Computing the Canonical Lift of Genus 2 Curves in Odd Characteristics
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
English Abstract
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and if available the Hilbert modular polynomials to compute the canonical lift of A. As an application, if q = p n , we show ...Read more >
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and if available the Hilbert modular polynomials to compute the canonical lift of A. As an application, if q = p n , we show how to use the canonical lift to count the number of points on A in quasi-quadratic time Õ(n 2), this is a direct extension of Satoh's original algorithm for elliptic curves. We give a detailed description with the necessary optimizations for an efficient implementation.Read less <
English Keywords
Abelian variety
Arithmetic invariants of genus 2 curves
Modular polynomials
Canonical lift
Point counting
ANR Project
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Origin
Hal imported