A Methodology for Differential-Linear Cryptanalysis and Its Applications

In 1994 Langford and Hellman introduced a combination of differential and linear cryptanalysis under two default independence assumptions, known as differential-linear cryptanalysis, which is based on the use of a differential-linear distinguisher constructed by concatenating a linear approximation with a (truncated) differential with probability 1. In 2002, by using an additional assumption, Biham, Dunkelman and Keller gave an enhanced version that can be applicable to the case when a differential with a probability of smaller than 1 is used to construct a differential-linear distinguisher. In this paper, we present a new methodology for differential-linear cryptanalysis under the original two assumptions implicitly used by Langford and Hellman, without using the additional assumption of Biham et al. The new methodology is more reasonable and more general than Biham et al.’s methodology, and apart from this advantage it can lead to some better differential-linear cryptanalytic results than Biham et al.’s and Langford and Hellman’s methodologies. As examples, we apply it to attack 10 rounds of the CTC2 block cipher with a 255-bit block size and key, 13 rounds of the DES block cipher, and 12 rounds of the Serpent block cipher. The new methodology can be used to cryptanalyse other block ciphers, and block cipher designers should pay attention to this new methodology when designing a block cipher.