A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
This addresses cryptographic security for systems relying on elliptic curves, but it appears incremental as it builds on existing index-calculus techniques.
The paper tackles the elliptic curve discrete logarithm problem by proposing a new Las Vegas algorithm that leverages properties of elliptic curve groups, achieving a non-generic approach with similarities to index-calculus methods for finite fields.
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.