Displaying similar documents to “Counting points in medium characteristic using Kedlaya's algorithm.”

Rigid cohomology and p -adic point counting

Alan G.B. Lauder (2005)

Journal de Théorie des Nombres de Bordeaux

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I discuss some algorithms for computing the zeta function of an algebraic variety over a finite field which are based upon rigid cohomology. Two distinct approaches are illustrated with a worked example.

On Elkies subgroups of ℓ -torsion points in elliptic curves defined over a finite field

Reynald Lercier, Thomas Sirvent (2008)

Journal de Théorie des Nombres de Bordeaux

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As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic p , there exists an algorithm that computes, for ℓ an Elkies prime, ℓ -torsion points in an extension of degree ℓ - 1 at cost O ˜ ( ℓ max ( ℓ , log q ) 2 ) bit operations in the favorable case where ℓ ≤ p / 2 . We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the p -adic approach followed by Joux and Lercier to get an algorithm...

Topics in computational algebraic number theory

Karim Belabas (2004)

Journal de Théorie des Nombres de Bordeaux

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We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the system.