A Las Vegas Algorithm to Solve the Elliptic Curve Discrete Logarithm Problem
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 on 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. The algorithm has no restriction on the finite field over which the elliptic curve is defined.
KeywordElliptic curve discrete logarithm problem
We are indebted to the anonymous referees for their careful reading of the manuscript and detail comments. Due to lack of time, we were not able to incorporate the new research directions suggested. However, those comments have certainly piqued our interest and we thank the referees for those.
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