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Paper 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 PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystemdiscrete logarithmsPollard lambda search
Contact author(s)
Igor Semaev @ wis kuleuven ac be
History
2003-08-11: received
Short URL
https://ia.cr/2003/166
License
Creative Commons Attribution
CC BY
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