Paper 2020/929

Local XOR Unification: Definitions, Algorithms and Application to Cryptography

Hai Lin and Christopher Lynch

Abstract

Unification techniques have been proven to be useful for formal analysis of cryptographic systems. In this paper, we introduce a new unification problem called local XOR unification, motivated by formal analysis of security of modes of operation. The goal in local XOR unification is to find a substitution making two terms equivalent modulo the theory of exclusive-or, but each variable is only allowed to be mapped to a term from a given set of terms. We present two versions of the local XOR unification problem, and give algorithms to solve them, proving soundness, completeness and termination.