This paper introduces streamlined constant-time variants of Euclid’s algorithm, both for polynomial inputs and for integer inputs. As concrete applications, this paper saves time in (1) modular inversion for Curve255...
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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 Play Station 3. This paper shows how to solve the same ECD...
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ISBN:
(纸本)9783642193781
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 Play Station 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.
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