Observations of Skipjack-like Structure with SP/SPS Round Function

Impossible differential cryptanalysis is an important tool for evaluating the security level of a block cipher, and the key step of this cryptanalysis is to find the longest impossible differential. This paper focuses on retrieving impossible differentials for m-cell Skipjack-like structure with SP/SPS round function (named SkipjackSP and SkipjackSPS resp.). Up to now, known longest impossible differentials in m-cell Skipjack-like structures is m2 rounds. In this paper, we provide some new m2 rounds impossible differentials for these two structures. Further, we prove that if P layer is chosen from binary matrices, we can always retrieve m2 + 1 rounds impossible differentials for these two structures, and m2 + 2 rounds impossible differentials for SkipjackSP. Moreover, if P layer satisfies some satiable conditions, we may further obtain m2 + 2 rounds impossible differential for SkipjackSPS. Our results show that we should choose P layer carefully when employing these two structures