基于多元优化的批量图像隐写载体选择方法

王仰光; 姚远志; 俞能海

doi:10.13700/j.bh.1001-5965.2023.0380

基于多元优化的批量图像隐写载体选择方法

doi: 10.13700/j.bh.1001-5965.2023.0380

1.
中国科学技术大学网络空间安全学院，合肥 230027
2.
合肥工业大学计算机与信息学院，合肥 230601

基金项目:

国家重点研发计划基金(2018YFB0804102)；国家自然科学基金(61802357)；中央高校基本科研业务费专项资金(WK3480000009)

详细信息

通讯作者:
E-mail：yaoyz@hfut.edu.cn

中图分类号: TP309.2
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出版历程
- 收稿日期: 2023-06-16
- 录用日期: 2023-09-02
- 网络出版日期: 2023-11-08
- 整期出版日期: 2025-07-31

Cover selection method for batch image steganography based on multivariate optimization

1.
School of Cyber Science and Technology，University of Science and Technology of China，Hefei 230027，China
2.
School of Computer Science and Information Engineering，Hefei University of Technology，Hefei 230601，China

Funds:

National Key Research and Development Program of China (2018YFB0804102); National Natural Science Foundation of China (61802357); The Fundamental Research Funds for the Central Universities (WK3480000009)

More Information

Corresponding author: E-mail：yaoyz@hfut.edu.cn

摘要

摘要:
批量图像隐写通过载体选择在多张载体图像中嵌入秘密信息，为社交网络中的隐蔽通信提供有效的途径。与传统的图像隐写相比，批量图像隐写的关键科学问题是在保证抗检测性能的情况下设计有效的载体选择方法。基于此，提出一种基于多元优化的批量图像隐写载体选择方法，通过联合分析嵌入失真、图像相关性、嵌入容量三元因素，将批量图像隐写中的载体选择建模为多元优化问题。同时，针对社交网络可能对载密图像进行压缩的情况，在批量图像隐写载体选择时设计了秘密信息分片与重组策略，提升了批量图像隐写的鲁棒性。充分的实验结果表明：所提方法在抗检测性能、嵌入容量和鲁棒性上取得了令人满意的效果，为基于社交网络的隐蔽通信提供了技术支撑。
- 多元优化 /
- 批量图像隐写 /
- 载体选择 /
- 抗检测性 /
- 鲁棒性
Abstract:
Batch image steganography provides an effective means for covert communication on social networks by embedding secret messages into multiple cover images through cover selection. Compared with traditional image steganography, a key challenge of batch image steganography lies in designing an effective cover selection method while ensuring good undetectability performance. In this paper, a multivariate optimization-based cover selection method for batch image steganography was proposed. By jointly analyzing embedding distortion, image correlation, and embedding capacity, this method modelled the cover selection for batch image steganography as a multivariate optimization problem. Additionally, to enhance the batch image steganography robustness against the possible compression of images after steganography by social networks, a secret message fragmentation and reassembly strategy was designed. Experimental results demonstrate that the proposed method for batch image steganography achieves satisfactory performance in undetectability, embedding capacity, and robustness, providing technical support for covert communication on social networks.
- multivariate optimization /
- batch image steganography /
- cover selection /
- undetectability /
- robustness

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图 1 集成分类器流程示意图

Figure 1. Flowchart of ensemble classifier process

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图 2 基于多元优化的批量图像隐写载体选择方法

Figure 2. Cover selection method for batch image steganography based on multivariate optimization

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图 3 10000张JPEG图像的嵌入失真分布

Figure 3. Embedding distortion for 10000 JPEG images

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图 4 空域图像和JPEG图像隐写后的SVD变化幅度展示

Figure 4. Change in SVD of spatial domain and JPEG images after steganography

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图 5 10000张JPEG图像的嵌入容量分布

Figure 5. Embedding capacity for 10000 JPEG images

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图 6 不同权值下的错误检测概率分布

Figure 6. Probability distributions of false detections for different weights

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表 1 单因素下的抗检测性分析

Table 1. Undetectability analysis under single-factor conditions

方法	P_E
方法	k=1000	k=2000	k=3000	k=4000	k=5000
Rand	0.2564	0.2266	0.2122	0.2012	0.1974
Dis	0.3410	0.3065	0.2872	0.2679	0.2520
IS	0.3442	0.3049	0.2786	0.2690	0.2520
EC	0.3522	0.3163	0.2900	0.2729	0.2553

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表 2 不同条件下的错误检测概率（QF=60）

Table 2. Probability of false detections under different conditions (QF = 60)

嵌入率	特征集	方法	P_E
嵌入率	特征集	方法	k=1000	k=2000	k=3000	k=4000	k=5000
0.4	cfstar	Rand	0.3058	0.2835	0.2732	0.2600	0.2600
		Liao^[13]	0.3696	0.3311	0.3095	0.2954	0.2801
		Wang^[14]	0.3760	0.3478	0.3239	0.3049	0.2989
		本文方法	0.3802	0.3482	0.3285	0.3053	0.2966
	ccJRM	Rand	0.2900	0.2686	0.2585	0.2490	0.2488
		Liao^[13]	0.3508	0.3253	0.3009	0.2865	0.2677
		Wang^[14]	0.3598	0.3360	0.3138	0.2985	0.2882
		本文方法	0.3630	0.3381	0.3168	0.2989	0.2895
0.5	cfstar	Rand	0.2502	0.2203	0.2023	0.1905	0.1885
		Liao^[13]	0.3115	0.2630	0.2388	0.2241	0.2085
		Wang^[14]	0.3167	0.2803	0.2540	0.2359	0.2244
		本文方法	0.3221	0.2869	0.2557	0.2353	0.2236
	ccJRM	Rand	0.2298	0.2022	0.1887	0.1747	0.1725
		Liao^[13]	0.2840	0.2485	0.2300	0.2108	0.1913
		Wang^[14]	0.2936	0.2640	0.2406	0.2213	0.2022
		本文方法	0.2990	0.2675	0.2430	0.2199	0.2055

