基于秘密仿射变换和零知识证明的多变量代理签名方案的研究

【作者】 李智星；

【导师】 许春根；

【作者基本信息】 南京理工大学 ， 应用数学， 2012， 硕士

【摘要】 随着网络技术的高速发展,数字签名也在电子政务和电子商务等诸多方面得到了广泛的应用。代理签名作为数字签名中的一员,主要应用在电子选举,电子现金,电子拍卖等方面,而且根据功能的不同,又相继出现了如代理盲签名,提名代理签名,门限代理签名等不同的代理签名方案。但是这些代理签名方案大部分都是基于传统的公钥密码体制,在面对未来量子计算机的诞生时,它们将受到很严重的威胁。为了能够面对未来量子计算机带来的危机,多变量公钥密码体制(MPKC)作为能够抵御未来基于量子计算机的攻击的候选者之一。本论文结合了多变量的性质,使用有限域上的二次多变量多项式构造代理签名体制,利用了多变量同构问题(IP),选取以Rainbow结构的多项式作为中心映射,并且基于安全性的考虑,在签名方案基础上增加了秘密仿射变换的性质,使公钥多项式并非像其在原模型当中一样为私钥的直接合成,而是隐藏部分私钥,减少攻击者获得的信息量；同时签名验证是对中间过程某结果的验证,提出了一种基于多变量签名体制的代理保护型签名方案；再根据零知识证明的方法,结合证书签名,提出了一种基于IP模式零知识证明的证书代理签名方案。更多还原

【Abstract】 With the fast development of network, the digital signatures have wide application in electronic government affairs and electronic commercial affairs and many other affairs. Proxy Signature is one of the digital signatures. The main application of Proxy Signature is in electronic election, electronic cash and electronic auction etc. According to the different environments, people propose many types, such as proxy blind signature and nomination proxy signature threshold proxy signature etc. But most of them are based on traditional public cryptosystem. They will be vulnerable when the quantum computer is emerged in the future.Multivariate public cryptosystem is one of the public key cryptosystem resistant to attack quantum computers. Combine with multivariate properties and the Isomorphism of Polynomials Problem which is a fundamental problem of multivariate cryptography, I propose a proxy signature scheme with the central map is chose a rainbow multivariate polynomials. In terms of the security, I combine the secret affine transformation with the signature to hidden part of the private key. Moreover, I propose a certificated-based proxy signature scheme with Zero-knowledge Proofs of Knowledge and IP scheme.更多还原