Arithmétique, Géométrie, Cryptographie et Théorie des Codes
18 au 22 mai 2015
Cette conférence porte sur les interactions entre l’arithmétique, la géométrie algébrique et les sciences de l’information et de la communication et plus particulièrement le codage et la cryptologie. 

Les thèmes abordés seront:
– Théorie des nombres, comportement asymptotique de familles de corps globaux.
– Géométrie arithmétique, courbes algébriques sur des corps finis ou sur des corps de nombres, variétés abéliennes : méthodes de comptage de points, aspects théoriques, effectifs et algorithmiques.
– Théorie des codes, codes algébriques, codes géométriques
construits à partir de courbes algébriques ou de variétés de dimension supérieures, algorithmes de décodage algébriques.
– Cryptographie, courbes elliptiques et variétés abéliennes : problème du logarithme discret, pairings, calcul explicite d’isogénies.
– Fonctions booléennes, fonctions courbes, fonctions APN: construction de familles de fonctions courbes et hypercourbes.

Comité scientifique & Comité d’organisation

Alp Bassa (University of Bogazici)
Alain Couvreur (INRIA – LIX)
David Kohel (Aix-Marseille Université)


On idempotent quadratic functions and the weight distribution of subcodes of Reed-Muller codes

An Analogue of Vosper’s Theorem for Extension Fields

Valuations of Exponential Sums, Congruences for L-Functions, and

Computing  $L$-functions of superelliptic curves

An upper bound on the number of points of a projective variety and a proof of a conjecture of Ghorpade and Lachaud

Of Kisin varieties and Galois deformation rings

Class Formula in Positive Characteristic

Algebraic Curves with Many Rational Points over Non-Prime Finite Fields

Tsfasman-Boguslavsky Conjecture for Polynomial Systems
and Generalized Hamming Weights of Projective Reed-Muller Codes

Computing Discrete logarithms in GF(p n): Practical Improvement of the Individual Logarithm Step

Weil Bounds of Higher Orders

An Analogue of a Theorem of Tallini on Plane Curves over Finite Fields

  • Everett Howe (Center for Communications Research, San Diego)

Polarizations on E x E and genus-4 curves with many points

Towards maximal singular curves over finite fields

A Simplified Setting for Discrete Logarithms in Small Characteristic Finite Fields

On double sparse compressed sensing via coding theory and its different applications

Bounding Brill-Noether loci over finite fields, with applications to Jacobian arithmetic

On extremal traces and RM in genus 2

On the Number of Points of Algebraic Sets  over Finite Fields

  • Christine Lauter (Microsoft Research Redmon)

A new hard problem?  (Ring) Learning With Errors

Covariant Algebra of the Binary Nonic and the Binary Decimic

  • Bernard Le Stum (Université Rennes 1)

An Introduction to Rigid Cohomology

Structural Cryptanalysis of McEliece Schemes with Algebraic Geometry Codes

Estimates on the Number of Rational Points of Singular Complete Intersections over a Finite Field and Applications

  • Tohru Nakashima (Kyoto University)

AG Codes from Restriction of Vector Bundles to Divisors

Some developments on towers over cubic finite fields

Power Decoding of Hermitian One-Point Codes in Sub-Quadratic Time

Bad Reduction of Genus Three Curves with Complex Multiplication

Graph based strategy to exhibit good recursive towers

Algebraic cycles on varieties over finite fields

A new proof of a Thomae like-formula for non hyperelliptic genus 3 curves

  • Yieh-Dar Shieh (Aix-Marseille Université)

Character theory and Sato-Tate groups

Branches and Descent

Slightly more practical quantum factoring through number theory

Adelic points of elliptic curves

  • Claudio Stirpe (IIS Marconi, Anagni)

New results on class numberone problem for function fields

Generators of the group of modularunits

Computing the image of Galois representations attached to elliptic curves

On the Torsion-Limit for Algebra Function Fields

  • Florent Ulpat-Rovetta (Aix-Marseille Université)

Construction of genus two curve starting from their invariants in characteristic 5

Field extensions and index calculus on algebraic curve

  • Serge Vladuts (Aix-Marseille Université)

Locally recoverable codes on algebraic curves