Improving the parallelized Pollard lambda search on anomalous binary curves

The best algorithm known for finding logarithms on an elliptic curve (E) is the (parallelized) Pollard lambda collision search. We show how to apply a Pollard lambda search on a set of equivalence classes derived from E, which requires fewer iterations than the standard approach. In the case of anomalous binary curves over F2m , the new approach speeds up the standard algorithm by a factor of 2m.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Robert P. Gallant, Robert J. Lambert, Scott A. Vanstone
• Keywords: MOC 2000, Pollard Lambda, Pollard Lambda Collision, Pollard Lambda Search