5 citations · 13 across the 13 of their papers we have counts for
9 papers · 1 filter
Fast evaluation of Riemann theta functions in any dimension
Noam D. Elkies, Jean Kieffer
We describe an algorithm to numerically evaluate Riemann theta functions in any dimension in quasi-linear time in terms of the required precision, uniformly on reduced input. This…
The asymptotic distribution of Elkies primes for reductions of abelian varieties is Gaussian
Alexandre Benoist, Jean Kieffer
We generalize the notion of Elkies primes for elliptic curves to the setting of abelian varieties with real multiplication (RM), and prove the following. Let be an abelian vari…
Spanning isogeny classes of principally polarized abelian surfaces with RM
Jean Kieffer
We describe how isogenies between principally polarized abelian surfaces (PPAS) with real multiplication (RM) can be decomposed into elementary isogeny types. This leads to a strat…
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
Raymond van Bommel, Shiva Chidambaram, Edgar Costa +1
We describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface over with geometric endomorphism ring equal to , compute…
Counting points on abelian surfaces over finite fields with Elkies's method
Jean Kieffer
We generalize Elkies's method, an essential ingredient in the SEA algorithm to count points on elliptic curves over finite fields of large characteristic, to the setting of p.p. ab…
Upper bounds on the heights of polynomials and rational fractions from their values
Jean Kieffer
Let be a univariate polynomial or rational fraction of degree defined over a number field. We give bounds from above on the absolute logarithmic Weil height of in terms…
Evaluating modular equations for abelian surfaces
Jean Kieffer
We design efficient algorithms to evaluate modular equations of Siegel and Hilbert type for abelian surfaces over number fields or finite fields using complex approximations. Their…
Sign choices in the AGM for genus two theta constants
Jean Kieffer
Existing algorithms to compute genus 2 theta constants in quasi-linear time use Borchardt sequences, an analogue of the arithmetic-geometric mean for four complex numbers. In this…
Accelerating the Couveignes Rostovtsev Stolbunov key exchange protocol
Jean Kieffer
We study a key exchange protocol based on isogenies between ordinary elliptic curves over a finite field, first mentioned by Couveignes and investigated by Rostovtsev and Stolbunov…