A reduction of the space for the parallelized Pollard lambda search on elliptic curves over prime finite fields and on anomalous binary elliptic curves

Igor Semaev

Paper 2003/166 Original: eprint.iacr.org/2003/166 ↗

A reduction of the space for the parallelized Pollard lambda search on elliptic curves over prime finite fields and on anomalous binary elliptic curves

Igor Semaev

Abstract

Let $E$ be an elliptic curve defined over a prime finite field $F_p$ by a Weierstrass equation. In this paper we introduce a new partition of $E(F_p)$ into classes which are generally larger than $\{\pm R\}$. We give an effective procedure to compute representatives of such classes. So one can iterate the pseudorandom function, related to a discrete logarithm problem in $E(F_p)$, on the set of representatives of classes and get probably some speed up in computing discrete logarithms. The underlying idea how to enlarge known classes on anomalous binary elliptic curves is given.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2003-08-11: last updated; 2003-08-11: published
Short URL: https://ia.cr/2003/166
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2003/166,
      author = {Igor Semaev},
      title = {A reduction of the space for the parallelized Pollard lambda search on elliptic curves over prime finite fields and on anomalous binary elliptic curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/166},
      year = {2003},
      url = {https://eprint.iacr.org/2003/166}
}