QRKE: Extensions

TL;DR

This paper introduces QRKE extensions that leverage permutable Chebyshev polynomials for quantum-resistant cryptographic protocols, including key exchange, encryption, and authentication schemes, with improved computation efficiency.

Contribution

It presents novel quantum-resistant cryptographic methods based on Chebyshev polynomials, expanding their application to encryption, authentication, and signatures.

Findings

Chebyshev polynomial-based key exchange resists quantum attacks

Faster computation methods for T polynomial values

New encryption and signature schemes using Chebyshev polynomials

Abstract

Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers are suitable for creating a Diffie-Hellman-like key exchange algorithm that is able to withstand attacks using quantum computers. The algorithm takes advantage of the commutative properties of Chebyshev polynomials of the first kind. We show how T polynomial values can be computed faster and how the underlying principle can further be used to create public key encryption methods, as well as certificate-like authentication-, and signature schemes.