Authentication Schemes Using Polynomials Over Non-Commutative Rings

TL;DR

This paper introduces two novel authentication schemes leveraging polynomials over non-commutative rings, aiming to enhance security in digital identity verification through complex algebraic structures.

Contribution

It proposes new authentication protocols based on non-commutative rings and polynomial problems, extending cryptographic methods beyond traditional commutative frameworks.

Findings

Schemes are based on the intractability of polynomial symmetrical decomposition.

Includes a zero-knowledge interactive proof of knowledge.

Provides a foundation for more secure authentication methods.

Abstract

Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through the use of logon passwords. Knowledge of the password is assumed to guarantee that the user is authentic.Internet business and many other transactions require a more stringent authentication process. The aim of this paper is to propose two authentication schemes based on general non-commutative rings. The key idea of the schemes is that for a given non-commutative ring; one can build polynomials on additive structure and takes them as underlying work structure. By doing so, one can implement authentication schemes, one of them being zero-knowledge interactive proofs of knowledge, on multiplicative structure of the ring. The security of the schemes is based on the intractability of the polynomial symmetrical decomposition problem over the given non-commutative ring.