视觉密码的彩色栅格地图分存算法

目的 现有栅格地图安全保护技术主要有：基于混沌理论的图像加密技术、数字图像置乱技术和图像信息隐藏技术，这些技术不适用于丢失容忍、解密简单、共享份图像顺序可交换、权限控制等应用场合。图像分存技术可应用于上述场合，其中基于视觉密码的图像分存技术秘密图像恢复时运算简单，仅利用人眼视觉系统或借助简单计算设备，便可以获得恢复图像的信息。但运用于彩色栅格地图分存的彩色视觉密码方案，存在像素扩展度较大、秘密图像颜色受限等问题。为解决该问题，基于异或运算给出了概率型彩色视觉密码方案定义，并构造了一种概率型（k，n）彩色视觉密码方案。方法 在方案设计前，首先给出RGB颜色集合、彩色像素异或运算、共享份异或运算和基于异或运算的概率型（k，n）彩色视觉密码方案等定义。基于异或运算的概率型（k，n）彩色视觉密码方案定义包括对比条件、安全性条件和防串扰条件3个部分。根据定义，给出概率型（k，n）-CVCS（color visual cryptography scheme）的详细构造方法，该方法以（k，k）彩色视觉密码方案为基础，通过设计扩展变换算子f，将k个共享份随机等概地扩充到n个共享份，实现了（k，n）彩色栅格地图分存算法，解决了彩色栅格地图分存算法存在像素扩展度大、恢复图像视觉效果差的问题。随后，从定义的对比条件、安全性条件和防串扰条件3个方面，对本文方案有效性进行了理论证明。结果 为验证方案的有效性，利用本文算法构造出的（3，4）方案对具体的栅格地图进行分存，随机选择3个共享份XOR（exclusive or异或）后可以得到原栅格地图，而任意单个、两个共享份XOR只能得到杂乱无章的噪声图像，无法获取原栅格地图的任何信息。同时，运用其他彩色视觉密码方案对相同栅格地图进行分存，实验结果表明，本文方案像素不扩展，在视觉效果上具有更优的结果，计算得到的恢复图像峰值信噪比也优于其他相关方案。结论 本文方案无像素扩展，在减小系统开销的同时，改善了栅格地图的视觉效果，且无需对栅格地图进行半色调处理。

Color raster map-sharing algorithm based on visual cryptography

Objective Raster map data (hereinafter referred to as raster map) refer to a paper topographic map of various scales and a digital product of numerous professionally used color maps. A raster data file is formed according to existing papers, films, and other topographic maps by scanning, geometric correction, and color correction. Such file is consistent with a topographic map in content, geometric precision, and color and has the characteristics of a digital image and a large amount of data. Security protection technologies that are commonly used for raster maps include the image encryption technology based on chaos theory, digital image scrambling technology, and image information-hiding technology. These technologies have a common shortcoming, that is, a single carrier in the transmission is generally through a channel to achieve. When the channel has a failure or damage, the receiver cannot correctly receive the original image information. These technologies do not apply to the loss of tolerance, simple decryption, exchangeable share orders, permission control, and other applications. Image sharing technology can be adopted to the above occasions. The basic principle is to encrypt secret image information into multiple shared copies of the image and distribute it to multiple participants. In this process, only the authorized participant subset can decrypt (restore) the secret image, whereas the non-authorized subset cannot. The image sharing technology has the characteristic of loss of tolerance; that is, when part of the shared image is lost, the secret image can still be decrypted. Research on image sharing technology has mainly focused on the two aspects of image sharing technology based on polynomials and visual cryptography. The former mainly shares a secret image to multiple shadow images by using Shamir''s polynomial sharing algorithm and then uses interpolation principle to yield the exact recovery of the secret image. However, the method has a high computational complexity. The latter has an advantage of simple recovery process of the secret image. The image recovery information can be obtained by using human visual system or with a simple computing device. Nevertheless, large pixel expansion and limited color of the secret image are yielded. To solve this problem, this study defines and constructs a probabilistic (k, n) color visual cryptography scheme based on exclusive or XOR operation. Method The application of handheld devices and the requirements for outdoor applications of raster maps have increased the demands for the decryption operation in a simple image sharing technology. Before the design of the scheme, this study defines the RGB color set, color pixel XOR operation, shared XOR operation, and probabilistic (k, n) color visual cryptography scheme based on XOR operation. The definition of probabilistic (k, n) color visual cryptography scheme based on XOR operation includes three parts, namely, contrast, security, and anti-crosstalk conditions. A detailed construction method for the probabilistic (k, n) color visual cryptography scheme is provided according to the definition. The construction method based on the (k, k) color visual cryptography scheme makes k expansion shares randomly extended to n shares by expanding operator f. A (k, n) color raster map-sharing algorithm is achieved, which solves the problem of large pixel expansion and poor image visual effect of the color raster map-sharing algorithm. The scheme validity is proven from three aspects, namely, definition, safety, and anti-crosstalk conditions. Result We use a (3, 4) scheme based on the proposed algorithm in decomposing the specific raster map sharing to verify the validity of the visual cryptography scheme. The original raster map can be obtained by randomly selecting three shared copies of XOR, and any single or two shares can yield only a messy noise image by XOR, which cannot generate any information of the original raster map. When we use another color visual cryptography scheme to share the same raster map, the experimental results show that the pixels of the proposed scheme do not expand and that the visual effects present good results. The peak-signal-to-noise ratio of the recovered image is better than that of other related schemes. Conclusion we construct a probabilistic (k, n) color visual cryptography scheme based on XOR operation and provide a secret sharing and restoration algorithm. The validity of the color visual cryptography scheme is theoretically proven in the experiment. The scheme is applied to existing color raster map sharing. Unlike other schemes, the proposed scheme exhibits no pixel expansion, reduces system overhead, improves the visual effect of raster map, and does not require halftone processing for the raster map.