Efficient arithmetic on Koblitz curves (2000)
| Venue: | Designs, Codes, and Cryptography |
| Citations: | 65 - 0 self |
BibTeX
@ARTICLE{Solinas00efficientarithmetic,
author = {Jerome A. Solinas},
title = {Efficient arithmetic on Koblitz curves},
journal = {Designs, Codes, and Cryptography},
year = {2000},
pages = {195--249}
}
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Abstract
Abstract. It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 % faster than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.
