文章基本信息

标题：Experimental Analysis of Cheon's Algorithm against Pairing-friendly Curves
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作者：Tetsuya Izu ; Masahiko Takenaka ; Masaya Yasuda 等
期刊名称：Information and Media Technologies
电子版ISSN：1881-0896
出版年度：2011
卷号：6
期号：4
页码：1175-1184
DOI：10.11185/imt.6.1175
出版社：Information and Media Technologies Editorial Board
摘要：Let G be an additive group generated by an element G of prime order r . The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α on inputs G , α G , α ^dG ∈ G for a positive integer d dividing r -1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3¹²⁷). Moreover, based on our experimental results, we estimate the required cost of Cheon's algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter d is chosen.