Cryptology ePrint Archive: Report 2010/575

A Discrete Logarithm Attack on Elliptic Curves

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.

Category / Keywords: public-key cryptography /

Date: received 11 Nov 2010

Contact author: mail at ottojohnston com

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Version: 20101111:223802 (All versions of this report)

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