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Generating Prime Order Elliptic Curves: Difficulties and Efficiency (2005)
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| Venue: | Considerations, in International Conference on Information Security and Cryptology – ICISC 2004, Lecture Notes in Computer Science |
| Citations: | 4 - 4 self |
BibTeX
@INPROCEEDINGS{Konstantinou05generatingprime,
author = {Elisavet Konstantinou and Aristides Kontogeorgis and Yannis C. Stamatiou and Christos Zaroliagis},
title = {Generating Prime Order Elliptic Curves: Difficulties and Efficiency},
booktitle = {Considerations, in International Conference on Information Security and Cryptology – ICISC 2004, Lecture Notes in Computer Science},
year = {2005},
pages = {261--278},
publisher = {Springer}
}
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Abstract
Abstract. We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber ones, uniquely determined by the CM discriminant D. In attempting to construct prime order ECs using Weber polynomials two difficulties arise (in addition to the necessary transformations of the roots of such polynomials to those of their Hilbert counterparts). The first one is that the requirement of prime order necessitates that D ≡ 3 (mod 8), which gives Weber polynomials with degree three times larger than the degree of their corresponding Hilbert polynomials (a fact that could affect efficiency). The second difficulty is that these Weber polynomials do not have roots in Fp. In this paper we show how to overcome the above difficulties and provide efficient methods for generating ECs of prime order supported by a thorough experimental study. In particular,
Keyphrases
prime order elliptic curve weber polynomial cm discriminant class field polynomial weber one complex multiplication prime order ec crucial step hilbert counterpart special type prime order necessitates first one thorough experimental study corresponding hilbert polynomial efficient method second difficulty necessary transformation prime field fp prime order
