Factorisation patterns of division polynomials
The choice of an elliptic curve for the implementa- tion of an elliptic curve cryptosystem requires count- ing the number of points on such a curve over a fi- nite field. An improvement of Schoof’s algorithm for counting the number of rational points on an ellip- tic 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.
SeriesProceedings of the Japan Academy / Series A Mathematical sciences 80(2004) nr. 5, s. 79-82
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