# A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem

## TL;DR

This paper introduces a novel Las Vegas algorithm tailored for the elliptic curve discrete logarithm problem, leveraging specific properties of elliptic curve groups, and sharing similarities with index-calculus methods for finite fields.

## Contribution

It presents a new non-generic algorithm based on elliptic curve group properties, expanding the toolkit for solving elliptic curve discrete logarithms.

## Key findings

- Algorithm depends on elliptic curve group properties
- Shares similarities with index-calculus for finite fields
- Offers a potentially more efficient approach

## Abstract

In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the group of rational points of an elliptic curve and is thus not a generic algorithm. The algorithm that we describe has some similarities with the most powerful index-calculus algorithm for the discrete logarithm problem over a finite field.