A Discrete Logarithm Attack on Elliptic Curves.
Otto Johnston · 2010
ABSTRACT. We give an improved index calculus attack for a large class of elliptic curves. Our algorithm works by efficiently transferring the group structure of an elliptic curve to a weaker group. The running time of our attack poses a significant and realistic threat to the security of the elliptic curves in this class. As a consequence of our construction, we will also derive entirely new point counting algorithms. These algorithms set new run-time complexity records. We discuss implementations of these algorithms and give examples. 1.