Paper 2020/1349

Key Dependency of Differentials: Experiments in the Differential Cryptanalysis of Block Ciphers Using Small S-boxes

Howard M. Heys

Abstract

In this paper, we investigate the key dependency of differentials in block ciphers by examining the results of numerous experiments applied to the substitution-permutation network (SPN) structure using 4-bit S-boxes. In particular, we consider two cipher structures: a toy 16-bit SPN and a realistic 64-bit SPN. For both ciphers, we generate many different experimental results by inserting the S-boxes used in many lightweight cipher proposals and applying different forms of round key generation. It is demonstrated that, in most circumstances, with enough rounds in the cipher, the probability distribution (across all keys) of the differential probability follows the distribution expected in the theoretically ideal scenario. However, this does not occur consistently for all S-boxes and all approaches to round key generation. Consequently, it is possible that a cipher may have more susceptibility to differential cryptanalysis for some subset of the cipher keys than is implied when employing the standard assumptions used in analyzing a cipher’s security.