基于稀疏矩阵的Arnold数字图像加密算法

doi:10.11772/j.issn.1001-9081.2015.03.726

计算机应用 ›› 2015, Vol. 35 ›› Issue (3): 726-731.DOI: 10.11772/j.issn.1001-9081.2015.03.726

基于稀疏矩阵的Arnold数字图像加密算法

江帆^1,2, 吴小天^2,3, 孙伟^1,2,4

1. 中山大学软件学院, 广州 510006;
2. 中山大学信息技术教育部重点实验室, 广州 510006;
3. 中山大学信息科学与技术学院, 广州 510006;
4. 中国科学院信息工程研究所信息安全国家重点实验室, 北京 100093

收稿日期:2014-09-05 修回日期:2014-11-26 出版日期:2015-03-10 发布日期:2015-03-13
通讯作者: 吴小天
作者简介:江帆(1989-),男,安徽亳州人,硕士研究生,主要研究方向:图像加密、信息隐藏;吴小天(1985-),男,广东开平人,博士,主要研究方向:视觉密码、加密域信号处理、信息隐藏孙伟(1972-),男,江苏连云港人,教授,博士,主要研究方向:多媒体信息安全、计算机图形学
基金资助:
中国博士后科学基金资助项目(2014M552269);广东省自然科学基金资助项目(S2013010013728)

Arnold digital image encryption algorithm based on sparse matrix

JIANG Fan^1,2, WU Xiaotian^2,3, SUN Wei^1,2,4

1. School of Software, Sun Yatsen University, Guangzhou Guangdong 510006, China;
2. Key Laboratory of Information Technology (Ministry of Education), Sun Yatsen University, Guangzhou Guangdong 510006, China;
3. School of Information Science and Technology, Sun Yatsen University, Guangzhou Guangdong 510006, China;
4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China

Received:2014-09-05 Revised:2014-11-26 Online:2015-03-10 Published:2015-03-13

摘要/Abstract

摘要：

针对原有Arnold数字图像加密算法中常见的密钥空间不足的问题,提出了一种基于稀疏矩阵的Arnold数字图像加密算法——SMA;同时为了进一步提高该基于稀疏矩阵的Arnold数字图像加密算法的安全性,利用图像分层及三层加密结构的思想来加以改进,提出了安全性提升算法——3SMA(3 round SMA)。SMA算法的加密流程首先利用Arnold变换将明文图片扩散到一个较大的稀疏矩阵中,再去除稀疏矩阵中的无效元素得到密文;解密时输入密文图片,依照预先计算好的对换表将密文中的像素调整回原来的位置得到明文。3SMA算法使用三个不同的轮密钥,每一轮都处理明文图像中的两个颜色分量以达到加密的目的。实验表明,与已有的Arnold数字图像加密算法进行对比时,SMA与3SMA算法具有更高的安全性。

关键词: 数字图像加密, Arnold变换, 对称加密算法, 稀疏矩阵, 图像置乱

Abstract:

For the common key space shortage problem found in existing Arnold digital image encryption algorithm, a new digital image encryption algorithm-SMA (Sparse Matrix Arnold) based on sparse matrix and Arnold transformation was proposed and in order to further improve the security of the algorithm, an improved algorithm-3SMA (3 round SMA) using the ideas of multi-layered decomposition and three-tier structure encryption was proposed. The SMA algorithm adopted Arnold transform to spread the plaintext picture into a large sparse matrix, and then removed invalid sparse matrix elements to get the cipher text. While, the decryption of SMA needed to enter the cipher text picture, and moved pixels in cipher text picture back to their original positions in accordance with the previously computed swapping table. The 3SMA algorithm comprised three different round keys. Each round, the improved algorithm needed to process two color components of the plaintext picture to achieve the purpose of encryption. The experimental results show that the proposed encryption algorithm and its improvement obtain higher security compared to Arnold encryption algorithms analyzed.

Key words: digital image encryption, Arnold transform, symmetric encryption algorithm, sparse matrix, image scrambling

中图分类号:

TP309

江帆, 吴小天, 孙伟. 基于稀疏矩阵的Arnold数字图像加密算法[J]. 计算机应用, 2015, 35(3): 726-731.

JIANG Fan, WU Xiaotian, SUN Wei. Arnold digital image encryption algorithm based on sparse matrix[J]. Journal of Computer Applications, 2015, 35(3): 726-731.

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基于稀疏矩阵的Arnold数字图像加密算法

Arnold digital image encryption algorithm based on sparse matrix

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