Linear Attacks On SNOW 3G And SNOW-V Using Automatic Search

Abstract

Abstract In this paper, a linear attack model of SNOW 3G and SNOW-V based on automatic search technology is proposed. We first describe the linear approximation of Finite State Machine transformation, which allows a wider range of automatic search, then model it with the automatic search technology based on SAT/SMT program. Adopting this generic method, we seek out a binary linear approximation of SNOW 3G with correlation of $2^{-21.92}$ which has been verified by test. Treating this binary approximation as a mask of an 8-bit distribution in a fixed field, we provide a method to obtain the 8-bit distribution. The binary approximation is used in a fast correlation attack with expected time and memory complexity $2^{184.67}$, given $2^{173.96}$ key stream words. For the full version of SNOW-V, considering the linear relationship between Linear Feedback Shift Register parts at three successive moments, we search out a distinguisher with correlation of $2^{-175.51}$, which results in a distinguishing attack with an expected complexity of $2^{351.02}$.