References*** cite conference

author =Joan Daemen ,Lars Knudsen ,Vincent Rijmen

title = The Block Cipher Square

booktitle = 4th International Workshop onFast Software Encryption (FSE '97), Volume 1267 of Lecture Notes in Computer Science

pages = pp.149–165

publisher =Springer-Verlag

date = January 1997

location =Haifa

url = http://www.esat.kuleuven.ac.be/~cosicart/pdf/VR-9700.PDF

format =PDF

accessdate = 2007-02-15

* cite conference

author = Carl D'Halluin, Gert Bijnens, Vincent Rijmen,Bart Preneel

title = Attack on Six Rounds of Crypton

booktitle = 6th International Workshop on Fast Software Encryption (FSE '99)

pages = pp.46–59

publisher = Springer-Verlag

date = March 1999

location =Rome

url = http://citeseer.ist.psu.edu/479905.html

format = PDF/PostScript

accessdate = 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

booktitle = 7th International Workshop on Fast Software Encryption (FSE 2000)

pages = pp.213–230

publisher = Springer-Verlag

date = April 2000

location =New York City

url = http://www.schneier.com/paper-rijndael.html

format = PDF/PostScript

accessdate = 2007-03-06

* cite conference

author = Stefan Lucks

title = The Saturation Attack - a Bait for Twofish

booktitle = 8th International Workshop on Fast Software Encryption (FSE '01)

pages = pp.1–15

publisher = Springer-Verlag

date =September 14 2000

location =Yokohama

url = http://eprint.iacr.org/2000/046

format = PDF/PostScript

accessdate = 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

booktitle = 8th International Workshop on Fast Software Encryption (FSE '01)

pages = pp.165–173

publisher = Springer-Verlag

date = April 2001

location = Yokohama

url = http://www.cosic.esat.kuleuven.be/publications/article-83.pdf

format = PDF

accessdate = 2007-03-03

* cite paper

author = Jorge Nakahara, Jr., Paulo S.L.M. Barreto, Bart Preneel, Joos Vandewalle, Hae Y. Kim

title = SQUARE Attacks on Reduced-Round PES and IDEA Block Ciphers

date = 2001

url = http://citeseer.ist.psu.edu/548521.html

format = PDF/PostScript

accessdate = 2007-03-03

* cite conference

author = Yongjin Yeom, Sangwoo Park, Iljun Kim

title = On the Security of CAMELLIA against the Square Attack

booktitle = 9th International Workshop on Fast Software Encryption (FSE '02)

pages = pp.89–99

publisher = Springer-Verlag

date = February 2002

location =Leuven

url = http://maths.utime.cn:81/Crypt1998-2003/bibs/2365/23650089.htm

format = PDF

accessdate = 2007-03-03

* cite conference

author = Kyungdeok Hwang, Wonil Lee, Sungjae Lee, Sangjin Lee, and Jongin Lim

title = Saturation Attacks on Reduced Round Skipjack

booktitle = 9th International Workshop on Fast Software Encryption (FSE '02)

pages = pp.100–111

publisher = Springer-Verlag

date = February 2002

location = Leuven

url = http://maths.utime.cn:81/Crypt1998-2003/bibs/2365/23650100.htm

format = PDF

accessdate = 2007-03-03

* cite conference

author = Lars Knudsen, David Wagner

title = Integral cryptanalysis

booktitle = 9th International Workshop on Fast Software Encryption (FSE '02)

pages = pp.112–127

publisher = Springer-Verlag

date =December 11 2001

location = Leuven

url = http://citeseer.ist.psu.edu/506311.html

format = PDF/PostScript

accessdate = 2006-11-30

* cite paper

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

accessdate = 2007-03-03

* cite conference

author = Frédéric Muller

title = A New Attack against Khazad

booktitle = Advances in Cryptology -ASIACRYPT 2003

pages = pp.347–358

publisher = Springer-Verlag

date = December 2003

location =Taipei

url = http://www.mathmagic.cn/Crypt1998-2003/bibs/2894/28940347.htm

format = PDF

accessdate = 2007-03-03

* cite paper

author = Wu Wenling, Zhang Wentao, and Feng Dengguo

title = Improved Integral Cryptanalysis of FOX Block Cipher

date =August 25 2005

url = http://eprint.iacr.org/2005/292.pdf

format = PDF

accessdate = 2007-03-03

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