﻿ 基于秘密分享和直方图平移的多图像水印算法 Multi-Image Watermarking Algorithm Based on Secret Sharing and Histogram Shifting

Journal of Image and Signal Processing
Vol. 08  No. 02 ( 2019 ), Article ID: 29959 , 7 pages
10.12677/JISP.2019.82012

Multi-Image Watermarking Algorithm Based on Secret Sharing and Histogram Shifting

Zhuoying Zhao1,2, Jiazhi Zhang1,2, Xiaoqiang Zhang1,2*

1School of Information and Control Engineering, China University of Mining and Technology, Xuzhou Jiangsu

2Xuzhou Key Laboratory of Artificial Intelligence and Big Data, Xuzhou Jiangsu

Received: Apr. 3rd, 2019; accepted: Apr. 14th, 2019; published: Apr. 28th, 2019

ABSTRACT

To solve the problems of small embedding capacity and low security of image watermarking algorithm, a watermarking image can be decomposed into multiple shadow images with the secret sharing algorithm, and then the shadow images can be embedded into multiple carrier images by histogram shifting. This paper proposes a multi-image watermarking algorithm based on secret sharing and histogram shifting. In this algorithm, the watermarking image cannot be extracted by only one shadow image, and other shadow images must be used. Therefore, the algorithm security is improved. Meanwhile, the embedding capacity of image watermarking can be enlarged by increasing the number of carrier images. Algorithm analyses and experimental results show that the proposed algorithm is feasible.

Keywords:Image Watermarking, Secret Sharing, Histogram Shifting, Multiple Image Process

1中国矿业大学信息与控制工程学院，江苏 徐州

2徐州市人工智能与大数据重点实验室，江苏 徐州

Copyright © 2019 by author(s) and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

1. 引言

2. 理论基础

2.1. 秘密分享方案

Shamir的 $\left(k,n\right)$ 门限秘密分享方案的基本思想是：首先，要把秘密S分割成 $n$ 份影子信息；其次，分别将 $n$ 份影子信息分发给 $n$ 个参与者进行保管；最后，任意 $k\left(k\le n\right)$ 份影子信息联合起来才能恢复出S。

$f\left(x\right)={m}_{0}+{m}_{1}x+{m}_{2}{x}^{2}+\cdots +{m}_{k-1}{x}^{k-1}$(1)

2.2. 直方图平移算法

Ni等人提出了一种基于直方图平移的可逆水印算法 [8] ，其算法思想为：首先，绘出图像的灰度直方图，并找出其中的最大值点a和最小值点b，为方便讨论，不妨设 $a ；其次，将图像中所有在 $\left[a+1,b-1\right]$ 的灰度值加1，即将 $\left[a+1,b-1\right]$ 的直方图向右平移一位，从而像素值为 $a+1$ 的像素点的个数变为0；再次，在嵌入水印时，若水印值为1，则像素值为a的灰度值加1，即为 $a+1$ ；若水印值为0，则保持 $a$ 的像素值不变；最后，提取水印信息时，顺序扫描图像，若像素灰度值为a，则提取的水印信息为0；若像素灰度值为 $a+1$，则提取的水印信息为1 [9] 。若想恢复出原始宿主图像，只需把灰度值处在区间 $\left[a+1,b\right]$ 的灰度值减1即可。

3. 新多图像水印算法

3.1. 生成影子图像

3.2. 嵌入影子图像

$k\left(k\le n\right)$ 幅载体图像为 ${I}_{\text{1}},{I}_{\text{2}},\cdots ,{I}_{k}$，从 $n$ 幅影子图像中任选 $k$ 幅即 ${W}^{1},{W}^{2},\cdots ,{W}^{k}$ 作为水印信息，分别嵌入到 $k$ 幅载体图像中。根据秘密分享方案， $k$ 幅影子图像可以恢复出原水印图像。提出的多图像水印算法嵌入影子图像的详细步骤如下：

3.3. 提取影子图像及恢复载体图像

$\begin{array}{l}{w}_{ij}^{1}\left({x}_{1}\right)={m}_{0}+{m}_{1}{x}_{1}+{m}_{2}{x}_{1}^{2}+\cdots +{m}_{k-1}{x}_{1}^{k-1}\mathrm{mod}255\\ {w}_{ij}^{2}\left({x}_{2}\right)={m}_{0}+{m}_{1}{x}_{2}+{m}_{2}{x}_{2}^{2}+\cdots +{m}_{k-1}{x}_{2}^{k-1}\mathrm{mod}255\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }⋮\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\\ {w}_{ij}^{p}\left({x}_{k}\right)={m}_{0}+{m}_{1}{x}_{k}+{m}_{2}{x}_{k}^{2}+\cdots +{m}_{k-1}{x}_{k}^{k-1}\mathrm{mod}255\end{array}$(2)

4. 实验验证

Figure 1. Shadow images

Figure 2. Carrier images

Figure 3. Watermarked images

Figure 4. Extracted watermark image

5. 算法分析

5.1. 透明性

$\text{PSNR}=10\mathrm{lg}\frac{{255}^{2}}{\frac{1}{m×n}\underset{i=0}{\overset{m-1}{\sum }}\underset{j=0}{\overset{n-1}{\sum }}{\left(X\left(i,j\right)-{X}_{W}\left(i,j\right)\right)}^{2}}$ (3)

5.2. 鲁棒性

$\text{NC}=\frac{\underset{i=1}{\overset{m}{\sum }}\underset{j=1}{\overset{n}{\sum }}W\left(i,j\right){W}^{\prime }\left(i,j\right)}{\underset{i=1}{\overset{m}{\sum }}\underset{j=1}{\overset{n}{\sum }}{W}^{2}\left(i,j\right)}$ (4)

5.3. 安全性

5.4. 嵌入容量

5.5. 算法执行效率

$T\left(n\right)=O\left(\left(n-1\right)+\text{size}+\underset{i\in U\left(\text{peak}_\text{point},\text{zero}_\text{point}\right)}{\sum }h\left(i\right)+\frac{1}{2}h\left(\text{peak}_\text{point}\right)\right)$ (5)

6. 结论

Multi-Image Watermarking Algorithm Based on Secret Sharing and Histogram Shifting[J]. 图像与信号处理, 2019, 08(02): 83-89. https://doi.org/10.12677/JISP.2019.82012

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15. NOTES

*通讯作者。