Abstract
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.
Citation
Hugues Verdure. "Factorisation patterns of division polynomials." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 79 - 82, May 2004. https://doi.org/10.3792/pjaa.80.79
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