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On quadratic approximations in block ciphers. (English. Russian original) Zbl 1171.94361
Probl. Inf. Transm. 44, No. 3, 266-286 (2008); translation from Probl. Peredachi Inf. 44, No. 3, 105-127 (2008).
Summary: We consider quadratic approximations (of Boolean functions) of a special form and their potential applications in block cipher cryptanalysis. We show that the use of \(k\)-bent functions as ciphering functions extremely increases the resistance of ciphers to such approximations. We consider examples of 4-bit permutations recommended for use in S-boxes of the algorithms GOST 28147-89, DES, and \(s^{3}\)DES; we show that in almost all cases there exist more probable (than linear) quadratic relations of a special form on input and output bits of these permutations.
MSC:
94A60 Cryptography
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