Schoof's algorithm: Difference between revisions

Revision as of 09:32, 12 July 2016

Revision as of 16:18, 29 October 2016

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One could try to symbolically compute these points <math>(x^{q^{2}}, y^{q^{2}})</math>, <math>(x^{q}, y^{q})</math> and <math>q(x, y)</math> as functions in the [[Imaginary hyperelliptic curve#Coordinate ring|coordinate ring]] <math>\mathbb{F}_{q}[x,y]/(y^{2}-x^{3}-Ax-B)</math> of <math>E</math>

and thethen search for a value of <math>t</math> which satisfies the equation. However, the degrees get very large and this approach is impractical.

Schoof's idea was to carry out this computation restricted to points of order <math>l</math> for various small primes <math>l</math>.