The geometry of some parameterizations and encodings
COUVEIGNES, Jean-Marc
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
COUVEIGNES, Jean-Marc
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Language
en
Article de revue
This item was published in
Advances in Mathematics of Communications. 2014-12-01, vol. 8, n° 4, p. 22
AIMS
English Abstract
We report on current work on parameterization of low genera algebraic curves. For example, we prove that for $q$ a prime power that is large enough and prime to 6, a fixed positive proportion of all genus two curves over ...Read more >
We report on current work on parameterization of low genera algebraic curves. For example, we prove that for $q$ a prime power that is large enough and prime to 6, a fixed positive proportion of all genus two curves over the field with $q$ elements can be parameterized by 3-radicals. This results in the existence of a deterministic encoding into these curves when $q$ is congruent to 2 modulo 3. Abstract of a talk given at GEOCRYPT 2013, Papeete.Read less <
English Keywords
encodings
deterministic algorithms
finite fields
algebraic curves
parameterizations
radicals
torsors
ANR Project
Espaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes - ANR-12-BS01-0010
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported