## Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, discrete logarithms, Pollard lambda search

Contact author: Igor Semaev at wis kuleuven ac be

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