Improved Differential Characteristic Searching Methods

Abstract

The success probability of differential and linear cryptanalysis against block ciphers heavily depend on finding differential or linear paths with high statistical bias compared with uniform random distribution. For large number of rounds, it is not a trivial task to find such differential or linear paths. Matsui first investigated this problem and proposed a solution based on a branch and bound algorithm in 1994. Since then, the research on finding good concrete differential or linear path did not receive much attention. In this paper, we revisit the differential attack against several S-Box based block ciphers by carefully studying the differential characteristics. Inspired by Matsui's algorithm, we provide an improved solution with the aid of several searching strategies, which enable us to find by far the best differential characteristics for the two investigated ciphers (LBlock, TWINE) efficiently. Furthermore, we provide another way to evaluate the security of ciphers against differential attack by comparing the strength of the ciphers from differential characteristic's point of view, and we also investigate the accuracy when using the active S-Box to evaluate the security margin against differential attack, which is the common method adapted when new ciphers are designed.