Reversible data hiding in encrypted image based on multi-objective optimization

doi:10.11772/j.issn.1001-9081.2021061495

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (6): 1716-1723.DOI: 10.11772/j.issn.1001-9081.2021061495

Special Issue: 2021年全国开放式分布与并行计算学术年会(DPCS 2021)论文

• National Open Distributed and Parallel Computing Conference 2021 (DPCS 2021） • Previous Articles Next Articles

Reversible data hiding in encrypted image based on multi-objective optimization

Xiangyu ZHANG¹, Yang YANG¹(), Guohui FENG², Chuan QIN¹

^1.School of Optical?Electrical and Computer Engineering，University of Shanghai for Science and Technology，Shanghai 200093，China
^2.Southeast Digital Economic Development Institute，Quzhou Zhejiang 324000，China

Received:2021-08-23 Revised:2021-11-07 Accepted:2021-11-17 Online:2022-01-10 Published:2022-06-10
Contact: Yang YANG
About author:ZHANG Xiangyu， born in 1997， M. S. candidate. His research interests include reversible data hiding.
FENG Guohui， born in 1989， M. S. Her research interests include image processing.
QIN Chuan， born in 1980， Ph. D.， professor. His research interests include image processing， multimedia security.
Supported by:
Natural Science Foundation of Shanghai(21ZR1444600)

基于多目标优化的加密图像可逆信息隐藏

张翔宇¹, 杨阳¹(), 冯国徽², 秦川¹

^1.上海理工大学光电信息与计算机工程学院，上海 200093
^2.东南数字经济发展研究院，浙江衢州 324000

通讯作者: 杨阳
作者简介:张翔宇（1997—），男，浙江温州人，硕士研究生，主要研究方向：可逆信息隐藏
冯国徽（1989—），女，甘肃兰州人，硕士，主要研究方向：图像处理
秦川（1980—），男，安徽芜湖人，教授，博士，主要研究方向：图像处理、多媒体安全。
基金资助:
上海市自然科学基金资助项目(21ZR1444600)

Abstract

Abstract:

Focusing on the issues that the Reserving Room Before Encryption （RRBE） embedding algorithm requires a series of pre-processing work and Vacating Room After Encryption （VRAE） embedding algorithm has less embedding space， an algorithm of reversible data hiding in encrypted image based on multi-objective optimization was proposed to improve the embedding rate as well as reducing the algorithm process and workload. In this algorithm， two representative algorithms in RRBE and VRAE were combined and used in the same carrier， and performance evaluation indicators such as the amount of information embedded， distortion of direct decryption of image， extraction error rate， and computational complexity were formulated as the optimization sub-objectives. Then， the efficiency coefficient method was used to establish a model to solve the relative optimal solution of the application ratio of the two algorithms. Experimental results show that the proposed algorithm reduces the computational complexity of using RRBE algorithm alone， enables image processing users to flexibly allocate optimization objectives according to different needs in actual application scenarios， and at the same time obtains better image quality and a satisfactory amount of information embedding.

Key words: reversible data hiding, image encryption, multi-objective optimization, image quality, embedding rate

摘要：

针对加密前预留空间（RRBE）嵌入算法需要进行一系列的预处理工作，以及加密后腾出空间（VRAE）嵌入算法嵌入空间较小的缺点，为了在提高嵌入率的同时缩减算法流程和减少工作量，提出一种基于多目标优化的加密图像可逆信息隐藏算法。该算法将RRBE与VRAE中两个具有代表性的算法在同一载体中结合使用，并以信息嵌入量、直接解密图像失真、提取错误率、计算复杂度等性能评价指标作为优化子目标，再利用功效系数法建立模型求解出两种算法应用比例的相对最优解。实验结果表明，所提算法不仅能够降低单独使用RRBE算法的计算复杂度，还能使图像处理用户够根据实际应用场景中不同的需求灵活地分配优化目标，同时也能获得较好的图像质量和令人满意的信息嵌入量。

关键词: 可逆信息隐藏, 图像加密, 多目标优化, 图像质量, 嵌入率

CLC Number:

TP391

Xiangyu ZHANG, Yang YANG, Guohui FENG, Chuan QIN. Reversible data hiding in encrypted image based on multi-objective optimization[J]. Journal of Computer Applications, 2022, 42(6): 1716-1723.

张翔宇, 杨阳, 冯国徽, 秦川. 基于多目标优化的加密图像可逆信息隐藏[J]. 《计算机应用》唯一官方网站, 2022, 42(6): 1716-1723.

