基于同态加密的密文域可逆信息隐藏技术研究

doi:10.3969/j.issn.1671-1122.2021.04.008

摘要/Abstract

摘要：

为了提高嵌入容量和实现解密与提取信息的可分离性,文章将希尔伯特曲线和同态加密的特性运用到密文域可逆信息隐藏中。首先,图像拥有者对原始图像进行预处理,并在加密后构造密文镜像点。然后,信息隐藏者通过同态加法对目标像素点进行秘密信息嵌入。最后,接收方不仅可以提取秘密信息,还可以无损地恢复原始图像。实验证明,文章方案不但能够实现解密与提取信息的可分离性,而且在保证图像质量的前提下,最大嵌入容量可达到69120 bits。

关键词: 可逆信息隐藏, 同态加密, 希尔伯特曲线, 预测误差扩展

Abstract:

In order to improve the embedding capacity and realize the separability of decryption and information extraction, the algorithm applies the characteristics of Hilbert curve and homomorphic encryption to reversible data hiding in the encrypted domain. First, the image owner preprocesses the original image and constructs the ciphertext mirror point (CMP) after encryption. Then, the data hider embeds the secret information on the target pixel through homomorphic addition. Finally, the receiver can not only extract the secret information, but also restore the original image lossless. Experiments have proved that this scheme can not only realize the separability of decryption and extraction of information, but also the maximum embedding capacity can reach 69120 bits under the guarantee of image quality.

Key words: reversible data hiding, homomorphic encryption, hilbert curve, prediction error expansion

中图分类号:

TP309

林文兵, 张敏情, 周能, 孔咏骏. 基于同态加密的密文域可逆信息隐藏技术研究[J]. 信息网络安全, 2021, 21(4): 73-80.

LIN Wenbing, ZHANG Minqing, ZHOU Neng, KONG Yongjun. Research on Technology of Reversible Data Hiding in Encrypted Domain Based on Homomorphic Encryption[J]. Netinfo Security, 2021, 21(4): 73-80.

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PSNR/dB
图像	n	嵌入容量/bpp
图像	n	0.015	0.029	0.044	0.059	0.073	0.088	0.103
Lena	1	48.40	45.07	42.22	40.10	38.44	37.19	36.21
	2	54.27	51.39	48.54	46.15	45.31	43.87	42.64
	3	54.92	51.98	49.12	47.59	45.64	44.40	43.65
	4	52.11	49.31	47.45	45.21	44.27	42.47	41.16
Hill	1	51.60	45.65	41.36	38.50	36.44	34.98	34.24
	2	52.42	51.34	48.03	45.52	43.18	41.27	39.77
	3	53.18	52.04	50.65	47.44	46.54	45.31	43.56
	4	52.74	51.50	49.09	46.80	45.51	44.85	42.82
Plane	1	42.66	41.04	39.33	37.51	36.08	35.33	34.78
	2	46.65	42.65	41.88	41.01	40.21	39.31	38.16
	3	47.55	45.28	42.50	41.85	41.66	40.88	40.21
	4	47.37	44.63	41.59	40.88	39.22	39.03	38.64
Man	1	43.79	40.92	39.53	38.28	37.29	36.47	35.84
	2	45.73	43.80	41.88	40.08	39.50	38.68	37.54
	3	46.57	44.22	42.68	40.83	40.05	39.25	38.33
	4	46.28	43.03	41.72	39.90	38.95	38.01	37.83

嵌入容量/ bits	PSNR/ dB
嵌入容量/ bits	m = 4	m = 8	m = 16	m = 32
3 840	38.780	54.179	54.922	54.053
7 680	35.901	51.160	51.984	50.774
11 520	33.623	46.931	49.118	46.691
15 360	32.483	45.934	46.587	45.670
19 200	31.648	45.141	45.636	44.997
23 040	30.715	43.991	44.401	43.148
26 880	30.093	43.285	43.651	42.539
30 720	29.569	42.569	42.872	41.869
46 080	27.709	39.654	39.731	38.732
69 120	25.956	36.329	36.899	35.903

文献	性能特征
文献	是否可逆	是否可分离	计算复杂度	信息嵌入保护机制
文献[20]	是	是	O(k³)	多层湿纸编码
文献[22]	是	是	O(k)	Paillier的同态特性
本文算法	是	是	O(k)	Paillier的同态特性

嵌入容量/ bits	PSNR/ dB
嵌入容量/ bits	Lena	Hill	Man	Plane
3840	54.922	53.179	46.566	47.549
7680	51.984	52.038	44.221	45.280
11520	49.118	50.647	42.683	42.502
15360	46.587	47.444	40.833	41.851
19200	45.636	46.538	40.051	41.655
23040	44.401	45.310	39.246	40.883
26880	43.651	43.555	38.326	40.214
30720	42.872	42.558	37.616	39.924
46080	39.731	38.759	35.176	37.536
69120	36.899	35.107	33.114	35.288