椭圆曲线与自适应DNA编码的混沌图像加密算法  

Chaotic image encryption algorithm based on elliptic curve and adaptive DNA coding

作　　者：肖定汉 禹思敏[1] 王倩雪[1] Xiao Dinghan;Yu Simin;Wang Qianxue(College of Automation,Guangdong University of Technology,Guangzhou 510006,China)

机构地区：[1]广东工业大学自动化学院,广州510006

出　　处：《中国图象图形学报》2023年第11期3428-3439,共12页Journal of Image and Graphics

基　　金：国家自然科学基金项目(61901304);广东省自然科学基金项目(2022A1515010005)。

摘　　要：目的当前大多数的混沌图像加密算法采用与明文相关的对称加密方式,存在密钥冗余以及一次一密模式难以实现的问题,为此,提出一种新的椭圆曲线与自适应DNA(deoxyribonucleic acid)编码结合的混沌图像加密算法。方法算法利用椭圆曲线的公钥密码体制达成密钥共识,结合4维Lorenz超混沌系统产生共识密钥序列用于自适应DNA编码加密,在DNA编解码的扩散过程中内嵌中间密文状态反馈的动态扩散—自适应置换结构以抵抗分割攻击与选择明文攻击,加密过程的密文状态在解密端能够自适应同步,无需额外传输。结果算法的密钥空间为2256,足以抵抗穷举攻击。通过对多幅不同尺寸的测试图像进行仿真,比特变化率(number of bit change rate,NBCR)均接近50%,密文各方向上的相邻像素相关性均接近于0,信息熵接近理想值8,并且全部通过NIST SP800-22随机性测试以及抗差分攻击分析。其他混沌图像加密算法进行对比分析,结果表明,本文算法具有极高的实用性和安全性。结论本文算法完善了密钥冗余的问题,提高了算法的可行性,同时通过实验验证了算法的安全性,适合用于对各种尺寸的图像进行加密及相关的信息安全保障。Objective With the rapid development of computer networks,digital images,as an important part of informa⁃tion transmission,are also widely transmitted through the Internet.Digital images used in national administration,military defense,commercial intelligence,and other fields may contain some sensitive private information.Therefore,during its transmission,the security of an image must be considered.Chaotic systems are characterized by ergodicity,sensitivity to initial conditions,and long-term unpredictability.Therefore,many scholars use these systems in designing image encryp⁃tion algorithms.To resist chosen-plaintext attacks,most traditional image encryption algorithms based on the chaotic sys⁃tem adopt symmetric encryption methods related to plaintext information in the process of key generation or encryption.This kind of algorithm uses the same key to encrypt and decrypt information.Before transmission,the relevant key needs to be transmitted to the receiver through a secret channel.This one-time pad mode means that the number of keys that need to be stored and transmitted increases along with the number and frequency of communications.These keys do not contain information and are redundant data that bring unnecessary burden to users.In addition,the high-frequency transmission of these keys can greatly increase the risk of exposing secret channels,thus leading to adverse effects.To solve these prob⁃lems,this paper proposes a chaotic image encryption algorithm based on elliptic curve and adaptive DNA coding.Method The proposed algorithm adopts the public key cryptosystem of an elliptic curve to make the communication parties reach the key consensus without transmitting the secret private key.To reach the goal of the key consensus,the consensus element is transformed into the initial values of the improved four-dimensional hyperchaotic Lorenz system and is then combined with the four-dimensional hyperchaotic Lorenz system to generate the consensus chaotic key sequence for adaptive DNA coding encryption.T

关 键 词：图像加密 椭圆曲线 超混沌系统 自适应DNA编码 动态扩散 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]