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

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(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.