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QUADRATIC APPROXIMATIONS OF THE SPECIAL TYPE FOR THE 4-BIT PERMUTATIONS IN SBOXES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2008. № 1(1).

We consider quadratic approximations (for Boolean functions) of the special type and study the ability of applicationthem in nonlinear cryptanalysis of block ciphers. For 4-bit permutations with the most high nonlinearity recommended for usingin S-boxes of GOST 28147-89, DES, s3DES we show that for the all of them (excepting only one) there are quadratic equalitiesof the special type on input and output bits with probability more high than any linear equality has
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  • Title QUADRATIC APPROXIMATIONS OF THE SPECIAL TYPE FOR THE 4-BIT PERMUTATIONS IN SBOXES
  • Headline QUADRATIC APPROXIMATIONS OF THE SPECIAL TYPE FOR THE 4-BIT PERMUTATIONS IN SBOXES
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 1(1)
  • Date:
  • DOI
Keywords
к-бент-функция , S-блок , квадратичный криптоанализ
Authors
References
Biham E., Biryukov A. How to strengthen DES using existing hardware // Advances in Cryptology - ASIACRYPT '94, 4th International Conference on the Theory and Applications of Cryptology. (Wollongong, Australia. November 28 - December 1, 1994): Proc. Springer, 1995. P. 398 - 412 (LNCS V. 917).
Kim К., Park S., Lee S. Reconstruction of s2DES S-Boxes and their Immunity to Differential Cryptanalysis // Korea - Japan Workshop on Information Security and Cryptography. (Seoul, Korea. October 24 - 26, 1993): Proc. P. 282 - 291.
Шнайер Б. Прикладная криптография. Протоколы, алгоритмы, исходные тексты на языке Си. М.: Триумф, 2002.
Heys H.M., Tavares S.E. Substitution-permutation networks resistant to differential and linear cryptanalysis // J. Cryptology. 1996. V. 9. No.1.P. 1-19.
Ростовцев А.Г., Маховенко Е.Б. Введение в теорию итерированных шифров. СПб.: НПО «Мир и Семья», 2003.
Токарева Н.Н. Описание k-бент-функций от четырех переменных // Дискр. анализ и исслед. операций. 2008. В печати.
Krotov D.S. Z4-linear Hadamard and extended perfect codes // Proc. of the Int. Workshop on Coding and Cryptography WCC 2001, Jan. 8 - 12, 2001. Paris, France, 2001. P. 329 - 334.
Кротов Д. С. Z4-линейные совершенные коды//Дискрет. анализ и исслед. операций. Сер. 1. 2000. Т. 7. № 4. С. 78-90.
Tokareva N.N. On k-bent functions // Вестник ТГУ. Приложение. 2007. № 23. С. 74 - 76.
Токарева Н.Н. О квадратичных аппроксимациях в блочных шифрах // Пробл. передачи информ. 2008. Т. 44. № 3. С. 105-127.
Токарева Н.Н. Бент-функции с более сильными свойствами нелинейности: k-бент-функции // Дискр. анализ и исслед. операций. 2007. Сер. 1. Т. 14. № 4. С. 76 - 102.
Иванов А.В. Использование приведенного представления булевых функций при построении их нелинейных аппроксимаций // Вестник ТГУ. Приложение. 2007. № 23. С. 31 - 35.
Tapiador J. M. E., Clark J. A., Hernandez-Castro J. С. Non-linear Cryptanalysis Revisited: Heuristic Search for Approximations to S-Boxes // 11th IMA International Conference (Cirencester, UK. December 18 - 20, 2007). Springer, 2007. P. 99-117 (LNCS V. 4887).
Nakahara J., Preneel B., Vandewalle J. Experimental Non-Linear Cryptanalysis // COSIC Internal Report. Katholieke Universiteit Leuven. 2003. 17 p.
Shimoyama T., Kaneko T. Quadratic relation of S-box and its application to the linear attack of full round DES // Advances in Cryptology - CRYPTO'98, 18th Annual International Cryptology Conference. (Santa Barbara, California. USA. August 23 -27, 1998). Proc. Springer, 1998. P. 200-211 (LNCS V. 1462).
Biham E., Shamir A. Differential cryptanalysis of DES-like cryptosystems //J. Cryptology. 1991. V. 4. No. 1. P. 3 - 72.
Knudsen L.R., Robshaw M.J.B. Non-linear approximation in linear cryptanalysis // Advances in Cryptology -EUROCRYPT'96. Workshop on the theory and application of cryptographic techniques (Saragossa, Spain. May 12-16, 1996). Proc. Springer Verlag, 1996. P. 224 - 236 (LNCS V. 1070).
Matsui M. Linear cryptanaly sis method for DES cipher // Advances in Cryptology - EUROCRYPT'93. Workshop on the theory and application of cryptographic techniques (Lofthus, Norway. May 23-27, 1993). Proc. Berlin: Springer, 1994. P. 386 - 397 (LNCS V. 765).
QUADRATIC APPROXIMATIONS OF THE SPECIAL TYPE FOR THE 4-BIT PERMUTATIONS IN SBOXES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2008. № 1(1).
QUADRATIC APPROXIMATIONS OF THE SPECIAL TYPE FOR THE 4-BIT PERMUTATIONS IN SBOXES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2008. № 1(1).
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