Cryptanalysis of block ciphers and weight divisibility of some binary codes

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 F2 into F2 are related to the weight distribution of a binary linear code CF of length 2 − 1 and dimension 2m. In particular, the weight divisibility of CF 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 F2m , the associated code CF 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.