**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**Date: **received 31 Dec 2009, withdrawn 2 Jan 2010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**Available format(s): **(-- withdrawn --)

**Version: **20100102:131655 (All versions of this report)

**Short URL: **ia.cr/2009/638

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