基于格的群签名研究

发布时间：2018-11-15 07:27

【摘要】：群签名是指群成员能够以匿名的方式代表整个群体进行签名,验证者只能验证这个签名是合法的签名,但不能确定是哪个群成员所签署的,如果签名发生争议,群管理员可以利用追踪密钥确定签名者的身份,即群签名具有匿名性和可追踪性。这两个特殊的性质使得群签名在选举、新闻发布、电子商务等领域有着广泛的应用前景。盲签名是指,接收者在不让签名者获取所签署消息具体内容的情况下所采取的一种特殊的数字签名,并且签名者不能追踪签名,也就是说,即使签名被公开,签名者也无法得知自己在何时、为何人签署了这个消息,但这个签名是可以被验证的正确的签名。群盲签名融合了群签名和盲签名的特性,因此具有盲性和匿名性等特点。由于这些优良特性,群盲签名技术可以用来构造安全的、多个银行参与的电子现金系统。在构造群盲签名方案时,需要对消息进行盲化处理,从而使得签名者不知道所签署消息的真正内容。现有的大部分数字签名方案都是基于传统的数论难题,这些难题不能抵抗量子攻击,并且运算复杂。而格公钥密码作为后量子密码的代表之一,具有抵抗量子攻击、代数结构简单、良好的困难性归约以及可证明安全等优点。因此,构造基于格的签名方案具有重要的理论意义和现实意义。本文围绕群签名和盲签名的相关理论展开讨论,针对群签名的构造、安全性分析及其应用进行了探索和研究。本文的工作主要有以下两个方面：1.构造了第一个基于格的群盲签名方案。方案的理论依据是GKV群签名方案和王凤和盲签名方案。该方案的优点是,用户在加入群组的过程中,通过使用零知识证明协议,使得群管理员不能获取群成员的签名密钥,从而不能冒充群成员生成合法的签名,因此该方案可以抵抗陷害攻击。除此之外,对该方案所满足的其他安全特性进行了详细的分析及论证。2.给出了对LLLS群签名的改进方案,并对其安全性进行了分析。在签名阶段,原方案使用的是两个不同的矩阵,而改进方案使用的是同一矩阵；在验证阶段,原方案需要验证两个等式同时成立,而改进方案只需验证一个等式成立即可。因此,改进的方案与原方案相比,更加简洁高效,运算量更小。
[Abstract]:Group signature means that a group member can sign on behalf of the whole group anonymously. The verifier can only verify that the signature is legal, but it is not certain which group member signed it. The group administrator can use the tracing key to determine the identity of the signer, that is, the group signature is anonymous and traceable. These two special properties make group signature have a wide application prospect in election, news release, electronic commerce and so on. Blind signature is a special digital signature adopted by the receiver without giving the signer access to the specific contents of the signed message, and the signer cannot trace the signature, that is, even if the signature is made public, Nor can the signer know when or why he signed the message, but the signature is the correct signature that can be verified. Group blind signature combines the characteristics of group signature and blind signature, so it has the characteristics of blindness and anonymity. Because of these advantages, group blind signature techniques can be used to construct secure, multi-bank participating electronic cash systems. When constructing a group blind signature scheme, it is necessary to blind the message so that the signer does not know the true content of the signed message. Most of the existing digital signature schemes are based on traditional number theory problems, which cannot resist quantum attacks and are complex in operation. As one of the representatives of post-quantum cryptography, lattice public key cryptography has the advantages of resisting quantum attack, simple algebraic structure, good difficulty reduction and provable security. Therefore, it is of great theoretical and practical significance to construct a lattice-based signature scheme. In this paper, the theory of group signature and blind signature is discussed, and the construction, security analysis and application of group signature are discussed. The main work of this paper is as follows: 1. The first group blind signature scheme based on lattice is constructed. The theoretical basis of the scheme is GKV group signature scheme and Wang Fenghe blind signature scheme. The advantage of this scheme is that in the process of joining the group, the user can not obtain the signature key of the group member by using the zero-knowledge proof protocol, so the group administrator can not generate the legal signature by impersonating the group member. Therefore, the scheme can resist the framing attack. In addition, the other security characteristics of the scheme are analyzed and demonstrated in detail. 2. An improved scheme of LLLS group signature is presented and its security is analyzed. In the signature stage, the original scheme uses two different matrices, while the improved scheme uses the same matrix. In the verification stage, the original scheme needs to verify that the two equations hold at the same time, while the improved scheme only needs to verify the validity of one equation. Therefore, compared with the original scheme, the improved scheme is more concise and efficient, with less computation.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.91

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