基于离散分数傅立叶和哈特里变换的图像加密  

Image encryptions based on discrete fractional Fourier and Hartley transforms

作　　者：郑路[1] 冉启文[1] 游宏[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2008年第3期316-319,共4页Journal of Natural Science of Heilongjiang University

摘　　要：为了得到用于图像加密的新的离散算法,一类离散算子M(σ,τ)被用来给出离散分数傅立叶变换(DFrFT)和离散分数哈特里变换(DFrHT)新的定义形式。同时,构造并且研究了一类具有赫尔米特特征向量和随机特征值的矩阵W(α).通过分析它们的特征分解形式发现:新DFr-FT和DFrHT的定义下给出的离散算法几乎具有离散算法本身所渴望的全部性质。另外,在具有随机特征值的情况下,构造矩阵W(α)可以被分解成一系列离散分数傅立叶变换加权求和的形式,而且分数阶数是规则递增的。加权系数则是随机特征值向量的离散傅立叶变换结果。作为实际应用的例子,这两类方法被用于图像加密,数值模拟的结果证实了这种方法的可行性。In order to present a new discrete algorithm for image encryptions, a discrete operator is proposed to give the new definition of the discrete fractional Fourier transformation （DFrFT） and the discrete fractional Hartley transformation （DFrHT）. A kind of matrix W（α） which has Hermitian eigenvectors and a random eigenvalues is studied. It is found by analyzing their characteristic decompositions that the new definitions of DFrFT and DFrHT proposed almost all hoped properties of discrete algorithms. Moreover, when W（α） has random eigenvalue, it can be written as a weighted sum of a series of DFrFTs, and the orders of these DFrFTs are increasing regularly. As a practical example, these two methods are used for image encryption, and the numerical simulation results demonstrate the feasibility of the proposed method.

关 键 词：图像加密 离散分数傅立叶变换 离散分数哈特里变换 

分 类 号：TN911.73[电子电信—通信与信息系统]