Malaysian Journal of Mathematical Sciences, March 2026, Vol. 20, No. 1
A Modular Matrix Approach to Symmetric Encryption Inspired by NTRU Principles
Salem, M. H. and Neamah, A. A.
Corresponding Email: ammara.meamah@uokufa.edu.iq
Received date: 24 May 2025
Accepted date: 13 August 2025
Abstract:
NTRU is an efficient quantum-resistant lattice-based public-key encryption scheme, but based on polynomial ring computations, which could introduce algebraic vulnerabilities and implementation cost to some uses. In this paper, we introduce a novel symmetric cryptosystem derived from the NTRU cryptography algorithm, using effective matrix computations over traditional polynomial algebra. The structure of the proposed system is based on the use of self-invertible matrices, which eliminate the need for explicit matrix inversion during decryption, ensuring more efficient calculation while retaining a strong mathematical security guarantee. Experimental results demonstrate that the system is lightweight and scalable and can be applied to data protection, image protection, and communication protection on constrained devices such as the Internet of Things (IoT) and embedded systems. In addition, the proposed construction offers an adaptive and secure cryptosystem, which is well-suited for the requirements of modern information security infrastructures that necessitate an efficient, secure, and lightweight encryption system.
Keywords: symmetric encryption; NTRU cryptosystem; self-invertible matrices; matrix-based cryptography.
