Image encryption scheme based on a new secure variant of Hill cipher and 1D chaotic maps

Abstract

This article suggests a new image encryption algorithm based on a secure variant of Hill Cipher (HC) and three improved one-dimensional (1D) chaotic maps. The proposed scheme fully satisfies the two basic concepts of security, namely confusion and diffusion. The confusion is ensured by the product of a vector consisting of the key-pixel couple and a 2 × 2 Hill matrix on the one hand, and the addition of another pseudo-random translation vector on the other hand. And the diffusion is ensured by a strong avalanche effect that links each encrypted pixel to its adjacent. The chaotic sequences used come from 1D chaotic maps with excellent statistical proprieties. The proposed algorithm aims to encrypt pixel-by-pixel all types of images, even those with a high correlation of adjacent pixels or a black background, and to make the encryption system more secure. So, the simulation results performed on a database of color and grayscale images show that the histogram of a cipher image produced a uniform distribution, a higher entropy, a correlation among image pixels that was significantly decreased; Also, the proposed algorithm has great performance in terms of sensitivity, UACI and NPCR.