基于椭圆曲线和双线性对的数字签名的研究

【作者】 王洪涛；

【导师】 李大兴；

【作者基本信息】 山东大学 ， 应用数学， 2006， 博士

【摘要】 在本文中，我们针对现有的某些数字签名方案存在实现效率低、安全性不高的因素，讨论并提出了多种基于椭圆曲线和双线性对的更为高效安全数字签名方案，并给出了相应的正确性证明、安全性分析和优势所在。 自从Diffie和Hellman于1976年首次提出数字签名概念以来，数字签名引起了学术界和计算机网络界的广泛重视。ISO于1984年9月专门为此立项，指定SC20下属的WG2负责制定该标准，这表明了ISO对数字签名的重视。SC20将数字签名正式分为三类：带印章的数字签名、带影子的数字签名和使用Hash函数的数字签名。1985年，EIGamal设计了一种既可用于加密又可以用于签名的数字签名方案；1991年，NIST提出了基于EIGamal的数字签名方案的数字签名标准(DSS)及其算法标准(DSA)。与此同时，各种数字签名方案也不断被提出和应用。比较著名的数字签名体制有RSA、Rabin、EIGamal、Schnorr、DSS、Diffie-Hellman等。随着数字签名研究的深入，近几年来，产生了不少特殊的数字签名，如代理签名、盲签名、多重签名、门限签名和群签名等。由这些签名又产生了很多更特殊的签名，如代理多重签名、多重代理签名、多重代理多重签名和门限群签名等等。由于这些特殊的数字签名有着很好的性能，从而使得在电子商务、公共资源的管理、重要军事命令的签发、投票选举、金融合同的签署等方面有着广泛的应用前景。因此，这是一个十分值得重视且有极大应用价值的研究领域。这也是作者为什么要选这些特殊的数字签名作为研究课题的原因。 代理签名是一个相对比较新的概念，它是由Mambo等人于1996年首次提出的。在Mambo等人明确提出代理签名的概念以前，人们在讨论其他一些问题时，如分布网络环境中的身份认证、访问控制等，已提出签名权利的代理问题，并且根据实际需要，给出和应用了一些完全委托型代理签名体制。Mambo等人的主要贡献是提出了部分委托型代理签名的概念，为数字签名的研究与应用开辟了一个新领域。 盲签名体制是一个协议，包括两个实体：消息发送者和签名者。它允许发送者让签名者对给定的消息签名，并且没有泄露关于消息和消息签名的任何信息。1982年，Chaum首次提出盲签名概念，并利用盲签名技术提出了第一个电子现金方案。利用盲签名技术可以完全保护用户的隐私权，因此，盲签名技术在诸多电子现金方案中被广泛使用。更多还原

【Abstract】 As present many digital signature schemes have the following disadvantages: low efficience and security, this paper brings forward eleven more efficienct and secure digital signature schemes based on ECC and bilinear parings. Furthermore, according to every new scheme, we give the corresponding correctness proof, security analysis and the advantage.Since the Diffie and Hellman put forward the digital signature conception in 1976, digital signature caused the extensive value of the academic circles and the calculator network field. The ISO signed an item for this exclusively in September of 1984. The WG2 of the appointed SC20 inferiorities’ was responsible for establishment these standards. That expresses the emphasis of ISO on digital signature. The SC20 formally divided digital signature into three types: taking the digital signature of an official seal, taking the digital signature of the shadow and using digital signature of the Hash function. In 1985, ElGamal designed a kind of digital signature that can used in the digital signature and that encryption can used for a signature again. In 1991, the NIST put forward the digital signature standard(DSS) and digital signature algorithm(DSA). At the same time, various digital signature schemes also are put forward continuously with application. The digital signature schemes that are famous contain RSA, Rabin, EIGamal, Schnorr, DSS, Diffie-Hellman etc. In the last few years, along with digital signature study thoroughly, many special of digital signature were produced, such as proxy signature, blind signature, multi-signature, threshold signature and group signature etc. A lot of more special signatures were produced again by these signatures, such as proxy multi-signature, multi-proxy signature and multi-proxy multi-signature etc. Because these special digital signature have good properties: making to orderany in the management, important military of the electronic commerce, public resources thus of countersign, election by ballot, the financial contract sign etc. This is a very worthy of value and have biggest applied value of research realm. This is also author why want to choose these special digital signature as the topic.The conception of proxy signature was first introduced by Mambo, Usuda, and Okamoto in 1996. In the proxy signature scheme, an original signer is allowed to delegate更多还原