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On the construction of prime order elliptic curves
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| Venue: | Progress in cryptology—INDOCRYPT 2003, Springer Lecture Notes in Computer Science |
| Citations: | 5 - 1 self |
BibTeX
@INPROCEEDINGS{Konstantinou_onthe,
author = {Elisavet Konstantinou and Yannis C. Stamatiou and Christos Zaroliagis},
title = {On the construction of prime order elliptic curves},
booktitle = {Progress in cryptology—INDOCRYPT 2003, Springer Lecture Notes in Computer Science},
year = {},
pages = {309--322}
}
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Abstract
Abstract. We consider a variant of the Complex Multiplication (CM) method for constructing elliptic curves (ECs) of prime order with additional security properties. Our variant uses Weber polynomials whose discriminant D is congruent to 3 (mod 8), and is based on a new transformation for converting roots of Weber polynomials to their Hilbert counterparts. We also present a new theoretical estimate of the bit precision required for the construction of the Weber polynomials for these values of D. We conduct a comparative experimental study investigating the time and bit precision of using Weber polynomials against the (typical) use of Hilbert polynomials. We further investigate the time efficiency of the new CM variant under four different implementations of a crucial step of the variant and demonstrate the superiority of two of them. 1
Keyphrases
prime order elliptic curve weber polynomial bit precision time efficiency new cm variant complex multiplication elliptic curve comparative experimental study crucial step new transformation hilbert counterpart hilbert polynomial additional security property different implementation new theoretical estimate variant us weber polynomial prime order
