Security Analysis and Improvement on an Image Encryption Algorithm Using Chebyshev Generator

Abstract

Chaotic map including Chebyshev’s polynomial have been studied and used in many cryptographic areas recently due to its low cost of computation and high level of security. Some research works have been proposed to use Chebyshev’s polynomial in image encryption by setting up two-stage encryption algorithms. Pixels of a plain image are first permuted by a Permutation process. Then each pixel values are changed by a Diffusion process. A two-stage image encryption algorithm is generally believed to be more secure than a single stage image encryption algorithm.
In this paper, however, we demonstrate a recent two-stage image encryption algorithm proposed by Wang et al., is insecure against chosen plaintext attack. An attacker may be able to decrypt a cipher image after knowing some ciphers of images which are chosen by the attacker. We present an subtle but efficient improvement over Wang et al.’s algorithm so that it is not only immune to the attack we presented but also statistically improved when experiment is conducted to measure pixels’ correlation, NPCR and UACI.