5 citations · 13 across the 13 of their papers we have counts for
14 papers
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…
A database of basic numerical invariants of Hilbert modular surfaces
Eran Assaf, Angelica Babei, Ben Breen +8
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
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…
Certified Newton schemes for the evaluation of low-genus theta functions
Jean Kieffer
Theta functions and theta constants in low genus, especially genus 1 and 2, can be evaluated at any given point in quasi-linear time in the required precision using Newton schemes…
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…
Degree and height estimates for modular equations on PEL Shimura varieties
Jean Kieffer
We define modular equations in the setting of PEL Shimura varieties as equations describing Hecke correspondences, and prove upper bounds on their degrees and heights. This extends…
Computing isogenies from modular equations in genus two
Jean Kieffer, Aurel Page, Damien Robert
We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be eit…
Towards practical key exchange from ordinary isogeny graphs
Luca De Feo, Jean Kieffer, Benjamin Smith
We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate ke…
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…