Figures/Tables 11

Fig. 1 System model of proposed algorithm

Tab. 1 Block classification and marking conditions

条件	块类型	块描述	块标识位
$m > n a$	Bad	不能嵌入信息	00
$m = n 0 = 0$	G-I	所有的像素都为1	11
$m = n 1 = 0$	G-Ⅱ	所有的像素都为0	10
$1 ≤ m ≤ n a, n 0 < n 1$	G-Ⅲ	大多数像素为1	011
$1 ≤ m ≤ n a, n 1 < n 0$	G-Ⅳ	大多数像素为0	010

Tab. 1 Block classification and marking conditions

条件	块类型	块描述	块标识位
$m > n a$	Bad	不能嵌入信息	00
$m = n 0 = 0$	G-I	所有的像素都为1	11
$m = n 1 = 0$	G-Ⅱ	所有的像素都为0	10
$1 ≤ m ≤ n a, n 0 < n 1$	G-Ⅲ	大多数像素为1	011
$1 ≤ m ≤ n a, n 1 < n 0$	G-Ⅳ	大多数像素为0	010

Fig. 2 Images in different stages

Fig. 3 Six standard test images

Tab. 2 Experimental results of Lena under different X （S=16）

X	直接解密图像 PSNR/dB	嵌入率/bpp	恢复图像 PSNR/dB	$d 1 (X)$	$d 2 (X)$	$d 3 (X)$	$d 4 (X)$	评价函数 $F (X)$
1	37.93	0.004 9	+∞	0.000 98	0.000 98	0.000 98	0.999 000	0.005 5
204	38.68	0.350 0	+∞	0.199 20	0.199 20	0.926 40	0.800 800	0.418 2
408	39.63	0.690 0	+∞	0.389 40	0.398 40	0.985 50	0.601 600	0.553 9
684	41.32	1.160 0	+∞	0.668 00	0.668 00	0.995 20	0.332 000	0.619 7
816	42.43	1.380 0	+∞	0.796 90	0.796 90	0.997 50	0.203 100	0.598 9
1 023	45.26	1.710 0	+∞	0.999 00	0.999 00	1.000 00	0.000 977	0.176 7

Tab. 2 Experimental results of Lena under different X （S=16）

X	直接解密图像 PSNR/dB	嵌入率/bpp	恢复图像 PSNR/dB	$d 1 (X)$	$d 2 (X)$	$d 3 (X)$	$d 4 (X)$	评价函数 $F (X)$
1	37.93	0.004 9	+∞	0.000 98	0.000 98	0.000 98	0.999 000	0.005 5
204	38.68	0.350 0	+∞	0.199 20	0.199 20	0.926 40	0.800 800	0.418 2
408	39.63	0.690 0	+∞	0.389 40	0.398 40	0.985 50	0.601 600	0.553 9
684	41.32	1.160 0	+∞	0.668 00	0.668 00	0.995 20	0.332 000	0.619 7
816	42.43	1.380 0	+∞	0.796 90	0.796 90	0.997 50	0.203 100	0.598 9
1 023	45.26	1.710 0	+∞	0.999 00	0.999 00	1.000 00	0.000 977	0.176 7

Tab. 3 Experimental data corresponding to relative optimal solution of Lena under different S

S	X	嵌入率/bpp	直接解密图像 PSNR/dB	恢复图像 PSNR/dB	提取错误率	执行时长/s	$d 1 (X)$	$d 2 (X)$	$d 3 (X)$	$d 4 (X)$	评价函数 $F (X)$
4	11 264	1.64	39.71	48.56	0.15	7.27	0.687 5	0.687 5	0.937 3	0.312 5	0.610 0
8	2 755	1.51	40.07	59.08	0.01	5.88	0.672 6	0.672 6	0.981 6	0.327 4	0.617 5
12	1 218	1.28	41.42	64.70	0.00	5.05	0.669 1	0.669 1	0.991 5	0.330 9	0.619 1
16	684	1.16	41.37	+∞	0.00	6.50	0.668 0	0.668 0	0.995 2	0.322 0	0.619 7
20	437	1.02	42.03	+∞	0.00	5.30	0.668 0	0.668 0	0.996 9	0.333 2	0.619 9
24	303	0.89	42.16	+∞	0.00	5.14	0.665 8	0.665 8	0.997 8	0.334 2	0.620 1
28	223	0.81	42.37	+∞	0.00	5.18	0.666 9	0.666 9	0.998 4	0.333 1	0.620 2
32	170	0.70	42.21	+∞	0.00	5.31	0.664 1	0.664 1	0.998 8	0.335 9	0.620 2
36	130	0.63	42.43	+∞	0.00	5.08	0.642 7	0.642 7	0.998 9	0.357 3	0.619 6

Tab. 3 Experimental data corresponding to relative optimal solution of Lena under different S

