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基于椭圆曲线上的数字签名、签密方案的研究

The Research on Digital Signature Schemes and Signcryption Schemes Based on Elliptic Curves

【作者】 刘维华

【导师】 辛小龙;

【作者基本信息】 西北大学 , 计算数学, 2008, 硕士

【摘要】 随着信息技术的高速发展和计算机网络技术的广泛应用,信息安全问题显得越来越重要,已经成为国内外计算机和网络应用领域普遍关注的热门研究课题。数字签名作为认证的主要手段,为信息安全提供了重要的技术支撑。1985年Koblitz和Miler分别提出在椭圆曲线上构造密码系统(EEC)的思想,基于椭圆曲线上的具有签密功能的数字签名方案整合了加密、解密、数字签名三种技术,比单独进行加密、解密、数字签名节省了计算量和通信成本。本文对椭圆曲线上的基于证书和基于身份的数字签名方案进行了深入地研究。主要工作如下:介绍了椭圆曲线公钥密码系统理论和基于证书和基于身份的数字签名理论。在基于证书的椭圆曲线上的数字签名和签密方案中,选取了具有代表性的赵的数字签密方案,指出了赵的方案不完全满足数字签密的安全特性。针对赵方案的缺陷,提出了一种理想的数字签密方案,此方案满足消息的机密性、完整性、签名方程的不可伪造、可身份认证、防抵赖、前向安全性、密文的公开验证性,且能抵抗Bob的恶意伪造攻击等8项安全性能。利用椭圆曲线上双线性对的性质,另辟新径,构造了一个新的签名方案。这种方案可以同时满足公开验证性和前向安全性及其他安全特性,不需要利用双私钥,并把这种签名思想应用到基于身份的门限签密方案中,从而使得基于身份的门限签密方案也同时具有前向安全性和公开验证性且满足其他特性。通过对基于证书的公钥密码体系与基于身份的公钥密码体系的比较,指出了现有的基于身份的公钥密码体系的优点及存在的问题。利用椭圆曲线上双线性对的性质以及基于椭圆曲线上的CDLP难解问题和双线性对上CDHP难解问题,提出了一个不需要用户公钥证书,也不需要密钥托管的密钥分发新协议,并结合Cha-Cheon签名给出了安全性和性能分析。

【Abstract】 With the rapid development of information technique and the large-scale application of network technique, information security is becoming more and more important, and is becoming a generally concerned research topic in domestic and international computer and network application field. As the main means of the authentication, the digital signature has provided an important technique for information security.In 1985, Koblitz and Miller independently proposed using the group of points on an elliptic curve defined over a finite field to construct cryptosystem, which is elliptic curves cryptosystems(ECC). The signcryption scheme based on elliptic curves combines encryption、decryption> digital signature technology, which needs less communication and computation than encryption、decryptions digital signature separately. In this paper, the certificate-based digital signature scheme and identity-based digital signature scheme are discussed. The main works are as follows:The public key cryptosystems and the certificate-based digital signature scheme and identity-based digital signature scheme on elliptic curve are introduced.Among the certificate-based digital signcryption schemes based on elliptic curves , as a example of Zhao’s digital signcryption scheme ,the paper describes that Zhao’s scheme does not all satisfy secure requirements of digital signcryption schemes .To get over the drawbacks of Zhao’s scheme ,the paper proposed an ideal digital signcryption scheme which satisfies the confidentiality、integrality、unforgeability signature、authentications non-repudiations forward security、public verification of ciphers resist Bob’s evil forge signature scheme.The paper proposes a new digital signature scheme based on the properties of bilinear pairing, the scheme satisfies security of digital signcryption simultaneously, such as public verification and forward security, which does not need double private keys. And then, applying this technology to identity-based threshold signcryption scheme, security of scheme is same.Comparing identity-based cryptosystems with certificate-based cryptosystems, the advantages and inherent drawbacks of existent identity-based cryptosystems are analyzed . And then, a new secure key issuing protocol based on the difficult problem of ellipse (CDLP, CDHP) and the properties of bilinear pairing are proposed, which doesn’t require certificates to guarantee the authenticity of public keys and doesn’t require key escrow. At last, a security and performance analyses of new Chan-Cheon signature scheme are given.

  • 【网络出版投稿人】 西北大学
  • 【网络出版年期】2008年 08期
  • 【分类号】TP393.08
  • 【下载频次】231
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