Security Analysis of an (m, m) Visual Cryptography Scheme Using Quasi-Orthogonal Matrices under Conditions of Partial Key Compromise
Abstract
Security Analysis of an (m, m) Visual Cryptography Scheme Using Quasi-Orthogonal Matrices under Conditions of Partial Key Compromise
Incoming article date: 09.01.2026This paper considers a modification of the (m, m) visual cryptography scheme using quasi-orthogonal matrices. The use of Mersenne matrices with two-level values {a, -b} is proposed. The scenario of partial key compromise is investigated, where a potential attacker knows the structure of the key matrix but lacks information about its specific level values {a, -b}. Numerical modeling of the restoration process for grayscale secret images using Mersenne matrices of a fixed order and structure with different sets of level parameters has been conducted. It is shown that even with extremely small deviations of the level values from the true ones, the restoration of a visually distinguishable image becomes impossible. The obtained results confirm that the use of Mersenne matrices expands the key space compared to the earlier (m, m) scheme using Hadamard matrices and provides an additional layer of protection in visual cryptography tasks.
Keywords: Image with a secret, Hadamard matrices, Mersenne matrices, matrix multiplication