Computing the 2-adic Canonical Lift of Genus 2 Curves
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Leer menos
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Idioma
en
Communication dans un congrès
Este ítem está publicado en
ICMC 2021 - 7th International Conference on Mathematics and Computing, 2021-03-02, Shibpur / Virtual.
Resumen en inglés
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined over k. We first compute modular polynomials in function of invariants with good reduction modulo two. We then use these ...Leer más >
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined over k. We first compute modular polynomials in function of invariants with good reduction modulo two. We then use these modular polynomials to compute the canonical lift of genus 2 curves in even characteristic. The lifted Frobenius is characterized by the reduction behaviors of the Weierstrass points over k. This allows us to compute the cardinality of the Jacobian variety. We give a detailed description with the necessary optimizations for an efficient implementation.< Leer menos
Palabras clave en inglés
Arithmetic invariants of genus 2 curves
Modular polynomials
Canonical lift
Point counting
Proyecto ANR
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Orígen
Importado de HalCentros de investigación