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Abstract: We propose a method for increasing the speed of scalar multiplication on binary anomalous (Koblitz) elliptic curves. By introducing a generator which produces random pairs (k, [k]P ) of special shape, we exhibit a specific setting where the number of elliptic curve operations is reduced by 25% to 50% compared with the general case when k is chosen uniformly. This generator can be used when an ephemeral pair (k, [k]P ) is needed by a cryptographic algorithm, and especially for Elliptic... (Update)
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BibTeX entry: (Update)
@article{ coron01fast,
author = "Jean-S{\'e}bastien Coron and David M'Ra{\"\i}hi and Christophe Tymen",
title = "Fast Generation of Pairs $(k,[k]{P})$ for {Koblitz} Elliptic Curves",
journal = "Lecture Notes in Computer Science",
volume = "2259",
pages = "151--??",
year = "2001",
url = "citeseer.ist.psu.edu/coron01fast.html" }
Citations (may not include all citations):257 Elliptic curve cryptosystems (context) - Koblitz - 1987
101 A survey of fast exponentiation methods - Gordon - 1998
49 CM-curves with good cryptographic properties (context) - Koblitz - 1991
20 Speeding up discrete log and factoring based schemes via pre.. - Boyko, Peinado et al. - 1998
12 cient multiplication on certain non-supersingular elliptic c.. (context) - Meier, Sta - 1993
6 cient finite field basis conversion (context) - Jr, Yin - 1998
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