田 玉 萍

(黑河学院数学系　黑龙江 黑河 164300)



基于离散分数阶Fourier变换本征矢量分解的图像加密算法

田 玉 萍

(黑河学院数学系黑龙江 黑河 164300)

摘要针对目前采用分数阶傅里叶变换对图像进行加密的算法中，其主要存在密钥敏感性较差等不足，提出一种将离散分数阶Fourier变换与指数随机相位掩膜、Logistic混沌映射结合起来进行加密的新算法。该算法在加密过程采用离散分数阶Fourier变换本征矢量分解的方法进行运算，显著提高了加密系统的安全性能。首先，对原始图像进行Logistic映射混沌置乱处理，接着与第一个指数随机矩阵A相乘，之后再经α阶离散的分数阶Fourier变换；其次，与第二个指数随机矩阵B相乘,再经β阶离散的分数阶Fourier变换；最后，利用Logistic映射对图像再次进行置乱处理来获得最终的密文图像。仿真结果表明：与其他类似加密机制相比，该加密系统兼顾了更强的密钥敏感性以及更高的安全性。

关键词图像加密离散分数阶Fourier变换本征矢量分解密钥敏感性混沌置乱

IMAGE ENCRYPTION ALGORITHM BASED ON EIGENVECTOR DECOMPOSITION OF DISCRETE FRACTIONAL FOURIER TRANSFORM

Tian Yuping

(Department of Mathematics,Heihe College,Heihe 164300,Heilongjiang,China)

AbstractCurrent algorithms use discrete fractional Fourier transform (DFRFT) to encrypt images, they have the shortcoming of poor sensitivity in key. In light of this, we proposed a new algorithm, which combines the discrete fractional Fourier transform with exponential random phase mask and Logistic chaotic mapping for encryption. In encryption process the algorithm adopts the method of discrete fractional Fourier transform eigenvector decomposition for computing, and this significantly improves the safety performance of the encryption system. First, it conducts Logistic mapping chaotic scrambling processing on original image, then is multiplied by the first exponential random matrix A, after that the DFRFT of order α is applied; Secondly, it is multiplied by the second exponential random matrix B, then the DFRFT of order β is applied again; Finally, it uses Logistic mapping to scramble the image once again to get the final ciphertext image. Simulation results showed that compared with other similar encryption mechanisms, the proposed encryption system considered both the stronger key sensitivity and higher security.

KeywordsImage encryptionDiscrete fractional Fourier transformEigenvector decompositionKey sensitivityChaotic scrambling

0引言

随着计算机网络以及多媒体技术的快速发展，数字图像不仅涉及了个人隐私的安全性，而且也涉及了国家信息保密的安全性，其在传输过程中容易遭受非法攻击和泄露，因此数字图像信息安全已经成为了当今时代具有重要现实意义的研究课题，图像加密技术也越来越受到人们密切的关注与重视[1-4]。

分数阶Fourier变换[5,6]是一种与具有交叉项干扰的二次型时频分布有显著差异的新型时频分析工具。……