A Robust Image Encryption Algorithm Based on a 32-bit Chaotic System

Abstract

In these years, image encryption systems based on chaotic maps have received considerable attention from researchers. For the security of encryption algorithms, it is important to ensure that chaotic systems can produce high quality pseudo-random sequences. However, when a chaotic system that theoretically has good random performance is deployed in a limited precision platform, its random performance will deteriorate. We prove that even if the precision reaches 256-bit, the piecewise linear chaotic map still fails to achieve the desired random performance. Moreover, in the case of low precision, the cascade structure commonly used in mixed chaotic maps will aggravate the problem of random degeneration. To generate good pseudo-random numbers in low-precision platforms, we propose a positive integer random sequence generator, called 32-bit PL_PWLCM&LM, which comprises two 32-bit PL_PWLCMs and one 32-bit logistic map in parallel. In our proposed image encryption system, we adopt the permutation algorithm with four pixels as a permutation unit and the diffusion algorithm based on rows and columns. The security and performance analyses prove that the proposed scheme is a secure, robust, and fast image encryption algorithm. Source codes are shared on GitHub: https://github.com/cuclihao/Pic_Enc_V3.

Keywords

• Image encryption
• chaotic map
• finite precision
• permutation-diffusion network
• security analysis