Zero-knowledge authentication schemes from actions on graphs, groups, or rings

TL;DR

This paper introduces a general framework for creating zero-knowledge authentication schemes based on actions of semigroups on sets, utilizing computationally hard problems like graph isomorphism and graph colorability.

Contribution

It presents a novel, general method for constructing zero-knowledge schemes from semigroup actions, with concrete examples based on NP-hard problems.

Findings

Forgery is NP-hard in the proposed schemes

Multiple hard problems can be employed, such as (Sub)graph Isomorphism and Diophantine problems

Framework is versatile and not dependent on specific algebraic properties

Abstract

We propose a general way of constructing zero-knowledge authentication schemes from actions of a semigroup on a set, without exploiting any specific algebraic properties of the set acted upon. Then we give several concrete realizations of this general idea, and in particular, we describe several zero-knowledge authentication schemes where forgery (a.k.a. impersonation) is NP-hard. Computationally hard problems that can be employed in these realizations include (Sub)graph Isomorphism, Graph Colorability, Diophantine Problem, and many others.