基于格的代理签名方案的研究

发布时间：2018-05-06 21:35

本文选题：格 + 代理签名　；参考：《电子科技大学》2016年硕士论文

【摘要】：随着移动互联网和通信技术的快速发展,数字签名方案的应用越来越广泛,不同的应用背景下,产生了许多数字签名的特殊形式,代理签名方案就是其中比较重要的一种。代理签名方案具有重要的研究价值和应用前景,因此得到广泛关注和研究。近年来,随着量子计算机的不断发展,当前已经用于实际应用的基于离散对数、大整数因子分解等困难问题的代理签名方案在量子计算机环境下的安全性受到了威胁,现有的基于格的代理签名方案的提出非常有限,且已有的方案存在着一些问题。哈希函数在现代密码学领域扮演者很重要的角色,它作为许多密码算法和协议的基础结构模块,在算法安全方面起着重要的作用。传统的密码学哈希函数一般用于字符串到字符串的映射,由于计算需求,从字符串映射到矩阵的哈希函数在一些密码方案中提到过,但没有说明其具体的实现过程,另外,随着后量子密码逐渐成为热点,以格为代表的后量子密码已经成为研究热点,基于格困难问题构建哈希函数成为可能。本文中,我们对格上离散高斯分布、原象可抽样函数、“盆景树”、拒绝采样技术以及矩阵原像采样函数进行了研究,同时对格上困难问题的归约进行分析,做了以下几个方面的研究:1.一个由字符串映射到固定规模矩阵的哈希函数:对格上从最坏情况困难问题到平均情况困难问题的归约过程进行分析,基于平均情况困难问题,构造了一个能够从任意长度字符串映射到要求大小矩阵的哈希函数,并对其单向性和抗碰撞性进行了证明;2.基于原像取样的代理签名方案:在GPV数字签名方案基础上,使用格基派生技术,构造了一个新的的基于格的代理签名方案。该方案在保持安全性不变的情况下,降低了签名过程的复杂度,降低了公钥长度,节约了开销。3.基于拒绝采样的代理签名方案:在LYU数字签名方案的基础上,根据拒绝采样方法以及原像矩阵取样函数,构造了另外一个基于格的代理签名方案,此方案摒弃了以往的基于格基派生技术的权利委托过程,大大减少了计算量和存储量,为后续继续研究基于格的代理签名方案打下了基础。
[Abstract]:With the rapid development of mobile Internet and communication technology, digital signature schemes are more and more widely used. Under different application background, many special forms of digital signature have emerged, among which proxy signature scheme is one of the most important. Proxy signature scheme has important research value and application prospect, so it has been widely paid attention to and studied. In recent years, with the development of quantum computer, the security of proxy signature scheme based on discrete logarithm, large integer factorization and other difficult problems has been threatened in quantum computer environment. The proposed lattice-based proxy signature schemes are very limited, and there are some problems in the existing schemes. Hash function plays an important role in the field of modern cryptography. As an infrastructure module of many cryptographic algorithms and protocols, hash function plays an important role in algorithm security. The traditional cryptographic hash function is generally used to map string to string. The hash function from string to matrix has been mentioned in some cryptographic schemes, but its implementation process is not explained. With the post-quantum cryptography gradually becoming a hot topic, lattice-represented post-quantum cryptography has become a research hotspot, and it is possible to construct hash functions based on lattice difficulties. In this paper, we study the discrete Gao Si distribution on the lattice, the original image sampling function, the bonsai tree, the rejection sampling technique and the matrix original image sampling function. At the same time, we analyze the reduction of the difficult problems on the lattice. Do the following research: 1. A hash function from string mapping to fixed scale matrix: the reduction process from worst-case difficulty problem to average difficulty problem on lattice is analyzed, based on the average difficulty problem. A hash function which can map from arbitrary length string to required size matrix is constructed, and its unidirectional and anti-collision properties are proved. Proxy signature scheme based on original image sampling: based on GPV digital signature scheme, a new lattice-based proxy signature scheme is constructed by using lattice-derived technique. This scheme can reduce the complexity of signature process, reduce the length of public key and save the cost of. 3. Proxy signature scheme based on rejection sampling: based on the LYU digital signature scheme, another lattice-based proxy signature scheme is constructed according to the rejection sampling method and the original image matrix sampling function. This scheme abandons the previous process of right delegation based on lattice derivation technology and greatly reduces the amount of computation and storage. It lays a foundation for further research on lattice-based proxy signature schemes.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN918

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