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表 3 不同条件下的错误检测概率（QF=75）

Table 3. Probability of false detections under different conditions (QF = 75)

嵌入率	特征集	方法	P_E
嵌入率	特征集	方法	k=1000	k=2000	k=3000	k=4000	k=5000
0.4	cfstar	Rand	0.3282	0.3067	0.2971	0.2866	0.2834
		Liao^[13]	0.4203	0.3879	0.3665	0.3566	0.3373
		Wang^[14]	0.4307	0.3948	0.3781	0.3632	0.3515
		本文方法	0.4275	0.3975	0.3847	0.3648	0.3525
	ccJRM	Rand	0.3128	0.2875	0.2813	0.2713	0.2689
		Liao^[13]	0.4002	0.3764	0.3542	0.3364	0.3234
		Wang^[14]	0.4036	0.3831	0.3639	0.3463	0.3358
		本文方法	0.4071	0.3846	0.3655	0.3512	0.3353
0.5	cfstar	Rand	0.2800	0.2521	0.2358	0.2220	0.2159
		Liao^[13]	0.3800	0.3379	0.3127	0.2896	0.2775
		Wang^[14]	0.3847	0.3474	0.3244	0.3031	0.2826
		本文方法	0.3943	0.3485	0.3285	0.3032	0.2890
	ccJRM	Rand	0.2564	0.2266	0.2122	0.2012	0.1974
		Liao^[13]	0.3410	0.3065	0.2872	0.2679	0.2520
		Wang^[14]	0.3510	0.3174	0.2919	0.2754	0.2660
		本文方法	0.3533	0.3203	0.2933	0.2777	0.2661

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表 4 不同条件下的错误检测概率（QF=90）

Table 4. Probability of false detections under different conditions (QF = 90)

嵌入率	特征集	方法	P_E
嵌入率	特征集	方法	k=1000	k=2000	k=3000	k=4000	k=5000
0.4	cfstar	Rand	0.3249	0.3132	0.3098	0.3016	0.2994
		Liao^[13]	0.4013	0.3938	0.3847	0.3810	0.3741
		Wang^[14]	0.4134	0.4060	0.3963	0.3827	0.3700
		本文方法	0.4213	0.4105	0.4047	0.3913	0.3784
	ccJRM	Rand	0.3168	0.2983	0.2919	0.2871	0.2846
		Liao^[13]	0.4009	0.3917	0.3778	0.3702	0.3612
		Wang^[14]	0.4146	0.3956	0.3841	0.3769	0.3620
		本文方法	0.4195	0.4004	0.3865	0.3780	0.3639
0.5	cfstar	Rand	0.2804	0.2599	0.2521	0.2407	0.2373
		Liao^[13]	0.3660	0.3576	0.3406	0.3320	0.3175
		Wang^[14]	0.3758	0.3655	0.3529	0.3326	0.3165
		本文方法	0.3824	0.3660	0.3551	0.3355	0.3210
	ccJRM	Rand	0.2671	0.2469	0.2370	0.2290	0.2277
		Liao^[13]	0.3648	0.3467	0.3275	0.3182	0.3056
		Wang^[14]	0.3662	0.3535	0.3396	0.3255	0.3053
		本文方法	0.3735	0.3568	0.3396	0.3285	0.3159

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表 5 Wang等的方法^[14]和本文方法嵌入容量的对比

Table 5. Comparison of embedding capacity between Wang et al.’s method^[14] and proposed method

QF	方法	嵌入容量/bit
QF	方法	k=1000	k=2000	k=3000	k=4000	k=5000
60	Wang^[14]	69254497	122784610	168444548	207175886	235671773
60	本文方法	69264640	122781191	168444548	207293584	235880610
75	Wang^[14]	88527118	157237348	216089517	267350520	309605320
75	本文方法	88540196	157251458	216143376	267350520	309758006
90	Wang^[14]	121091974	221886393	310810927	389066645	461304521
90	本文方法	121203657	222234100	311097664	389620084	462032474

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表 6 不同平均数据丢失率下的秘密信息恢复正确率

Table 6. Accuracy of secret information recovery under different average data loss rates %

数据冗余率	平均数据丢失率	恢复正确率
数据冗余率	平均数据丢失率	嵌入率为0.15	嵌入率为0.25
44.44	33.49	72	65
44.44	51.72	0	0
83.87	81.27	56	43
83.87	91.24	0	0

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表 7 4种载体选择方法的时间复杂度

Table 7. Time complexity of four cover selection methods s

方法	时间复杂度
Rand	0.0015
Liao等^[13]	6244.25
Wang等^[14]	10687.36
本文方法	10836.71

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