| 一般访问结构上基于异或运算的可视秘密共享方案 | |
| Alternative Title | XOR-based Visual Cryptographic Scheme for General Access Structure |
| 于钦屹 | |
| Subtype | 学士 |
| Thesis Advisor | 贾星星 |
| 2021-05-20 | |
| Degree Grantor | 兰州大学 |
| Place of Conferral | 兰州 |
| Degree Name | 理学学士 |
| Degree Discipline | 数学与应用数学 |
| Keyword | 可视秘密共享方案 异或运算 一般访问结构 整数线性规划 |
| Abstract | 可视秘密共享方案(VCS)加密时将秘密图像 S 利用布尔基矩阵加密为 n 个阴影图像并打印到透明胶片上，每位参与者持有一份透明胶片。透明胶片的大小由像素膨胀和秘密图像的大小决定。像素膨胀越小，透明胶片越小，越方便保存和携带。解密时对于给定的访问结构，授权集中的集合元素对应的参与者不用借助任何加密技术和计算，将透明胶片无序叠加就能恢复人类视觉系统可辨别的秘密图像 S;禁止集中对应的参与者不能通过任何方法获得关于秘密图像 S 的任何信息。恢复的秘密图像 S 的质量由对比度衡量，对比度越高，图像恢复质量越好。实现可视秘密共享方案主要有两种底层运算：布尔或运算(OR) 和布尔异或运算(XOR)。相较于基于或运算的可视秘密共享方案(OVCS)，基于异或运算的可视秘密共享方案(XVCS)可以提高对比度，解决或运算造成的视觉质量差的问题。因此， 本文兼顾对比度和像素膨胀，使用整数线性规划(ILP)和布尔异或运算，提出了一种一般访问结构上基于异或运算的可视秘密共享方案(XGVCS)。该方案将基矩阵的构造问题转化为在对比度和安全性条件限制下的最小像素膨胀问题，通过 LINGO 软件求解得到最小像素膨胀下基矩阵的构造方案。该方案不仅实现了基于异或运算的最优像素膨胀，还解决了大多数已提出的 XVCS 不具有授权集单调性的问题，实现了强访问结构下的秘密共享。最后， 本文通过实验对比发现相比于或方案，基于 XOR 运算的最优方案在对比度方面具有显著优势，证明了该方案的有效性。 |
| Other Abstract | The visual secret sharing scheme (VCS) for n participants in the set P encrypts the secret image S into n shadow images by randomly selected Boolean matrix and prints them to transparencies, each participant holds one. The size of the transparencies is determined by pixel expansion. The smaller the pixel expansion, the smaller the transparencies, the more convenient to save and carry transparencies. Decryption for a given access structure, participants corresponding to the set elements in the qualified set do not have to use any encryption techniques and calculations, disorderly stacking of transparencies can restore the secret image S by the human vision system;participants corresponding to the set elements in the forbidden set can not obtain any information about the secret image S by any method. And the quality of the recovered secret image S is measured by contrast, The higher the contrast, the better the recovery quality. There are two kinds of underlying operations to realize visual cryptographic scheme: Boolean OR operation and Boolean XOR operation. Compared with OR_based visual cryptographic scheme (OVCS), XOR_based visual cryptographic scheme (XVCS) can solve the problem of poor visual quality by improving the contrast without darkening the background of the restored secret image S. Therefore, this article takes into account both high contrast and low pixel expansion, uses integer linear programming (ILP) and Boolean XOR operations, proposes a XOR_based visual cryptographic scheme for general access structure (XGVCS). In this scheme, the construction problem of base matrix is transformed into the minimum pixel expansion problem under the condition of contrast and security. By LINGO, the construction scheme of base matrix under minimum pixel expansion is obtained. This scheme not only achieves optimal pixel expansion based on XOR operation, also addresses the problem that most of the proposed XVCS did not have the monotony of the qualified set, the secret sharing on strong access structure is realized. Finally, the experimental comparison shows that the optimal scheme based on XOR operation has significant advantages in contrast, which proves the effectiveness of thescheme. |
| Pages | 32 |
| URL | 查看原文 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | https://ir.lzu.edu.cn/handle/262010/461896 |
| Collection | 数学与统计学院 |
| Affiliation | 数学与统计学院 |
| First Author Affilication | School of Mathematics and Statistics |
| Recommended Citation GB/T 7714 | 于钦屹. 一般访问结构上基于异或运算的可视秘密共享方案[D]. 兰州. 兰州大学,2021. |
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