Image encryption algorithm based on the finite fields in chaotic maps

Abstract With the advancement of computer and communication technologies in data processing, storage, and increasing bandwidth of data transmission, the amount of multimedia data generation and sharing has increased exponentially. Therefore, the security of multimedia data becomes more important in transmission, processing, and storing the day-to-day. Cryptography is one of the important mechanisms in preserving the confidentiality, integrity, and availability of multimedia data such as images. In this research, a digital encryption method is presented based on Galois fields, consisting of two main stages of diffusion and permutation. At the Diffusion stage, using matrix multiplication operations in the GF (256), the overlapping rows and columns of image pixels are mixing. The permutation stage changes image pixels position by using The 2D chaotic map in GF (2n) or The 3D chaotic map in the GF field (2k). The proposed method, with a maximum of two rounds repetition of the main steps, reaches the optimal values of the parameters of the performance evaluation. By performing standard security tests, the proposed method is resistant to differential and statistical attacks and has yielded relatively good performance compared to similar digital image encryption methods.

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