﻿ 基于线性变换的彩色数字图像置乱算法

基于线性变换的彩色数字图像置乱算法Color Digital Image Scrambling Algorithm Based on Linear Transformation

Abstract: There are some problems that traditional color digital image scrambling algorithm has: small key space, weak anti-attack and low encryption intensity. In this paper, we present a new algorithm of color digital image scrambling algorithm based on linear transformation. In order to achieve the purpose of pixel scrambling, it randomly generates three matrices, operates with the three RGB matrices of the original color digital image, and then it will disrupt the position of the pixel scrambling. The simulation results show that the algorithm can change the gray image features of image, and has the advantages of stability, strong randomness and strong anti-attack.

1. 引言

2. 基于线性变换的图像置乱算法

$R={\left({r}_{ij}\right)}_{k×r},\text{}\left(i=1,2,\cdots ,k,\text{\hspace{0.17em}}j=1,2,\cdots ,r\right)$

$G={\left({g}_{ij}\right)}_{k×r},\text{}\left(i=1,2,\cdots ,k,\text{\hspace{0.17em}}j=1,2,\cdots ,r\right)$

$B={\left({b}_{ij}\right)}_{k×r},\text{}\left(i=1,2,\cdots ,k,\text{\hspace{0.17em}}j=1,2,\cdots ,r\right)$

${R}^{\prime }={P}_{1}R$ (1)

${G}^{\prime }={P}_{2}G$ (2)

${B}^{\prime }={P}_{3}B$ (3)

$R={P}_{1}^{-1}{R}^{\prime }$ (4)

$G={P}_{2}^{-1}{G}^{\prime }$ (5)

$B={P}_{3}^{-1}{B}^{\prime }$ (6)

3. 仿真实验与分析

Figure 1. Lena image scrambling and reduction map

Figure 2. The gray and grayscale histograms of the original image

Figure 3. The grayscale and histogram of the encrypted image

4. 结语

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