为丰富低维离散混沌系统的动力学特性以及克服脱氧核糖核酸(deoxyribonucleic acid,DNA)编码的引入使混沌图像加密系统安全性易于降低的问题,基于Arnold映射构建具有恒定正Lyapunov指数的2维离散混沌系统,并将其与DNA编码结合,设计一个混沌图像加密方案.所设计的混沌系统模型中不含非线性项,系统具有超混沌动力学行为;加密方案中用于加密的混沌序列为明文图像像素与密钥的加取模运算结果,图像按4×4大小予以分块,扩散算法中的DNA加减、异或、同或等运算分别基于DNA编码规则1、规则4和规则7.仿真实验和性能分析结果表明:加密方案的密钥空间达到2266,信息熵为7.9993 bit,密钥灵敏度达到10-15,平均像素变化率(number of pixel change rate,NPCR)、统一平均变化强度(unified average change intensity,UACI)、块平均变化强度(block average change intensity,BACI)分别为 99.6092％、33.4664％、26.7718％.
Image Encryption Scheme Based on 2D Discrete Chaotic System and Deoxyribonucleic Acid
In order to enrich the dynamic characteristics of a low-dimensional discrete chaotic system and overcome the problem of low security of chaotic image encryption system caused by the introduction of deoxyribonucleic acid(DNA)coding,a 2D discrete chaotic system with constant positive Lyapunov exponent was constructed based on Arnold map.In addition,a chaotic image encryption scheme was designed by combining the system with DNA coding.The designed chaotic system model did not have nonlinear terms and had hyperchaotic dynamic behavior.The chaotic sequence used for encryption in the encryption scheme was the result of addition and module operation between the plaintext image pixels and the key.Images were divided into blocks by the size of 4 × 4.The operations of DNA addition and subtraction,XOR,and XNOR in the diffusion algorithm were based on DNA coding rule 1,rule 4,and rule 7,respectively.The simulation and performance analysis results show that the key space of the encryption scheme is 2266;the information entropy is 7.999 3 bit;the key sensitivity is 10-15,and the average number of pixel change rate(NPCR),unified average change intensity(UACI),and block average change intensity(BACI)are 99.609 2％,33.466 4％,and 26.771 8％,respectively.
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