Reversible data hiding algorithm in encrypted domain based on secret image sharing

doi:10.11772/j.issn.1001-9081.2021050823

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (5): 1480-1489.DOI: 10.11772/j.issn.1001-9081.2021050823

Special Issue: 网络空间安全

• Cyber security • Previous Articles Next Articles

Reversible data hiding algorithm in encrypted domain based on secret image sharing

Zexi WANG¹^,², Minqing ZHANG¹^,²(), Yan KE¹^,², Yongjun KONG¹^,²

^1.Key Laboratory of PAP for Cryptology and Information Security （Engineering University of PAP），Xi’an Shaanxi 710086，China
^2.College of Cryptographic Engineering，Engineering University of PAP，Xi’an Shaanxi 710086，China

Received:2021-05-19 Revised:2021-09-22 Accepted:2021-10-14 Online:2022-03-08 Published:2022-05-10
Contact: Minqing ZHANG
About author:WANG Zexi， born in 1997，M. S. candidate. His research interestsinclude information security，data hiding.
ZHANG Minqing， Minqing，born in 1967，Ph. D.，professor. Her research interests include cryptology，data hiding.
KE Yan， born in 1991，Ph. D. His research interests includeinformation security，cryptology，data hiding.
KONG Yongjun， born in 1990，Ph. D. candidate. His researchinterests include information security，data hiding.
Supported by:
National Natural Science Foundation of China(61872384)

基于图像秘密共享的密文域可逆信息隐藏算法

王泽曦¹^,², 张敏情¹^,²(), 柯彦¹^,², 孔咏骏¹^,²

^1.网络与信息安全武警部队重点实验室（武警工程大学），西安 710086
^2.武警工程大学密码工程学院，西安 710086

通讯作者: 张敏情
作者简介:王泽曦（1997—），男，江苏徐州人，硕士研究生，主要研究方向：信息安全、信息隐藏
张敏情（1967—），女，陕西西安人，教授，博士，主要研究方向：密码学、信息隐藏 api_zmq@126.com
柯彦（1991—），男，河南南阳人，博士，主要研究方向：信息安全、密码学、信息隐藏
孔咏骏（1990—），男，江苏江阴人，博士研究生，主要研究方向：信息安全、信息隐藏。
基金资助:
国家自然科学基金资助项目(61872384)

Abstract

Abstract:

The current reversible data hiding algorithms in encrypted domain have the problems that the ciphertext images carrying secret have poor fault tolerance and disaster resistance after embedding secret data， once attacked or damaged， the original image cannot be reconstructed and the secret data cannot be extracted. In order to solve the problems， a new reversible data hiding algorithm in encrypted domain based on secret image sharing was proposed， and its application scenarios in cloud environment were analyzed. Firstly， the encrypted image was divided into n different ciphertext images carrying secret with the same size. Secondly， in the process of segmentation， the random quantities in Lagrange interpolation polynomial were taken as redundant information， and the mapping relationship between secret data and each polynomial coefficient was established. Finally， the reversible embedding of the secret data was realized by modifying the built-in parameters of the encryption process. When k ciphertext images carrying secret were collected， the original image was able to be fully recovered and the secret data was able to be extracted. Experimental results show that， the proposed algorithm has the advantages of low computational complexity， large embedding capacity and complete reversibility. In the （3，4） threshold scheme， the maximum embedding rate of the proposed algorithm is 4 bit per pixel （bpp）， and in the （4，4） threshold scheme， the maximum embedding rate of the proposed algorithm is 6 bpp. The proposed algorithm gives full play to the disaster recovery characteristic of secret sharing scheme. Without reducing the security of secret sharing， the proposed algorithm enhances the fault tolerance and disaster resistance of ciphertext images carrying secret， improves the embedding capacity of algorithm and the disaster recovery ability in the application scenario of cloud environment， and ensures the security of carrier image and secret data.

Key words: information security, secret image sharing, reversible data hiding, data disaster recovery, encrypted domain

摘要：

针对当前密文域可逆信息隐藏算法嵌入秘密信息后的携密密文图像的容错性与抗灾性不强，一旦遭受攻击或损坏就无法重构原始图像与提取秘密信息的问题，提出了一种基于图像秘密共享的密文域可逆信息隐藏算法，并分析了该算法在云环境下的应用场景。首先，将加密图像分割成大小相同的n份不同携密密文图像。然后，在分割的过程中将拉格朗日插值多项式中的随机量作为冗余信息，并建立秘密信息与多项式各项系数间的映射关系。最后，通过修改加密过程的内置参数，实现秘密信息的可逆嵌入。当收集k份携密密文图像时，可无损地恢复原始图像与提取秘密信息。实验结果表明，所提算法具有计算复杂度低、嵌入容量大和完全可逆等特点。在（3，4）门限方案中，所提算法的最大嵌入率可达4 bpp；在（4，4）门限方案中，其最大嵌入率可达6 bpp。所提算法充分发挥了秘密共享方案的容灾特性，在不降低秘密共享安全性的基础上，增强了携密密文图像的容错性与抗灾性，提高了算法的嵌入容量与云环境应用场景下的容灾能力，保证了载体图像与秘密信息的安全。

关键词: 信息安全, 图像秘密共享, 可逆信息隐藏, 数据容灾, 密文域

CLC Number:

TP309.7

Zexi WANG, Minqing ZHANG, Yan KE, Yongjun KONG. Reversible data hiding algorithm in encrypted domain based on secret image sharing[J]. Journal of Computer Applications, 2022, 42(5): 1480-1489.

