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

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.

💡 Research Summary

The paper introduces a novel public‑key setting based on the discrete logarithm problem (DLP) in the multiplicative group of non‑singular circulant matrices over a finite field 𝔽_q. After a brief review of traditional DLP platforms—namely the multiplicative group 𝔽_q^∗ and elliptic‑curve groups E(𝔽_q)—the authors motivate the need for alternative algebraic structures that can provide comparable security while offering superior computational efficiency, especially for constrained environments.

A circulant matrix is completely determined by its first row; the set of n × n circulant matrices forms a commutative ring isomorphic to the polynomial quotient ring 𝔽_q