A Public Key Cryptosystem Using Matrix Over the Finite Ring

Abstract This paper is the first of two complementary papers. In this paper, we present a novel algorithm in the field of cryptography, an area that has garnered significant attention from researchers. Our algorithm is based on matrix calculus over finite rings, enabling efficient encryption and decryption processes without requiring additional computational resources. A key feature of this approach is its formulation of a mathematical problem involving the solution of a system of nonlinear equations, which significantly enhances the system’s security and complexity. Furthermore, we provide a detailed mathematical proof of the algorithm’s correctness.