Study on the security of elliptic curve discrete logarithm problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 23650006
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Fundamental theory of informatics
• Research Institution: Japan Advanced Institute of Science and Technology
• Principal Investigator: MIYAJI Atsuko 北陸先端科学技術大学院大学, 情報科学研究科, 教授 (10313701)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 暗号・認証等 / 楕円曲線暗号 / 安全性評価

Outline of Final Research Achievements

An elliptic curve cryptosystem is based on elliptic curve discrete logarithm
problem (ECDLP).An elliptic curve is uniquely determined by mathematical parameters such as j-invariant, trace, etc.The security of ECDLP is different from each elliptic curve, and there exist some ECDLP whose security is extremely low compared with others.This is why it is very important to find relation between mathematical parameters of elliptic curve and security level of ECDLP.However, only a few elliptic curves can explicitly give their security level by using their mathematical parameters.Recently, Hitt proves relations between security level and mathematical parameters of hyper elliptic curve.Hirasawa and Miyaji applied Hitt's approach to ECDLP and presented new relations between mathematical parameters and embedding degrees.In this research, we further extended their conditions and found new explicit relations between elliptic-curve parameters and embedding degrees.

Free Research Field

情報セキュリティ