Boolean Polynomials, BDDs and CRHS Equations - Connecting the Dots with CryptaPath

Abstract

When new symmetric-key ciphers and hash functions are proposed they are expected to document resilience against a number of known attacks. Good, easy to use tools may help designers in this process and give improved cryptanalysis. In this paper we introduce CryptaPath, a tool for doing algebraic cryptanalysis which utilizes Compressed Right-Hand Side (CRHS) equations to attack SPN ciphers and sponge constructions. It requires no previous knowledge of CRHS equations to be used, only a reference implementation of a primitive. The connections between CRHS equations, binary decision diagrams and Boolean polynomials have not been described earlier in literature. A comprehensive treatment of these relationships is made before we explain how CryptaPath works. We then describe the process of solving CRHS equation systems while introducing a new operation, dropping variables.