Cryptanalysis of block ciphers and weight divisibility of some binary codes

Abstract : The resistance of an iterated block cipher to most classical attacks can be quantified by some properties of its round function. The involved parameters (nonlinearity, degrees of the derivatives...) for a function F from GF(2^m) into GF(2^m) are related to the weight distribution of a binary linear code C_F of length (2^m − 1) and dimension 2m. In particular, the weight divisibility of C_F appears as an important criterion in the context of linear cryptanalysis and of higher-order differential attacks. When the round function F is a power permutation over GF(2^m), the associated code C_F is the dual of a primitive cyclic code with two zeroes. Therefore, McEliece's theorem provides a powerful tool for evaluating the resistance of some block ciphers to linear and higherorder differential attacks.
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Anne Canteaut, Pascale Charpin, Marion Videau. Cryptanalysis of block ciphers and weight divisibility of some binary codes. Blaum, Mario and Farrell, Patrick G. and van Tilborg, Henk C.A. Information, coding, and mathematics: proceedings of the workshop honoring Prof. Bob McEliece on his 60th birthday, 687, Kluwer, pp.75-97, 2002, The Kluwer International Series in Engineering and Computer Science, 978-1-4020-7079-2. ⟨hal-00675327⟩

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