Fractal matrix speech encryption algorithm based on fractional order robust chaos

Abstract

The limitations of current speech encryption algorithms in planar dimensional transformation and encryption process, as well as the parameter discontinuity problem faced by fractional-order chaos, are optimized. In this paper, we propose a fractal matrix encryption algorithm for speech with high dimensionality based on fractional order robust chaos. The designed chaos equation utilizes the definition of differential fractional-order, the original integer-order robust chaos equation is transformed according to the definition of fractional-order differential and 3D fractional-FOHE exponential chaos is proposed. The fractional-order robust chaos effectively solves the problems of integer-order numerical aggregation and discontinuity of fractional-order chaos parameters. In the key proposed in the encryption algorithm, the nested and intermediate parameters are used to generate the key, which solves the problem of small key space at present. On this basis, an encryption scheme is proposed to change the one-dimensional speech matrix into cubic three-dimensional fractal matrix by using matrix transformation of space and to realize diffusion and obfuscation for the data in each three-dimensional fractal matrix. The proposed cubic 3D fractal matrix is irregular and self-similar. The core formulation in the encryption scheme utilizes the retrieval matrix of the chaotic sequence for the coordinate substitution operation of the cubic 3D fractal matrix and uses the algorithm to diffuse the values nested on the coordinates, breaking the current limitation of encryption only in low dimensions. Comparing the high-dimensional encryption algorithm proposed in this paper with other encryption literature, it is found that the designed algorithm has a larger key space, lower data correlation, and can resist a series of classical attacks. It provides a more practical encryption scheme for speech encryption.