Image Encryption Algorithm Based on Quadratic Proportional Fractal Interpolation

本文提出一个二次定比分形插值的模型，由其逆函数构造了一个新的分形动力系统，并从数值上验证了该动力系统的混沌特性。利用该分形混沌系统所生成的性能优良的伪随机数序列设计了一个图像加密算法，算法包括置乱和扩散两个阶段，置乱阶段应用约瑟夫遍历和排序算法打乱图像的行列像素位置。扩散阶段应用分形动力系统生成的混沌序列对图像行列进行按位加取模的双向扩散操作。论文对加密算法作了详细的性能分析，结果表明该算法具有优良的安全性能，可以抵抗多种攻击。A quadratic proportional fractal interpolation model is proposed, and a novel fractal dynamical system based on its inverse function is derived, whose chaotic properties are numerically analyzed and verified. Pseudo-random number sequences with excellent performance generated by the derived fractal chaotic system are employed to design an image encryption algorithm. The proposed image encryption algorithm consists of permutation stage and diffusion stage. In the first stage, row-column scrambling based on adaptive Josephus traversal and sorting of chaotic sequence is performed. In the second stage, the chaotic sequence generated by the fractal chaotic dynamical system performs a bit-wise addition-modulo diffusion operation on the rows and columns of the processed image. The detailed performances of the proposed image encryption algorithm are carried out. Experimental results show that the proposed algorithm has excellent security performance and can resist various attacks.