无损分享视觉密码研究

doi:10.3969/j.issn.1000-436x.2013.03.021

Abstract

Abstract:

According to the information loss during the secret image sharing process, the lossless sharing visual crypto-graphy was proposed. The optimizations of two parameters were simplified into one parameter. The matrices translation algorithm and the integer programming model were designed. Furthermore, the pixel expansion optimization algorithm was realized. The experimental results show that the algorithm achieves the optimal pixel expansion under lossless shar-ing, and can be used in general access structure.

Key words: isual cryptography, lossless sharing, pixel expansion, optimization algorithm

Bin YU,Zheng-xin FU. Lossless sharing visual cryptography[J]. Journal on Communications, 2013, 34(3): 165-170.

Figures/Tables 5

References 9

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原像素	共享份T₁	共享份T₂	T₁+T₂	概率		显示黑色的概率
原像素	共享份T₁	共享份T₂	T₁+T₂	概率	T₁	T₂	T₁+T₂
	e₁₁=0	e₁₂=0	0	c₀₁=0.5
0	e₂₁=0	e₂₂=1	1	c₀₂=0.0
	e₃₁=1	e₃₂=0	1	c₀₃=0.0	FC₀₁=0.5	FC₀₂=0.5	QC₀₁=0.5
	e₄₁=1	e₄₂=1	1	c₀₄=0.5
	e₁₁=0	e₁₂=0	0	c₁₁=0.0
1	e₂₁=0	e₂₂=1	1	c₁₂=0.5
	e₃₁=1	e₃₂=0	1	c₁₃=0.5	FC₁₁=0.5	FC₁₂=0.5	QC₁₁=1.0
	e₄₁=1	e₄₂=1	1	c₁₄=0.0

k					n
k	2	3	4	5	6	7	8	9	10
2	2	3	4	4	4	5	5	5	5
3		4	6	8	10	12	14	16	18
4			8	15	24	35	48	63	80
5				16	30	48	70	96	126
6					32	70	128	210	320
7						64	140	256	420
8							128	315	640
9								256	630
10									512

方案	通用存取结构	像素扩展度	相对差	信息损失	恢复计算复杂度
Droste方案^[3]	不适用	m₁	1/m₁	无	O(1)
Ateniese方案^[4]	适用	m₂	1/m₂	无	O(1)
Hsu方案^[9]	适用	1	QC1h?QC_0h	有	O(1)
本文方案	适用	m₀	1	无	O(1)

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Lossless sharing visual cryptography

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Figures/Tables 5

References 9

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k					n
k	2	3	4	5	6	7	8	9	10
2	2	3	4	4	4	5	5	5	5
3		4	6	8	10	12	14	16	18
4			8	15	24	35	48	63	80
5				16	30	48	70	96	126
6					32	70	128	210	320
7						64	140	256	420
8							128	315	640
9								256	630
10									512

k					n
k	2	3	4	5	6	7	8	9	10
2	2	3	4	4	4	5	5	5	5
3		4	6	8	10	12	14	16	18
4			8	15	24	35	48	63	80
5				16	30	48	70	96	126
6					32	70	128	210	320
7						64	140	256	420
8							128	315	640
9								256	630
10									512

k					n
k	2	3	4	5	6	7	8	9	10
2	2	3	4	4	4	5	5	5	5
3		4	6	8	10	12	14	16	18
4			8	15	24	35	48	63	80
5				16	30	48	70	96	126
6					32	70	128	210	320
7						64	140	256	420
8							128	315	640
9								256	630
10									512