基于椭圆曲线的认证密钥协商协议的研究及应用

发布时间：2018-10-23 20:46

【摘要】：椭圆曲线是20世纪最突出的数学理论之一,是代数几何中最重要的一类研究分支.椭圆曲线算术理论在密码学中有着广泛的应用.椭圆曲线公钥密码已日益成熟,由于其较强的安全性和较高的实现效率,已经开始逐步替代RSA公钥密码系统.近十年来基于椭圆曲线公钥密码技术的发展尤其值得人们关注.从公钥密码系统的安全性,实现效率,部署和管理成本等角度出发,人们提出了包括基于PKI的公钥密码,基于身份的公钥密码和无证书公钥密码等多种公钥密码体制. 为了解决传统公钥基础设施带来的复杂的证书管理问题,人们开始研究基于身份的公钥密码体制和无证书公钥密码体制.椭圆曲线双线性对是实现这些机制的一个很好的途径.但是由于双线性对的相关运算开销几乎是椭圆曲线点乘的20倍,其实现效率亟待提高. 为了提高相关协议的实现效率,我们给出了基于椭圆曲线密码的认证密钥协商协议新的定义和安全模型.并且,基于我们定义的安全模型,设计了不使用对的无证书双方认证密钥协商协议,不使用对的基于身份的多重认证密钥协商协议和电子商务环境中不使用对的基于身份的三方认证密钥协商协议.这些协议的实现主要基于椭圆曲线点乘来实现,从而避免了计算开销较大的双线性对运算.由于计算开销的节省,我们设计的基于椭圆曲线密码的认证密钥协商协议在达到了同样的安全要求前提下,具有更高的实现效率和实用价值.最后,基于对混沌映射的研究,我们提出了一种新的基于混沌映射的密钥协商协议,并给出了其安全性证明和效率分析.
[Abstract]:Elliptic curve is one of the most prominent mathematical theories in the 20th century and is the most important branch of algebraic geometry. Elliptic curve arithmetic theory is widely used in cryptography. Elliptic curve public key cryptosystem has become more and more mature. Because of its strong security and high efficiency, it has gradually replaced the RSA public key cryptosystem. The development of public key cryptography based on elliptic curve in recent ten years is especially worthy of attention. In view of the security, efficiency, deployment and management cost of public key cryptosystem, many kinds of public key cryptosystems, such as PKI based public key cryptosystem, identity-based public key cryptosystem and certificateless public key cryptosystem are proposed. In order to solve the complex certificate management problem brought by the traditional public key infrastructure, people begin to study the identity-based public key cryptosystem and the non-certificate public key cryptosystem. A bilinear pair of elliptic curves is a good way to realize these mechanisms. But because the cost of bilinear pair is almost 20 times that of elliptic curve point multiplication, its efficiency needs to be improved. In order to improve the efficiency of related protocols, we propose a new definition and security model of authentication key agreement protocol based on elliptic curve cryptography. In addition, based on the security model defined by us, we design the authentication key agreement protocol which does not use a pair of certificates. The identity-based multiple authentication key agreement protocol is not used in the electronic commerce environment and the identity-based three-party authentication key agreement protocol is not used in the e-commerce environment. The implementation of these protocols is mainly based on elliptic curve point multiplication, thus avoiding bilinear pairings with high computational overhead. Due to the saving of computing cost, the proposed authentication key agreement protocol based on elliptic curve cryptography has higher efficiency and practical value under the same security requirements. Finally, based on the study of chaotic mapping, we propose a new key agreement protocol based on chaotic mapping, and give its security proof and efficiency analysis.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：O187;TN918

【共引文献】