An improved image encryption algorithm with finite computing precision

Abstract

When a digital chaotic system is realized on hardware of finite computing precision, it will lead to short period orbits. Although many existing image encryption algorithms declared that the average cycle lengths of their digital chaotic systems are larger than the required cycle lengths in image encryption, there are still many period orbits whose lengths are far smaller than the average cycle length. To further improve security with finite precision, an improved cryptosystem is proposed based on a new two-dimensional chaotic map derived from the Sine map, the Chebyshev map and a linear function (2D-SCL). Performance estimation demonstrates that the 2D-SCL has good ergodicity, hyperchaotic behavior, large cycle lengths under low computing precisions, and its complexity is larger and more stable than that of several newly developed 2D chaotic maps. Thus we design an improved cryptosystem based on the 2D-SCL map. In the scheme, we combine the confusion and diffusion processes in one stage to improve the running speed. Based on the SHA-1 hash values of plain image and the chaotic sequence, a pseudorandom sequence is designed and then an anti-degradation method is introduced to improve the dynamic degradation of the 2D-SCL map under finite computing precision. Meanwhile, this algorithm also updates the initial values of the 2D-SCL map in real-time, thus enhancing the ability to resist known-plaintext and chosen-plaintext attacks. The largest precision is set at 2−16, and simulation results show that this algorithm has high security, low time complexity, and the ability to withstand common attacks.