Open Access
May 2004 Factorisation patterns of division polynomials
Hugues Verdure
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 79-82 (May 2004). DOI: 10.3792/pjaa.80.79


The choice of an elliptic curve for the implementation of an elliptic curve cryptosystem requires counting the number of points on such a curve over a finite field. An improvement of Schoof's algorithm for counting the number of rational points on an elliptic curve defined over a finite field takes advantage of some factor of the division polynomials. In this paper, we study the possible factorisations of such division polynomials.


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Hugues Verdure. "Factorisation patterns of division polynomials." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 79 - 82, May 2004.


Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1106.11019
MathSciNet: MR2062806
Digital Object Identifier: 10.3792/pjaa.80.79

Primary: 11T71 , 14H52

Keywords: division poynomial , Elliptic curve , factorisation

Rights: Copyright © 2004 The Japan Academy

Vol.80 • No. 5 • May 2004
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