王泽曦, 张敏情, 柯彦, 孔咏骏. 基于图像秘密共享的密文域可逆信息隐藏算法[J]. 《计算机应用》唯一官方网站, 2022, 42(5): 1480-1489.

Figures/Tables 13

Fig. 1 Framework of SIS-RDHED

Tab. 1 Variables and their descriptions

变量	说明
$I$	原始图像
$K e$	图像加密密钥
$K d$	数据隐藏密钥
$I e$	密文图像
$(p i, x i)$	第i个参与者属性标签
$(X i, Y i)$	密文图像的第i块像素对
$F i (x j)$	第j个参与者的第i块携密密文
$(X' i j, Y' i j)$	第j个参与者的第i块携密密文像素对
$I e m j$	第j个参与者携密密文图像

Tab. 1 Variables and their descriptions

变量	说明
$I$	原始图像
$K e$	图像加密密钥
$K d$	数据隐藏密钥
$I e$	密文图像
$(p i, x i)$	第i个参与者属性标签
$(X i, Y i)$	密文图像的第i块像素对
$F i (x j)$	第j个参与者的第i块携密密文
$(X' i j, Y' i j)$	第j个参与者的第i块携密密文像素对
$I e m j$	第j个参与者携密密文图像

Fig. 2 Schematic diagram of pixel pair merging

Fig. 3 Flow chart of SIS-RDHED based on Shamir （3，4） threshold

Fig. 4 Application framework of SIS-RDHED based on Shamir （3，4） threshold

Fig. 5 Test images

Tab. 2 Maximum embedding rates under different threshold parameters

$k$ 值	$n = 2$	$n = 3$	$n = 4$	$n = 5$
$2$	4.00	2.67	2.00	1.60
$3$	—	5.33	4.00	3.20
$4$	—	—	6.00	4.80
$5$	—	—	—	6.40

Tab. 2 Maximum embedding rates under different threshold parameters

$k$ 值	$n = 2$	$n = 3$	$n = 4$	$n = 5$
$2$	4.00	2.67	2.00	1.60
$3$	—	5.33	4.00	3.20
$4$	—	—	6.00	4.80
$5$	—	—	—	6.40

Fig. 6 Maximum embedding rate comparison of different algorithms for standard test images

Fig. 7 Comparison of Lena image rate distortion curve

Tab. 3 Time complexities of different encryption methods

算法	加密方式	时间复杂度
算法	加密方式	信息嵌入	信息提取	图像恢复
文献［3］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［6］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［10］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［11］算法	LWE加密	$O (N 2)$	$O (1)$	$O (N 2)$
文献［14］算法	Paillier加密	$O (N 3)$	$O (1)$	$O (N 3)$
文献［15］算法	Paillier加密	$O (N 3)$	$O (N 3)$	$O (N 3)$
文献［16］算法	秘密共享	$O (N)$	$O (1)$	$O (N l o g 2 N)$
文献［18］算法	秘密共享	$O (N)$	$O (N 2)$	$O (N l o g 2 N)$
文献［19］算法	秘密共享	$O (N)$	$O (1)$	$O (N l o g 2 N)$
文献［20］算法	秘密共享	$O (N)$	$O (N 2)$	$O (N l o g 2 N)$
本文算法	秘密共享	$O (N)$	$O (N 2 l o g 2 N)$	$O (N l o g 2 N)$

Tab. 3 Time complexities of different encryption methods

算法	加密方式	时间复杂度
算法	加密方式	信息嵌入	信息提取	图像恢复
文献［3］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［6］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［10］算法	流加密	$O (1)$	$O (1)$	$O (1)$
文献［11］算法	LWE加密	$O (N 2)$	$O (1)$	$O (N 2)$
文献［14］算法	Paillier加密	$O (N 3)$	$O (1)$	$O (N 3)$
文献［15］算法	Paillier加密	$O (N 3)$	$O (N 3)$	$O (N 3)$
文献［16］算法	秘密共享	$O (N)$	$O (1)$	$O (N l o g 2 N)$
文献［18］算法	秘密共享	$O (N)$	$O (N 2)$	$O (N l o g 2 N)$
文献［19］算法	秘密共享	$O (N)$	$O (1)$	$O (N l o g 2 N)$
文献［20］算法	秘密共享	$O (N)$	$O (N 2)$	$O (N l o g 2 N)$
本文算法	秘密共享	$O (N)$	$O (N 2 l o g 2 N)$	$O (N l o g 2 N)$

Fig. 8 Secret segmentation， reconstruction and and restoration of Lena image by SIS-RDHED based on Shamir（3，4） threshold

Fig. 9 Lena image reconstruction experimental histograms by SIS-RDHED based on Shamir（3，4） threshold

Fig. 10 Secret data extraction error diagrams of different number of ciphertexts carrying secret

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Reversible data hiding algorithm in encrypted domain based on secret image sharing

基于图像秘密共享的密文域可逆信息隐藏算法

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