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Title:
A Discrete Logarithm Attack on Elliptic Curves
Authors: Otto Johnston
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.
ePrint: https://eprint.iacr.org/2010/575
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