Research Paper 楕円曲線上の離散対数問題の安全性に関する研究

宮地, 充子

Description
楕円曲線上の離散対数問題 (ECDLP)は利用する楕円曲線E/F(p)により安全性が異なるため,安全性を何らかの手法で評価できることが望ましい.E/F(p)上のECDLPはE/F(p)から有限体F(p)の拡大体上のF(p^k)上への写像により,有限体上の離散対数問題(DLP)へ帰着する.この結果E/F(p)上のECDLPが拡大体F(p^k) 上のDLPと等価の安全性となる.本研究では,超楕円曲線上のHittによるアプローチを楕円曲線上に応用し,楕円曲線の元の個数に新たなパラメータr, L を導入し,このパラメータで楕円曲線E/F(p)のトレースと元の個数,拡大次数を記述することに成功した. : 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.
研究種目:挑戦的萌芽研究
研究期間:2011~2014
課題番号:23650006
研究者番号:10313701
研究分野:情報セキュリティ
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https://dspace.jaist.ac.jp/dspace/bitstream/10119/12817/1/23650006seika.pdf

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