Fast Chaotic Image Encryption Algorithm Using a Novel Divide and Conquer Diffusion Strategy

Abstract

To protect image privacy in real-time transmission, a fast chaotic image encryption algorithm using a novel divide and conquer diffusion strategy is proposed in this paper. Firstly, a fast pseudo-random sequence generator is constructed using 2D hyperchaotic systems. And by performing bitwise XOR operation between two integer sequences obtained from different systems, the final key stream used for diffusion will have better randomness and unpredictability. Secondly, to achieve divide and conquer diffusion, the plain image is divided into three parts, then a parallel CBC-based diffusion method can simultaneously act on upper and bottom parts (or left and right parts), which achieves a time complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {O}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$W+H$ </tex-math></inline-formula> ). Moreover, within the diffusion process, the mechanism of information interaction on the central row or column further enhances avalanche effect to resist differential attack. Thirdly, the session key of the proposed algorithm is a mixture of the plain image’s hash value and a true random sequence, which not only improve plaintext sensitivity but also realize one-time pad. Finally, experimental results indicate the superiority of our algorithm to resist statistical, chosen-plaintext, entropy, and other common attacks. Furthermore, by comparison with previous works, our algorithm preforms much faster execution speed with only average of 0.08s to encrypt images of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$512\times 512$ </tex-math></inline-formula> , while it provide the same or even higher level of security. Therefore, the proposed algorithm can meet security and efficiency requirements of real-time communications of image data.