# On Asymmetric Unification for the Theory of XOR with a Homomorphism

## TL;DR

This paper develops a new automata-based decision procedure for asymmetric unification in the XOR theory with a homomorphism, addressing a gap in algorithms for cryptographic protocol analysis.

## Contribution

It introduces a novel automata-based decision procedure for asymmetric unification in ACUNh and adapts existing methods to improve analysis capabilities.

## Key findings

- Developed a new automata-based decision procedure for asymmetric-ACUNh.
- Adapted asymmetric combination procedures for improved unification.
- Compared new approach with variant unification methods.

## Abstract

Asymmetric unification, or unification with irreducibility constraints, is a newly developed paradigm that arose out of the automated analysis of cryptographic protocols. However, there are still relatively few asymmetric unification algorithms. In this paper we address this lack by exploring the application of automata-based unification methods. We examine the theory of xor with a homomorphism, ACUNh, from the point of view of asymmetric unification, and develop a new automata-based decision procedure. Then, we adapt a recently developed asymmetric combination procedure to produce a general asymmetric- ACUNh decision procedure. Finally, we present a new approach for obtaining a solution-generating asymmetric-ACUNh unification automaton. We also compare our approach to the most commonly used form of asymmetric unification available today, variant unification.