Diophantine Solutions Based Permutation for Image Encryption

Abstract

A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system. The resulting solutions are then used for rearranging the positions of the bits and pixels in the ciphered sequence. The performance of such a technique is compared to GRP and Xiang permutation algorithms. From this permutation algorithm an efficient chaos-based block cipher using a chaotic logistic map is proposed. Statistical analyses of this system show a high security level and non-propagation of errors.