Efficient reversible data hiding scheme based on two-dimensional modulo operations

doi:10.11772/j.issn.1001-9081.2023060900

Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (6): 1880-1888.DOI: 10.11772/j.issn.1001-9081.2023060900

Special Issue: 网络空间安全

• Cyber security • Previous Articles Next Articles

Efficient reversible data hiding scheme based on two-dimensional modulo operations

Yue LI¹^,², Dan TANG¹^,²(), Minjun SUN¹^,², Xie WANG¹^,³, Hongliang CAI¹^,², Qiong ZENG¹^,²

^1.School of Software Engineering，Chengdu University of Information Technology，Chengdu Sichuan 610225，China
^2.Sichuan Province Engineering Technology Research Center of Support Software of Informatization Application （Chengdu University of Information Technology），Chengdu Sichuan 610225，China
^3.Key Laboratory of Sichuan University for Aviation Manufacturing and Ground Command Software （Chengdu University of Information Technology），Chengdu Sichuan 610225，China

Received:2023-07-11 Revised:2023-09-25 Accepted:2023-09-25 Online:2023-10-31 Published:2024-06-10
Contact: Dan TANG
About author:LI Yue， born in 1997， M. S. candidate. Her research interests include information hiding， digital watermarking.
SUN Minjun， born in 1998， M. S. candidate. His research interests include coding theory， distributed storage.
WANG Xie， born in 1970， M. S.， associate professor. His research interests include computer software and theory， big data analysis.
CAI Hongliang， born in 1983， Ph. D.， associate professor. His research interests include coding theory， visual cryptography.
ZENG Qiong， born in 1976， M. S.， lecturer. Her research interests include data mining.
Supported by:
Major Special Project of Sichuan Science and Technology Department(2022ZDZX0001);Key R & D Project of Sichuan Science and Technology Department(2022YFG0037)

基于二维模运算的高效率可逆信息隐藏方案

李越¹^,², 唐聃¹^,²(), 孙敏钧¹^,², 王燮¹^,³, 蔡红亮¹^,², 曾琼¹^,²

^1.成都信息工程大学软件工程学院, 成都 610225
^2.四川省信息化应用支撑软件工程技术研究中心(成都信息工程大学), 成都 610225
^3.航空制造及地面指挥软件四川省高校重点实验室(成都信息工程大学), 成都 610225

通讯作者: 唐聃
作者简介:李越（1997—），女，四川成都人，硕士研究生，主要研究方向：信息隐藏、数字水印
孙敏钧（1998—），男，四川叙永人，硕士研究生，主要研究方向：编码理论、分布式存储
王燮（1970—），男，四川成都人，副教授，硕士，主要研究方向：计算机软件与理论、大数据分析
蔡红亮（1983—），男，山西临汾人，副教授，博士，主要研究方向：编码理论、视觉密码
曾琼（1976—），女，四川成都人，讲师，硕士，主要研究方向：数据挖掘。
基金资助:
四川省科技厅重大专项(2022ZDZX0001);四川省科技厅重点研发项目(2022YFG0037)

Abstract

Abstract:

Aiming at the problem of low embedding efficiency and anti-detection capability when using Reversible Data Hiding （RDH） to protect data in scenarios with large data volume delivery， an efficient reversible data hiding scheme based on two-dimensional modulo operations was proposed. Firstly， a larger amount of information was embedded in smaller modified pixel values by modulo operations， then the number of embedded bits was increased by combining with an enhanced base conversion system， and finally the reversibility was conferred by using the halving method in combination with a double image. Simulation experiments conducted on the USC-SIPI standard image library show that the Peak Signal-to-Noise Ratio （PSNR） value of the steganographic image by the proposed scheme is about 40 dB when embedding up to 1 million bits of secret information， and the steganographic image can effectively resist the static attacks of RS （Regular Singular） steganalysis， Pixel-Difference Histogram （PDH） steganalysis， and bit-plane steganalysis. Therefore， the proposed scheme effectively improves the embedding efficiency of the original image， and has good anti-detection capability at the same time.

Key words: Reversible Data Hiding (RDH), enhanced base, modulo operation, key value, high efficiency

摘要：

针对在较大数据量传递的场景中使用可逆信息隐藏（RDH）保护数据时嵌入效率和抗检测能力较低的问题，提出一种基于二维模运算的高效率可逆信息隐藏方案。首先通过模运算较小的修改像素值嵌入较大的信息量，再结合增强的进制转换系统增加嵌入位数，最后使用折半法结合双图像赋予可逆性。在USC-SIPI标准图像库上进行的仿真实验结果表明，在嵌入高达100万比特秘密信息时，所提方案的隐写图像的峰值信噪比（PSNR）值保持在40 dB左右，且该隐写图像可有效抵抗RS（Regular Singular）隐写分析、像素差直方图（PDH）隐写分析和位平面隐写分析的静态攻击。因此，所提方案有效提高了对原始图像的嵌入效率，同时具有良好的抗检测能力。

关键词: 可逆信息隐藏, 增强进制, 模运算, 密钥值, 高效率

CLC Number:

TP309.2

Yue LI, Dan TANG, Minjun SUN, Xie WANG, Hongliang CAI, Qiong ZENG. Efficient reversible data hiding scheme based on two-dimensional modulo operations[J]. Journal of Computer Applications, 2024, 44(6): 1880-1888.

李越, 唐聃, 孙敏钧, 王燮, 蔡红亮, 曾琼. 基于二维模运算的高效率可逆信息隐藏方案[J]. 《计算机应用》唯一官方网站, 2024, 44(6): 1880-1888.

