On Matrix-Based Cryptography Using Matrix Norm and Special Integer Sequences

Abstract

In this paper, a novel matrix-based encryption approach based on the Affine Hill cipher is presented. The key matrix is constructed using the Narayana integer sequence, and the Frobenius norm of the key matrix is used as a scaling factor in the key construction. This approach increases key matrix variation and influences the algebraic structure of the resulting ciphertexts. The security analysis demonstrates that the proposed method yields a larger and more structured key space compared to the classical Hill cipher.