基于Mordell型椭圆曲线的非对称光学多图像加密方法  

Asymmetric optical multi-image encryption method based on Mordell-type elliptic curve

作　　者：刘禹佳 张福琦 杜轶男 王瑞[4] LIU Yujia;ZHANG Fuqi;DU Yinan;WANG Rui(School of Electrical Engineering and Information Technology,Changchun Institute of Technology,Changchun 130012,China;College of communication engineering,Jilin university,Changchun 130012,China;CRRC Changchun Railway Vehicle Co.,Ltd.,Changchun 130113,China;Aviation University Air Force,Changchun 130012,China)

机构地区：[1]长春工程学院电气与信息工程学院,长春130012 [2]吉林大学通信工程学院,长春130012 [3]中车长春轨道客车股份有限公司,长春130113 [4]空军航空大学,长春130012

出　　处：《激光杂志》2023年第8期74-82,共9页Laser Journal

基　　金：吉林省科技发展计划基金(No.YDZJ202201ZYTS428);吉林省教育厅科学技术研究项目(No.JJKH20210671KJ)。

摘　　要：针对多幅图像光学加密方法存在的安全性问题,提出了一种Gyrator变换域下基于Mordell型椭圆曲线和联合变换相关器的光学多图像加密方法。将四幅原始图像转换为四幅二维码(Quick response code,QR),并将四幅QR码编码成复合图像;利用Mordell型椭圆曲线的同构参数,实现公钥和私钥的非对称分发;通过联合变换相关器,进行Gyrator变换域下的加密。仿真结果表明,所提方法对裁剪攻击和椒盐噪声攻击具有良好的稳健性,密文相邻像素相关性呈[0,255]整数区间中的均匀分布,密文信息熵达到7.9958,使用QR码能够较好地解决传统机密系统容量小、容错率低的隐患,破解Mordell型椭圆曲线同构参数的困难能够有效提升安全性,为多幅图像的光学加密提供了新的思路。Aiming at the security problems of multi-image optical encryption method,an optical multi-image en-cryption method based on Mordell-type elliptic curve and joint transform correlator in Gyrator transform domain is pro-posed.Convert four original images into four QR codes(Quick response codes,QR),and encode the four QR codes into composite images;use the isomorphic parameters of Mordell-type elliptic curves to realize asymmetric distribution of public and private keys;The joint transform correlator is used for encryption in the Gyrator transform domain.The simulation results show that the proposed method has good robustness against cropping attacks and salt-and-pepper noise attacks.The correlation between adjacent pixels of the ciphertext is uniformly distributed in the[0,255]integer interval,and the information entropy of the ciphertext reaches 7.9958.It can effectively solve the hidden dangers of small capacity and low fault tolerance rate of traditional secret systems,and the difficulty of cracking Mordell-type el-liptic curve isomorphism parameters can effectively improve the security,and provide a new idea for optical encryption of multiple images.

关 键 词：光学安全和加密 Mordell型椭圆曲线 联合变换相关器 Gyrator变换 多幅图像叠加 

分 类 号：O438[机械工程—光学工程]