Information and Media Technologies
Online ISSN : 1881-0896
ISSN-L : 1881-0896
Computing
Experimental Analysis of Cheon's Algorithm against Pairing-friendly Curves
Tetsuya IzuMasahiko TakenakaMasaya Yasuda
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2011 年 6 巻 4 号 p. 1175-1184

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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, αG, αdG ∈ 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.

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© 2011 Information Processing Society of Japan
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