Design and analysis of public-key encryption algorithms from computationally intractable problems.

(1)综述了近年来关于计算难处理问题的平均情况复杂度与最坏情况复杂度之间的差距的研究成果，并考虑了这类问题在密码学中的应用。(2)设计（超）椭圆曲线密码系统，并报告其软件实现的实际性能。(3)发展新的公钥加密方案的可证明安全性技术，并阐明应用方案相对于现有方案的优点。(4)冈本研究员组织了国际密码会议。ASIACRYPTO 2000（2000年12月，京都）作为项目主席和首席研究员，樱井是项目委员会的成员。超过250人参加了成功的会议。(5)研究员冈本开了第一个研讨会，“数论算法及其应用。包括南极洲人和计算机科学家在内的100多名研究人员参加了讨论。首席研究员樱井就该研究项目发表了讲话。

(1) Survey recent results on the gap between the average-case complexity and the worst-case complexity on computationally intractable problems, then consider the cryptographic application of these problem.(2) Design (hyper) elliptic-curve cryptosystems, and report their practical performances from software-implementation.(3) Develop new techniques of provable security in public-key encryption schemes, and clarify advantages of applied schemes over the existing schemes.(4) The investigator, Okamoto organized the international cryptographic conference. ASIACRYPTO2000 (Dec. 2000, Kyoto) as the Program-Chair and the head investigator, SAKURAI worked as a member of the Program-comittee. More than 250-people attended with successful conference.(5) The investigator, Okamoto opened the 1st workshop, "number-theoretic algorithms and their applications. " More than 100-researchers including mathematicans and computer-scientists attended for discussing. The head investigator, SAKURAI gave a talk as a result of this research-project.