Image Block Cipher Based on Parameterized Cosine Transform over Finite Fields

This paper proposes an image block cipher scheme based on a parameterized finite-field cosine transform (FFCT) and a nonlinear feedback of permutation polynomial over finite field. First, a plain image was mapped from the integer field to a finite field and divided into non-overlapping
$8\times 8$
subblocks. Subsequently, a parameterized FFCT was conducted for each block. Next, the nonlinearity in the cryptosystem was introduced by a feedback branch that received the FFCT output block, passed it through a nonlinear permutation polynomial mapping after delaying one block and added the result to the incoming plain image block. The initial FFCT output state before the first block was generated by a two-dimensional (2-D) logistic chaotic system. Finally, the transformed subblocks were merged into a single image as the ciphertext. The control parameters of the 2-D logistic chaotic system, the permutation polynomial, and the FFCT were used as cipher keys. The inherent nonlinearity of the permutation polynomial ensures the nonlinearity of the proposed cryptosystem. The modular operation of the FFCT and the permutation polynomial mapping over the finite field make the computation more efficient and ensure that the entire encryption and decryption system is strictly lossless one. Extensive experimental results show that the proposed image block cipher is feasible, efficient, and resist common classical attacks.