Using shifted conjugacy in braid-based cryptography

TL;DR

This paper explores alternative algebraic operations, specifically shifted conjugation, in braid-based cryptography, demonstrating their potential for secure protocols beyond traditional conjugacy-based methods.

Contribution

It introduces a Fiat--Shamir-style authentication protocol using left self-distributive operations, expanding the cryptographic toolkit with shifted conjugation and related structures.

Findings

Shifted conjugation can be used in braid-based cryptography.

The proposed protocol leverages high combinatorial complexity for security.

Alternative operations satisfy the self-distributive law, enabling new cryptographic schemes.

Abstract

Conjugacy is not the only possible primitive for designing braid-based protocols. To illustrate this principle, we describe a Fiat--Shamir-style authentication protocol that be can be implemented using any binary operation that satisfies the left self-distributive law. Conjugation is an example of such an operation, but there are other examples, in particular the shifted conjugation on Artin's braid group B\_oo, and the finite Laver tables. In both cases, the underlying structures have a high combinatorial complexity, and they lead to difficult problems.