Authentication from matrix conjugation

TL;DR

This paper introduces an authentication scheme based on the difficulty of solving the conjugacy search problem in a noncommutative matrix semigroup, providing a potential cryptographic protocol resistant to impersonation.

Contribution

It presents a novel authentication method utilizing matrix conjugation in a noncommutative polynomial matrix semigroup, linking security to the conjugacy search problem.

Findings

Security relies on the hardness of the conjugacy search problem.

Uses matrices over truncated multivariable polynomials as the platform.

Proposes a practical implementation for cryptographic authentication.

Abstract

We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative) semigroup, i.e., to recovering X from X^{-1}AX and A. The platform semigroup that we suggest here is the semigroup of nxn matrices over truncated multivariable polynomials over a ring.