The discrete logarithm problem in the group of non-singular circulant matrices

TL;DR

This paper investigates the discrete logarithm problem within the group of circulant matrices over finite fields, aiming to develop secure and efficient public key cryptosystems based on this mathematical structure.

Contribution

It introduces a study of the discrete logarithm problem in circulant matrices, proposing a new approach for cryptographic systems that are both secure and computationally efficient.

Findings

Potential for secure cryptosystems based on circulant matrices

Analysis of the discrete logarithm problem in this matrix group

Framework for fast cryptographic algorithms

Abstract

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key cryptosystems.