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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 F 2 m, the new approach speeds up the standard algorithm by a factor of √2m.

Improving the parallelized Pollard lambda search on anomalous binary curves