本文選題：格 + 代理簽名��； 參考：《電子科技大學》2016年碩士論文

【摘要】：隨著移動互聯網和通信技術的快速發(fā)展,數字簽名方案的應用越來越廣泛,不同的應用背景下,產生了許多數字簽名的特殊形式,代理簽名方案就是其中比較重要的一種。代理簽名方案具有重要的研究價值和應用前景,因此得到廣泛關注和研究。近年來,隨著量子計算機的不斷發(fā)展,當前已經用于實際應用的基于離散對數、大整數因子分解等困難問題的代理簽名方案在量子計算機環(huán)境下的安全性受到了威脅,現有的基于格的代理簽名方案的提出非常有限,且已有的方案存在著一些問題。哈希函數在現代密碼學領域扮演者很重要的角色,它作為許多密碼算法和協(xié)議的基礎結構模塊,在算法安全方面起著重要的作用。傳統(tǒng)的密碼學哈希函數一般用于字符串到字符串的映射,由于計算需求,從字符串映射到矩陣的哈希函數在一些密碼方案中提到過,但沒有說明其具體的實現過程,另外,隨著后量子密碼逐漸成為熱點,以格為代表的后量子密碼已經成為研究熱點,基于格困難問題構建哈希函數成為可能。本文中,我們對格上離散高斯分布、原象可抽樣函數、“盆景樹”、拒絕采樣技術以及矩陣原像采樣函數進行了研究,同時對格上困難問題的歸約進行分析,做了以下幾個方面的研究:1.一個由字符串映射到固定規(guī)模矩陣的哈希函數:對格上從最壞情況困難問題到平均情況困難問題的歸約過程進行分析,基于平均情況困難問題,構造了一個能夠從任意長度字符串映射到要求大小矩陣的哈希函數,并對其單向性和抗碰撞性進行了證明;2.基于原像取樣的代理簽名方案:在GPV數字簽名方案基礎上,使用格基派生技術,構造了一個新的的基于格的代理簽名方案。該方案在保持安全性不變的情況下,降低了簽名過程的復雜度,降低了公鑰長度,節(jié)約了開銷。3.基于拒絕采樣的代理簽名方案:在LYU數字簽名方案的基礎上,根據拒絕采樣方法以及原像矩陣取樣函數,構造了另外一個基于格的代理簽名方案,此方案摒棄了以往的基于格基派生技術的權利委托過程,大大減少了計算量和存儲量,為后續(xù)繼續(xù)研究基于格的代理簽名方案打下了基礎。
[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.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TN918

【參考文獻】

相關期刊論文 前2條

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2 祁明,L.Harn;基于離散對數的若干新型代理簽名方案[J];電子學報;2000年11期

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本文編號：1853989