Figures/Tables 15

Fig.1 LSB data hiding process

Fig.2 Schematic diagram of enhanced base

Fig. 3 Framework of efficient reversible data hiding scheme based on two-dimensional modulo operations

Fig.4 Function F(g)

Fig. 5 Embedding effects and reversibility test results

Tab.1 Comparative results of PSNR and SSIM

方案	密钥值	PSNR/dB			SSIM
方案	密钥值	$Z 1$	$Z 2$	平均值	$Z 1$	$Z 2$	平均值
本文方案	$m = 5$	56.38	56.41	56.40	0.999 87	0.999 87	0.999 87
	$m = 9$	53.41	53.40	53.41	0.999 75	0.999 75	0.999 75
	$m = 13$	50.97	50.97	50.97	0.999 54	0.999 54	0.999 54
	$m = 17$	49.28	49.30	49.29	0.999 35	0.999 35	0.999 35
文献［23］方案		51.26	49.52	50.39	0.999 61	0.999 42	0.999 52
文献［11］方案		47.70		47.70	0.999 13		0.999 13
文献［24］方案	$a = 2$	60.17	57.16	58.67	0.999 95	0.999 94	0.999 95
	$a = 3$	57.16	54.15	55.66	0.999 90	0.999 92	0.999 91
	$a = 4$	50.17	47.87	49.02	0.999 54	0.999 28	0.999 41
	$a = 5$	45.17	44.24	44.71	0.999 23	0.999 22	0.999 23
文献［22］方案		56.93	50.91	53.92	0.999 94	0.999 78	0.999 86

Tab.1 Comparative results of PSNR and SSIM

方案	密钥值	PSNR/dB			SSIM
方案	密钥值	$Z 1$	$Z 2$	平均值	$Z 1$	$Z 2$	平均值
本文方案	$m = 5$	56.38	56.41	56.40	0.999 87	0.999 87	0.999 87
	$m = 9$	53.41	53.40	53.41	0.999 75	0.999 75	0.999 75
	$m = 13$	50.97	50.97	50.97	0.999 54	0.999 54	0.999 54
	$m = 17$	49.28	49.30	49.29	0.999 35	0.999 35	0.999 35
文献［23］方案		51.26	49.52	50.39	0.999 61	0.999 42	0.999 52
文献［11］方案		47.70		47.70	0.999 13		0.999 13
文献［24］方案	$a = 2$	60.17	57.16	58.67	0.999 95	0.999 94	0.999 95
	$a = 3$	57.16	54.15	55.66	0.999 90	0.999 92	0.999 91
	$a = 4$	50.17	47.87	49.02	0.999 54	0.999 28	0.999 41
	$a = 5$	45.17	44.24	44.71	0.999 23	0.999 22	0.999 23
文献［22］方案		56.93	50.91	53.92	0.999 94	0.999 78	0.999 86

Fig.6 PSNR comparison among different schemes with MER of 0.25 bpp

Fig.7 PSNR comparison among different schemes with different MER

Fig. 8 Comparison of MER among different schemes

Tab.2 MER statistics

密钥值 $m$	MER/bpp	密钥值 $m$	MER/bpp
5	0.99	13	1.73
9	1.48	17	1.97

Tab.2 MER statistics

密钥值 $m$	MER/bpp	密钥值 $m$	MER/bpp
5	0.99	13	1.73
9	1.48	17	1.97

Fig. 9 PDH steganalysis

Fig. 10 Bit-plane steganalysis

Fig. 11 RS steganalysis

Tab.3 Overflow processing range comparison among various schemes

方案	密钥值	溢出处理范围
本文方案	$m = 5$	$[0,1) ⋃ (254, 255]$
	$m = 9$	$[0,2) ⋃ (253, 255]$
	$m = 13$	$[0,3) ⋃ (252, 255]$
	$m = 17$	$[0,4) ⋃ (251, 255]$
文献［23］方案		$[0,5) ⋃ (250, 255]$
文献［11］方案		$∅$
文献［24］方案	$a = 2$	$[0,2) ⋃ (253, 255]$
	$a = 3$	$[0,4) ⋃ (251, 255]$
	$a = 4$	$[0,8) ⋃ (247, 255]$
	$a = 5$	$[0,16) ⋃ (239, 255]$
文献［22］方案		$∅$

Tab.3 Overflow processing range comparison among various schemes

方案	密钥值	溢出处理范围
本文方案	$m = 5$	$[0,1) ⋃ (254, 255]$
	$m = 9$	$[0,2) ⋃ (253, 255]$
	$m = 13$	$[0,3) ⋃ (252, 255]$
	$m = 17$	$[0,4) ⋃ (251, 255]$
文献［23］方案		$[0,5) ⋃ (250, 255]$
文献［11］方案		$∅$
文献［24］方案	$a = 2$	$[0,2) ⋃ (253, 255]$
	$a = 3$	$[0,4) ⋃ (251, 255]$
	$a = 4$	$[0,8) ⋃ (247, 255]$
	$a = 5$	$[0,16) ⋃ (239, 255]$
文献［22］方案		$∅$

Tab. 4 Time complexity comparison among various schemes

方案	时间复杂度
本文方案	$O (n)$
文献［23］方案	$O (n)$
文献［11］方案	$O (n)$
文献［24］方案	$O (n)$
文献［22］方案	$O (n)$

Tab. 4 Time complexity comparison among various schemes

方案	时间复杂度
本文方案	$O (n)$
文献［23］方案	$O (n)$
文献［11］方案	$O (n)$
文献［24］方案	$O (n)$
文献［22］方案	$O (n)$

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Efficient reversible data hiding scheme based on two-dimensional modulo operations

基于二维模运算的高效率可逆信息隐藏方案

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