东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2014, Vol. 35 ›› Issue (1): 20-23.DOI: 10.12068/j.issn.1005-3026.2014.01.005

• 信息与控制 • 上一篇    下一篇

基于二维Logistic映射和二次剩余的图像加密算法

朱和贵，陆小军，张祥德，唐青松   

  1. (东北大学 理学院， 辽宁 沈阳110819)
  • 收稿日期:2012-04-19 修回日期:2012-04-19 出版日期:2014-01-15 发布日期:2013-07-09
  • 通讯作者: 朱和贵
  • 作者简介:朱和贵(1980-)，男，湖南双峰人，东北大学讲师，博士研究生；张祥德(1963-)，男，山东昌乐人，东北大学教授.
  • 基金资助:
    国家自然科学基金资助项目(61202085)；辽宁省自然科学基金资助项目(201202074).

A Novel Image Encryption Scheme with 2DLogistic Map and Quadratic Residue

ZHU Hegui， LU Xiaojun， ZHANG Xiangde， TANG Qingsong   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2012-04-19 Revised:2012-04-19 Online:2014-01-15 Published:2013-07-09
  • Contact: ZHANG Xiangde
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摘要： 针对公共网络中数字图像的安全传播问题，提出了一种基于二维Logistic混沌映射和二次剩余的图像加密算法.该加密算法利用二维Logistic映射的优良随机性，对明文图像进行2次置乱，极大地改变了图像像素位置.然后把置乱图像展开成二进制序列，按照8位一组进行分块，再利用二次剩余密码体制对每个分块进行加密，有效地改变了明文图像的信息.最后，对该算法进行直方图分析、信息熵分析、密钥敏感性分析以及明文图像和密文图像的相关系数分析等仿真实验.实验表明该算法能抵抗统计攻击、信息熵攻击，是一种较安全的图像通信方式.

关键词: 图像加密, 图像置乱, 图像扩散, 二维Logistic映射, 二次剩余

Abstract: Considering the importance of image transmission in the public net， a new image encryption algorithm was proposed based on the 2DLogistic chaos and quadratic residue. Firstly， the original image was shuffled twice with the 2DLogistic chaos map， and the positions of the original image were changed sufficiently. Then， the shuffled image was turned into a binary sequence， and every 8 bits were called a block. For each block， quadratic residue was applied to encrypt the block， then， the encrypted binary sequence was turned into the encrypted image. Therefore， the statistical information of plain image was changed drastically by the proposed scheme. The proposed image scheme was tested by various types of experiment and security analyses such as histogram analysis， information entropy， key sensitivity and correlation coefficient analysis. All these analyses demonstrated that the proposed scheme can resist statistical attack， information entropy attack， and it is very proper for secure image communication.

Key words: image encryption, image permutation, image diffusion, 2DLogistic map, quadratic residue

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