New integral attacks on SIMON

SIMON is a family of lightweight block ciphers publicly released by National Security Agency (NSA). Up to now, there have been many cryptanalytic results on it by means of impossible differential, integral, zero-correlation linear cryptanalysis and so forth. In this study, the authors analyse the characteristic of the Boolean functions of SIMON32 and find that the presentation of zero-sum property is influenced by the degree of the corresponding Boolean function. As a result, the zero-sum integral distinguisher for 14-round SIMON32 is identified which is same to the one given by Wang et.al. Inspired by this finding, they also experimentally find the zero-sum integral distinguisher for 16-round SIMON48. Then, the integral attacks on 22-round SIMON32, 22-round SIMON48/72 and 23-round SIMON48/96 are given. They improve the previous integral attack on SIMON32 from 21-round to 22-round, and the first integral attack on SIMON48 is proposed.