基于区域递增式彩色视觉密码的栅格地图多级分存算法研究

doi:10.11959/j.issn.1000-436x.2019193

通信学报 ›› 2019, Vol. 40 ›› Issue (9): 24-32.doi: 10.11959/j.issn.1000-436x.2019193

基于区域递增式彩色视觉密码的栅格地图多级分存算法研究

房礼国,付正欣,胡浩,沈刚,郁滨

信息工程大学，河南郑州 450001

修回日期:2019-03-28 出版日期:2019-09-25 发布日期:2019-09-28
作者简介:房礼国（1981- ），男，江苏盐城人，博士，信息工程大学副教授，主要研究方向为视觉密码和网络安全。|付正欣（1986- ），男，山东荷泽人，博士，信息工程大学讲师，主要研究方向为视觉密码和网络安全。|胡浩（1989- ），男，安徽池州人，博士，信息工程大学讲师，主要研究方向为视觉密码和网络安全等。|沈刚（1986- ），男，河南郑州人，博士，信息工程大学工程师，主要研究方向为视觉密码和网络安全等。|郁滨（1964- ），男，河南郑州人，博士，信息工程大学教授、博士生导师，主要研究方向为信息安全、无线网络安全技术、视觉密码等。
基金资助:
国家自然科学基金资助项目(41271392);国家自然科学基金资助项目(61602513);信息工程大学优秀青年基金资助项目(2016611303)

Research on algorithm for raster map multi-level sharing based on region incrementing color visual cryptography

Liguo FANG,Zhengxin FU,Hao HU,Gang SHEN,Bin YU

Information Engineering University,Zhengzhou 450001,China

Revised:2019-03-28 Online:2019-09-25 Published:2019-09-28
Supported by:
The National Natural Science Foundation of China(41271392);The National Natural Science Foundation of China(61602513);The Excellent Youth Foundation of Information Engineering University(2016611303)

摘要/Abstract

摘要：

针对栅格地图中涉密数据可分为不同图层的特点，设计了一种保护多层数据的区域递增式彩色视觉密码方案，并给出了具体应用流程。该方案首先对多个授权集合进行了优化，然后基于随机数设计了秘密分享和恢复算法，避免了生成和保存加密矩阵产生的额外开销。实验结果表明，该方案能够实现栅格地图数据多级分存，在大大降低方案像素扩展度的同时，实现了栅格地图数据的完全恢复。

关键词: 栅格地图多级分存, 区域递增视觉密码, 地图分层, 异或运算, 完全恢复

Abstract:

In view of the characteristics of raster map,important data of the map were divided into different map layers by using the idea of map segmentation.A regional incremental color visual cryptographic scheme for raster map sharing was designed,and a model based on this scheme was proposed.At the same time,the specific application process was given.In order to solve the problem of large pixel expansibility and poor visual effect of image recovery in traditional regional incremental visual cryptography scheme,random numbers and the access structure optimization were used.Construction of the method was simple and the additional overhead of generating and saving the encryption matrix was avoided.The experimental results show that the scheme can achieve multilevel raster map sharing with the map’s perfect recovery,meanwhile the extension of the scheme pixel is greatly reduced.

Key words: raster map multi-level sharing, region incrementing visual cryptography, map segmentation, XOR operation, perfect recovery

中图分类号:

TP208

房礼国,付正欣,胡浩,沈刚,郁滨. 基于区域递增式彩色视觉密码的栅格地图多级分存算法研究[J]. 通信学报, 2019, 40(9): 24-32.

Liguo FANG,Zhengxin FU,Hao HU,Gang SHEN,Bin YU. Research on algorithm for raster map multi-level sharing based on region incrementing color visual cryptography[J]. Journal on Communications, 2019, 40(9): 24-32.

图/表 8

表1

文中所用到的符号及其含义"

符号	含义
D	栅格地图数据
D_l	涉密程度为l的栅格地图分层数据
$φ = {1, 2, \dots, n}$	n个参与者集合
$S_{1}, S_{2}, \dots, S_{n}$	n个共享份
α	对比度
T_i	参与者i持有共享份
TSE	单个参与者持有共享份尺寸扩展
D(i,j)	D中像素坐标为(i,j)的颜色
D_l(i,j)	D_l中像素坐标为(i,j)的颜色
⊕	异或运算
S_t(i,j)	共享份S_t中像素坐标为(i,j)的颜色
m	像素扩展度
T ^ji	共享份T_i的第j部分区域
?	黑色
D	图像拼接

表1

图1

图2

图3

图4

图5

表3

表2

本文方案与相关方案的对比结果"

对比项	文献[5]	文献[6]	文献[7]	文献[8]	文献[13]	文献[14]	本文方案
存取结构	(2,n)	(2,n)	(k,n)	(k,n)	(k,n)	(k,n)	(k,n)
矩阵设计	Y	Y	Y	Y	Y	N	N
恢复算法	或运算	或运算	或运算	或运算	异或运算	异或运算	异或运算
图像类型	二值	二值	二值	二值	二值	二值	真彩
完全恢复	N	N	N	N	白像素完全恢复	解密区域完全恢复	完全恢复
像素总扩展(TSE)	—	$\leq \sum_{i = 2}^{n} m_{(i, n)}$	$\leq \sum_{i = 2}^{n} m_{(i, n)}$	$\leq \sum_{i = k}^{n} m_{(i, n)}$	$\leq \sum_{i = k}^{n} m_{(i, n)}$	$\sum_{t = k}^{n} (\begin{matrix} n - 1 \\ t - 1 \end{matrix})$	$\leq \sum_{t = k}^{n} (\begin{matrix} n - 1 \\ t - 1 \end{matrix})$

表2

参考文献 18

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k			n
k	2	3	4	5	6
2	1(1)	2(2)	2(2)	3(3)	3(3)
3	—	1(1)	6(2)	8(3)	10(4)
4	—	—	1(1)	15(3)	24(5)
5	—	—	—	1(1)	30(3)
6	—	—	—	—	1(1)

基于区域递增式彩色视觉密码的栅格地图多级分存算法研究

Research on algorithm for raster map multi-level sharing based on region incrementing color visual cryptography

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