A Hybrid Matrix-Based Cryptographic Framework Using Multiple Linear Recurrence Sequences

In this study, we propose a matrix-based transformation framework constructed from special integer sequences, including Fibonacci, Lucas, Pell, and Jacobsthal numbers. The approach is based on block-wise 2×2 matrix transformations that preserve key structural invariants, particularly the determinant, ensuring explicit invertibility of the scheme. By combining multiple recurrence-based matrices within a unified framework, the method provides flexible forward and inverse transformations without increasing matrix dimensions or introducing additional redundancy. The determinant-preserving property enables intrinsic consistency checking and supports an analytic error-detection and correction mechanism at the block level. Several illustrative examples are presented to demonstrate the applicability of the proposed scheme and its computational characteristics. The framework is purely algebraic and can be extended to other matrix families generated by linear recurrence relations, making it suitable for a wide range of applications in applied and computational mathematics.