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**2003/166**

**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

**Authors:**
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.

**ePrint:**
https://eprint.iacr.org/2003/166

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