公钥密码方案构造及安全证明的知识要点和方法论  

Key Points and Methodology in Constructions and Security Proofs of Public-key Cryptosysems

作　　者：赵臻 吴戈 赖建昌 蒋芃 朱斌瑞 穆怡 苏西洛 郭福春 ZHAO Zhen;WU Ge;LAI Jian-Chang;JIANG Peng;ZHU Bin-Rui;MU Yi;SUSILO Willy;GUO Fu-Chun(University of Wollongong,Wollongong,Australia)

机构地区：[1]伍伦贡大学

出　　处：《密码学报》2019年第1期1-17,共17页Journal of Cryptologic Research

摘　　要：公钥密码是现代密码学的重要组成部分,其研究的难点在于方案构造技巧以及安全证明技巧的双重多样性.本文首先归纳总结了构造可证明安全的公钥密码方案所需要掌握的知识要点,包括基本概念、数学基础、简单问题和困难问题、算法、安全模型以及安全归约证明.这些知识要点是学习方案构造以及安全证明的不可或缺的基础部分,也是最先需要掌握的部分.其次,根据作者自身的学习经历、指导学生的经验以及来自学生的反馈,本文给出了学习构造可证明安全的公钥密码方案的方法,包括方案构造学习、安全证明学习以及构造可证明安全密码方案.我们推荐了30个经典的方案及其证明用于该阶段的练习.最后,本文列出了在学习过程中所需要思考与总结的内容,这些内容是对所掌握的知识与技巧的提炼.通过反复地思考与总结能够进一步加深对知识与技巧的理解.希望这些工作能够对读者,尤其是对基础比较薄弱的读者,在掌握如何构造可证明安全的公钥密码方案方面起到一定的指引作用.Public-key cryptography(PKC) is an important branch of cryptography. The diversity of PKC scheme constructions and security proofs make the research in PKC a challenging task. This paper first summarizes the fundamental knowledge, which is required for provable security in the PKC settings, including basic concepts, mathematical foundation, easy and hard problems, algorithms,security models, and security reduction. Such knowledge is essential for the study of PKC scheme constructions and security proofs. This paper then presents the studies of methods for constructing a provably secure PKC schemes, including how to construct such a scheme, how to present security proofs, and how to construct such a scheme with provable security. 30 such schemes and their proofs for practices are illustrated. It also gives a summary of the way of thinking when studying PKC, which is helpful to further understand the techniques. This paper is expected to be helpful for the reader to understand how to construct provably secure public-key cryptographic schemes, especially for those with a weak cryptographic background.

关 键 词：公钥密码 方案构造 安全证明 知识要点 方法论 

分 类 号：TN918.1[电子电信—通信与信息系统]