An Enhanced Binary Characteristic Set Algorithm and Its Applications to Algebraic Cryptanalysis

Abstract

Efficient methods to solve boolean polynomial systems underly the effectiveness of algebraic attacks on cryptographic ciphers and the security of multi-variate cryptosystems. Amongst various polynomial solving algorithms, the binary characteristic set algorithm was recently proposed to solve boolean polynomial systems including those arising from ciphers. In this paper, we propose some novel techniques to enhance the existing characteristic set solver. Specifically, we incorporate the ElimLin procedure and apply basic statistical learning techniques to improve the performance of the characteristic set algorithm. Our experiments show that our enhanced solver EBCSA performs better than existing algebraic methods on some ciphers, including CANFIL and PRESENT ciphers. We also perform the first algebraic cryptanalysis on the PRINCE cipher and an algebraic attack on Toyocrypt in a more practical/realistic setting as compared to previous attacks.