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Title:
On the correct use of the negation map in the Pollard rho method
Authors: Daniel J. Bernstein, Tanja Lange, Peter Schwabe
Abstract:Bos, Kaihara, Kleinjung, Lenstra, and Montgomery recently showed that ECDLPs on the 112-bit secp112r1 curve can be solved in an expected time of 65 years on a PlayStation 3. This paper shows how to solve the same ECDLPs at almost twice the speed on the same hardware. The improvement comes primarily from a new variant of Pollard’s rho method that fully exploits the negation map without branching, and secondarily from improved techniques for modular arithmetic.
ePrint: https://eprint.iacr.org/2011/003
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