Enhanced Security in Post-Quantum Cryptography: A Comprehensive Lattice-Based Signature Scheme Using Matrix Groups
Alex Musa *
Department of Mathematics, University of Portharcourt, Nigeria.
Udoaka Otobong G
Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a robust lattice-based digital signature scheme that leverages matrix groups to enhance post-quantum security. Built on the hardness of lattice problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE), combined with the complexity of the Matrix Group Conjugacy Problem our scheme demonstrates both theoretical and practical security. We rigorously establish the (MGCP), mathematical foundations, analyze the computational complexity, and provide numerical simulations to evaluate performance. This approach contributes a unique blend of lattice and matrix group theory, offering new insights and possibilities in post-quantum cryptography.
Keywords: Lattice-based cryptography, digital signatures, matrix groups, Learning With Errors (LWE), Shortest Vector Problem (SVP), conjugacy problem, post-quantum cryptography, computational analysis