A Novel Digital Signature Scheme Using a Non-Commutative Algebraic Structure

Digital signature schemes are a cornerstone of modern public key cryptography, providing essential security services such as authentication, data integrity, and non-repudiation in open communication networks. Most classical digital signature constructions are based on commutative algebraic structures and rely on a single hard mathematical problem. In recent years, non-commutative algebraic frameworks have attracted increasing attention due to their potential to offer enhanced security and resistance to emerging cryptanalytic techniques. In this paper, we propose a novel digital signature scheme based on elliptic curves defined over a finite non-commutative ring. We first introduce a non-commutative ring $R$ constructed from an elliptic curve over the finite ring $ \mathbb{F}_{q}[\varepsilon]$ where $\varepsilon^4=\varepsilon^3$ and $(char(\mathbb{F}_q)\neq 2,3)$ \cite{1}. The proposed construction combines two well-known computationally hard problems: the elliptic curve discrete logarithm problem and the conjugacy problem in non-commutative rings. The proposed digital signature algorithm is designed by exploiting the interaction between these two problems, resulting in a hybrid cryptographic scheme that strengthens security compared to classical approaches based on a single hardness assumption. The scheme ensures the fundamental security properties required for digital signatures, including authentication, message integrity, and non-repudiation. Furthermore, we present a comprehensive security analysis of the proposed scheme and evaluate its resistance against four common types of cryptographic attacks. The results demonstrate that the use of non-commutative algebraic structures provides a promising direction for the design of secure and efficient digital signature schemes.