应用黄金比Haar小波实现图像加密

Golden ratio-haar wavelet in image encryption

探讨了Fibonacci序列,给出一些重要的相关性质.在此基础上研究了Fibonacci正交变换,进而将Fibonacci序列中的黄金比引入Hadamard变换,产生一种正交变换矩阵.为使正交变换矩阵的物理意义更加明确,提出一种基于黄金比(GR)的Haar小波变换,对所提出的黄金比Harr(GRH)小波在时、频域进行分析并将GRH应用于图像加密.实验结果表明,GRH变换不失为一种有效、便捷的可用于图像加密处理.与现有的图像加密算法相比,本文给出的方法具有图像加密所采用的矩阵构造便捷、加密算法简单、频域特性优良等特点;同时,加密矩阵正交、解密运算也简单.

Fibonacci sequence and some related important character are discussed. Fibonacci discrete orthogonal transforms are researched based on former. Golden ratio of Fibonacci is introduced into Hadamard transformation and orthogonal transformation matrix is got, a kind of transformation is produced based on golden ration-haar wavelet, and clear physical means of the orthogonal transformation in time and frequency domain are analyzed. At last, golden ratio-haar wavelet transform is researched in image encryption. The results of experiment indicate image encryption technique is efficient and facility. As compared to the existing transform, the obvious advantages of the matrix construction and algorithms are simple and have excellent character in frequency domain. Meanwhile decryption operation calculate easily with orthogonal encryption matrix.