On optimal size in truncated differential attacks

Abstract

Differential Cryptanalysis (DC) is one of the oldest known attacks on block ciphers. DC is based on tracking of changes in the differences between two messages as they pass through the consecutive rounds of encryption. However DC remains very poorly understood. In his textbook written in the late 1990s Schneier wrote that against differential cryptanalysis, GOST is “probably stronger than DES”. In fact Knudsen have soon proposed more powerful advanced differential attacks however the potential space of such attacks is truly immense. To this day there is no method which allows to evaluate the security of a cipher against such attacks in a systematic way. Instead, attacks are designed and improved in ad-hoc ways with heuristics [6–13,21]. The best differential attack known has time complexity of 2179 [13]. In this paper we show that for a given block cipher there exists an optimal size for advanced differential properties. This new understanding allows to considerably reduce the space to be searched for “good” truncated differential properties suitable for an attack.