25 citations · 83 across the 11 of their papers we have counts for
6 papers · 1 filter
Computing Isomorphisms between Products of Supersingular Elliptic Curves
Pierrick Gaudry, Julien Soumier, Pierre-Jean Spaenlehauer
The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for…
Counting points on genus-3 hyperelliptic curves with explicit real multiplication
Simon Abelard, Pierrick Gaudry, Pierre-Jean Spaenlehauer
We propose a Las Vegas probabilistic algorithm to compute the zeta function of a genus-3 hyperelliptic curve defined over a finite field , with explicit real multiplic…
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
Simon Abelard, Pierrick Gaudry, Pierre-Jean Spaenlehauer
We present a probabilistic Las Vegas algorithm for computing the local zeta function of a hyperelliptic curve of genus defined over . It is based on the approache…
Improvements to the number field sieve for non-prime finite fields
Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic +1
We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes…
Counting Points on Genus 2 Curves with Real Multiplication
Pierrick Gaudry, David Kohel, Benjamin Smith
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm red…
The -adic CM-method for genus 2
P. Gaudry, T. Houtmann, D. Kohel +2
We present a nonarchimedian method to construct hyperelliptic CM-curves of genus 2.