【作者】 张杰；

【导师】 张福泰；

【作者基本信息】 南京师范大学 ， 计算机应用技术， 2013， 硕士

【摘要】 可验证秘密分享(简称VSS)是信息安全和数据保密中的一项重要技术,并已被广泛应用于分布式密钥生成(简称DKG)、门限密码学、密钥托管和多方安全计算等诸多领域。可验证秘密分享自提出之后就引起了学者的广泛重视,特别是对于有限域上可验证秘密分享的研究,至此已经基本完善。近年来基于双线性对的密码体系在研究领域逐渐受到了人们的重视,许多双线性群上的密码方案和协议也应运而生。在这些方案中,秘密密钥通常是一个来自于双线性群的元素,因此如何可验证地分享这样的密钥,以及如何分布式地生成这样的密钥就成了非常重要并且亟待研究的一个问题。因此,本论文深入广泛地研究了双线性群上的可验证秘密分享及其应用,并且取得了相应的一些成果。针对双线性群上可验证秘密分享方案,首先提出了两个双线性群上高效的计算安全的可验证秘密分享方案。第一个方案采用多项式的方法来分享秘密,这种方法和已有的这类方案多少有些类似,但是具有更低的计算代价。第二个方案使用矩阵作为来分享秘密的工具,也就是所谓的门限线性可验证秘密分享,它包括了前一种方案。随后又提出了两个双线性群上高效的信息论安全的可验证秘密分享方案：一个基于多项式的方案,比已有的这类方案具有更高的效率；一个线性方案,包括了前一种方案。同时还对双线性群上的广义可验证秘密分享进行了研究,提出了双线性群上基于向量空间接入结构的可验证秘密分享方案。并对方案的安全性和复杂性做了详细论证。然后针对双线性群上可验证秘密分享方案的应用,认真研究了双线性群上的安全的分布式密钥生成,并用所提出的双线性群上基于向量空间接入结构的可验证秘密分享方案构造了相应的分布式密钥生成协议。最后对于双线性群上的可验证秘密分享在门限密码系统中的应用,主要研究了门限ElGamal加密,并给出了相应的方案。更多还原

【Abstract】 Verifiable secret sharing (VSS for short) is an important method for information security and data protecting. It has been extensively used in fields such as dis-tributed key generation(DKG for short), threshold cryptosystem, key escrow and secure multiparty computation. Many researchers have focused on VSS since the birth of its concept and some VSS schemes, especially in finite fields, have been well established by now. Recently, the bilinear pairing-based cryptography has re-ceived much attention from the research community. Many bilinear pairing-based cryptographic schemes and protocols have been available. As in many pairing-based cryptosystems, the secret keys are random elements in some bilinear groups, it is of great importance to investigate the verifiably sharing of such secrets, as well as the distributed generation of such secret keys.Thus, this thesis do deep and extensive researches on verifiable secret sharing over bilinear groups and its applications, and some results are gotten.For research on the schemes of verifiable secret sharing in bilinear groups, two efficient and computationally secure VSS schemes in bilinear groups are presented in this thesis. The first one uses the polynomial method to share a secret which is more or less similar with such schemes in existence but has lower computational cost than those existing schemes. The second one employs matrix as the tool for sharing and is often known as linear threshold VSS that includes the first one as a special case. And after that we propose two efficient and information-theoretic secure VSS schemes in bilinear groups:a polynomial one that is more efficient than similar schemes available, and a linear one that includes the former as a special case. Then for general VSS based on bilinear groups, we propose verifiable secret sharing scheme with vector space access structures for the first time. We also demonstrate the security and analyze the efficiency for the new scheme in this thesis.For research on the applications of verifiable secret sharing schemes in bilinear groups, we do a serious study with respect to secure distributed key generation and construct such protocol using our new proposed VSS scheme with vector space access structures in bilinear groups. At last for applications in threshold cryptosystem we primarily study the threshold ElGamal decryption from bilinear pairings and give such scheme.更多还原