Improved Linear Cryptanalysis of Reduced-round SIMON

SIMON is a family of ten lightweight block ciphers published by Beaulieu et al.\ from U.S. National Security Agency (NSA). In this paper we investigate the security of SIMON against different variants of linear cryptanalysis techniques, i.e.\ classical and multiple linear cryptanalysis and linear hulls. We present a connection between linear- and differential characteristics as well as differentials and linear hulls in SIMON. We employ it to adapt the current known results on differential cryptanalysis of SIMON into the linear setting. In addition to finding a linear approximation with a single characteristic, we show the effect of the linear hulls in SIMON by finding better approximations that enable us to improve the previous results.

Our best linear cryptanalysis employs average squared correlation of the linear hull of SIMON based on correlation matrices. The result covers 21 out of 32 rounds of SIMON32/64 with time and data complexity
and respectively. We have implemented our attacks for small scale variants of SIMON and our experiments confirm the theoretical biases and correlation presented in this work. So far, our results are the best known with respect to linear cryptanalysis for any variant of SIMON.