Elliptic divisibility sequences and the elliptic curve discrete logarithm problem

Rachel Shipsey; Christine Swart

Paper 2008/444 Original: eprint.iacr.org/2008/444 ↗

Elliptic divisibility sequences and the elliptic curve discrete logarithm problem

Rachel Shipsey

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 $\#E(\mathbb{F}_q) = q-1$.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2008-10-20: last updated; 2008-10-20: published
Short URL: https://ia.cr/2008/444
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2008/444,
      author = {Rachel Shipsey and Christine Swart},
      title = {Elliptic divisibility sequences and the elliptic curve discrete logarithm problem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/444},
      year = {2008},
      url = {https://eprint.iacr.org/2008/444}
}