## Cryptology ePrint Archive: Report 2009/638

Reducing Elliptic Curve Logarithm to Logarithm in a Finite Field $\mathbb{F}_q$ for Some Orders

Wei Yu, Kunpeng Wang, Bao Li

Abstract: We change elliptic curve discrete logarithm problem to discrete logarithm problem of $\mathbb{F}_q$ using elliptic divisibility sequences. And the method works for the situation $\#E(\mathbb{F}_q)=q-1,q\pm \sqrt{q},q\pm \sqrt{2q-1},q\pm \sqrt{3q-2},q+\sqrt{4q-3}$.

Category / Keywords: foundations / elliptic curve discrete logarithm problem, discrete logarithm problem, elliptic divisibility sequences.

Date: received 31 Dec 2009, withdrawn 2 Jan 2010

Contact author: yuwei_1_yw at 163 com

Available format(s): (-- withdrawn --)

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