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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Improving the parallelized Pollard lambda
search on anomalous binary curves


Authors: Robert Gallant, Robert Lambert and Scott Vanstone
Journal: Math. Comp. 69 (2000), 1699-1705
MSC (1991): Primary 94A60, 14Q05, 14H52
Published electronically: May 19, 1999
MathSciNet review: 1651754
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 $\sqrt{2m}$.


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Additional Information

Robert Gallant
Affiliation: Certicom Corp., 200 Matheson Blvd. W., Suite 103, Mississauga, Ontario, Canada L5R 3L7
Email: rgallant@certicom.com

Robert Lambert
Affiliation: Certicom Corp., 200 Matheson Blvd. W., Suite 103, Mississauga, Ontario, Canada L5R 3L7
Email: rlambert@certicom.com

Scott Vanstone
Affiliation: Certicom Corp., 200 Matheson Blvd. W., Suite 103, Mississauga, Ontario, Canada L5R 3L7
Email: svanstone@certicom.com

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01119-9
PII: S 0025-5718(99)01119-9
Received by editor(s): June 9, 1998
Received by editor(s) in revised form: October 15, 1998
Published electronically: May 19, 1999
Article copyright: © Copyright 2000 American Mathematical Society