S	X	嵌入率/bpp	直接解密图像 PSNR/dB	恢复图像 PSNR/dB	提取错误率	执行时长/s	$d 1 (X)$	$d 2 (X)$	$d 3 (X)$	$d 4 (X)$	评价函数 $F (X)$
4	11 264	1.64	39.71	48.56	0.15	7.27	0.687 5	0.687 5	0.937 3	0.312 5	0.610 0
8	2 755	1.51	40.07	59.08	0.01	5.88	0.672 6	0.672 6	0.981 6	0.327 4	0.617 5
12	1 218	1.28	41.42	64.70	0.00	5.05	0.669 1	0.669 1	0.991 5	0.330 9	0.619 1
16	684	1.16	41.37	+∞	0.00	6.50	0.668 0	0.668 0	0.995 2	0.322 0	0.619 7
20	437	1.02	42.03	+∞	0.00	5.30	0.668 0	0.668 0	0.996 9	0.333 2	0.619 9
24	303	0.89	42.16	+∞	0.00	5.14	0.665 8	0.665 8	0.997 8	0.334 2	0.620 1
28	223	0.81	42.37	+∞	0.00	5.18	0.666 9	0.666 9	0.998 4	0.333 1	0.620 2
32	170	0.70	42.21	+∞	0.00	5.31	0.664 1	0.664 1	0.998 8	0.335 9	0.620 2
36	130	0.63	42.43	+∞	0.00	5.08	0.642 7	0.642 7	0.998 9	0.357 3	0.619 6

Tab. 4 Comparison of entropy values before and after images encryption

图像	加密前的熵	加密后的熵
Airplane	6.677 6	7.991 4
Baboon	7.357 9	7.991 6
Barbara	7.632 1	7.991 4
Boat	7.123 8	7.991 3
Lena	7.445 6	7.991 7
Peppers	7.571 5	7.991 5

Tab. 5 Comparison of image embedding rate under different S

S	算法	Lena	Peppers	Barbara	Baboon	UCID
4	本文算法	1.64	1.60	1.21	0.73	1.27
	VRAE算法	0.06	0.06	0.06	0.06	0.06
	RRBE算法	2.35	2.30	1.73	1.02	1.83
8	本文算法	1.51	1.48	1.13	0.67	1.20
	VRAE算法	0.02	0.02	0.02	0.02	0.02
	RRBE算法	2.23	2.16	1.65	0.99	1.77
16	本文算法	1.16	1.09	0.83	0.54	1.00
	VRAE算法	0.004	0.004	0.004	0.004	0.004
	RRBE算法	1.71	1.59	1.21	0.80	1.49
32	本文算法	0.70	0.59	0.46	0.35	0.78
	VRAE算法	0.001	0.001	0.001	0.001	0.001
	RRBE算法	1.08	0.94	0.66	0.54	1.13

Tab. 6 Comparison of DPSNR of directly decrypted image and RPSNR of restored image under different S

S	算法	Lena		Peppers		Barbara		Baboon
S	算法	D_PSNR	R_PSNR	D_PSNR	R_PSNR	D_PSNR	R_PSNR	D_PSNR	R_PSNR
4	本文算法	39.71	48.56	39.90	47.01	41.48	46.49	39.69	42.51
	VRAE算法	37.93	43.49	37.94	41.93	37.93	41.50	37.94	39.64
	RRBE算法	40.88	+∞	41.21	+∞	45.18	+∞	50.68	+∞
8	本文算法	40.07	59.08	40.26	52.34	41.44	50.16	42.54	47.39
	VRAE算法	37.93	54.30	37.95	51.93	37.93	45.51	37.92	42.95
	RRBE算法	41.72	+∞	42.39	+∞	45.55	+∞	51.17	+∞
16	本文算法	41.37	+∞	41.48	+∞	41.96	54.75	42.38	51.97
	VRAE算法	37.93	+∞	37.94	+∞	37.94	49.84	37.93	47.09
	RRBE算法	45.28	+∞	45.82	+∞	48.51	+∞	52.06	+∞
32	本文算法	42.21	+∞	42.44	+∞	42.44	+∞	42.47	+∞
	VRAE算法	37.93	+∞	37.95	+∞	37.94	55.78	37.92	55.99
	RRBE算法	49.92	+∞	51.40	+∞	52.93	+∞	53.81	+∞

Tab. 7 Comparison of DPSNR and RPSNRof images in UCID image library

S	算法	D_PSNR	R_PSNR	S	算法	D_PSNR	R_PSNR
4	本文算法	40.88	45.61	16	本文算法	41.21	+∞
	VRAE算法	25.78	25.77		VRAE算法	25.78	25.77
	RRBE算法	44.55	+∞		RRBE算法	47.02	+∞
8	本文算法	40.82	48.67	32	本文算法	41.66	+∞
	VRAE算法	25.78	25.77		VRAE算法	25.78	25.77
	RRBE算法	44.91	+∞		RRBE算法	49.86	+∞

Tab. 8 Running time comparison when S=16

算法	Lena	Peppers	Barbara	Baboon	UCID
本文算法	6.50	6.05	5.51	5.30	4.32
VRAE算法	5.01	5.16	4.73	5.39	3.93
RRBE算法	13.44	12.92	12.86	12.68	7.86

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Reversible data hiding in encrypted image based on multi-objective optimization

基于多目标优化的加密图像可逆信息隐藏

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