**Elliptic divisibility sequences and the elliptic curve discrete logarithm problem**

*Rachel Shipsey and Christine Swart*

**Abstract: **We use properties of the division polynomials of an elliptic curve
$E$ over a finite field $\mathbb{F}_q$ together with a pure result about elliptic divisibility sequences from the 1940s to construct a very simple alternative to the Menezes-Okamoto-Vanstone algorithm for
solving the elliptic curve discrete logarithm problem in the case
where $\#E(\mathbb{F}_q) = q-1$.

**Category / Keywords: **public-key cryptography / elliptic divisibility sequences, elliptic curve cryptography, elliptic curve discrete log problem

**Date: **received 16 Oct 2008

**Contact author: **christine swart at uct ac za

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20081020:192618 (All versions of this report)

**Short URL: **ia.cr/2008/444

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