Students

  • Ph.D.
    • Julien Soumier, Ph.D. started in Oct. 2023.
      Algorithms for Isogenies of Abelian Varieties. Applications to post-quantum cryptography.
    • Antoine Leudière, Ph.D. started in Oct. 2021.
      Isogenies of Drinfeld modules and post-quantum cryptography.
    • Aude Le Gluher, Sep. 2018 - Dec. 2021.
      Analysis and simulation of the number field sieve.
    • Simon Abelard, Sep. 2015 - Sep. 2018.
      Point counting on hyperelliptic curves defined over finite fields of large characteristic.
  • Master's theses.
    • Julien Soumier, Mar.-Sep. 2023.
      Algorithms for Isogenies of Abelian Varieties.
    • Antoine Leudière, Apr.-Sep. 2021.
      Isogenies of Drinfeld modules and post-quantum cryptography.
    • Aude Le Gluher, Feb.-July 2018.
      Geometric algorithms for computing Riemann-Roch spaces.
    • Léo Barré, Feb.-Aug. 2017.
      Cube attacks and cube testers for the cryptanalysis of Trivium. Co-supervision with Marine Minier.

Preprints

Journal papers

  • Computing a group action from the class field theory of imaginary hyperelliptic function fields.
    With Antoine Leudière.
    Journal of Symbolic Computation, 125:102311, 2024.
    arXiv.
  • Dimension results for extremal-generic polynomial systems over complete toric varieties.
    With Matías Bender.
    Journal of Algebra, 646:156-182, 2024.
    arXiv.
  • Refined analysis of the asymptotic complexity of the Number Field Sieve.
    With Aude Le Gluher and Emmanuel Thomé.
    Mathematical Cryptology, 1(1):71-88, 2021.
    Published version.
  • A fast randomized geometric algorithm for computing Riemann-Roch spaces.
    With Aude Le Gluher.
    Mathematics of Computation, 89:2399-2433, 2020.
    arXiv.
  • Improved complexity bounds for counting points on hyperelliptic curves.
    With Simon Abelard and Pierrick Gaudry.
    Foundations of Computational Mathematics. 19(3):591-621, 2019.
    arXiv.
  • A polyhedral method for sparse systems with many positive solutions.
    With Frédéric Bihan and Francisco Santos.
    SIAM Journal on Applied Algebra and Geometry, 2(4):620-645, 2018.
    arXiv.
    Published version.
  • A quadratically convergent algorithm for structured low-rank approximation.
    With Éric Schost.
    Foundations of Computational Mathematics. 16(2):457-492, 2016.
    arXiv. Maple code.
  • Exact solutions in structured low-rank approximation.
    With Giorgio Ottaviani and Bernd Sturmfels.
    SIAM Journal on Matrix Analysis and Applications. 35(4):1521-1542, 2014.
    [pdf].
  • On the complexity of computing critical points with Gröbner bases.
    SIAM Journal on Optimization. 24(3):1382-1401, 2014.
    [pdf].
  • On the complexity of the generalized Minrank problem.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Journal of Symbolic Computation. 55:30-58, 2013.
    [pdf].
  • On the complexity of solving quadratic boolean systems.
    With Magali Bardet, Jean-Charles Faugère, Bruno Salvy.
    Journal of Complexity, 29(1):53-75, 2013.
    [pdf].
  • Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): algorithms and complexity.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Journal of Symbolic Computation, 46(4):406-437, 2011.
    [pdf]

Articles in conference proceedings

  • Counting points on genus-3 hyperelliptic curves with explicit real multiplication.
    With Simon Abelard and Pierrick Gaudry.
    Proceedings of the Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series 2, 2019.
    Published paper. arXiv.
  • Critical points computations on smooth varieties: degree and complexity bounds.
    With Mohab Safey El Din.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2016 (ISSAC 2016).
    Held in Waterloo, Canada.
    arXiv.
  • Computing small certificates of inconsistency of quadratic fewnomial systems.
    With Jean-Charles Faugère and Jules Svartz.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2016 (ISSAC 2016).
    Held in Waterloo, Canada.
    arXiv.
  • Sparse Gröbner bases: the unmixed case.
    With Jean-Charles Faugère, Jules Svartz.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2014 (ISSAC 2014).
    Held in Kobe, Japan.
    Erratum.
    arXiv.
  • Critical points and Gröbner bases: the unmixed case.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2012 (ISSAC 2012).
    Held in Grenoble, France.
    [pdf]
  • Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology.
    With Jean-Charles Faugère, Mohab Safey El Din.
    Proceedings of the International Symposium on Symbolic and Algebraic Computation 2010 (ISSAC 2010).
    Held in Munich, Germany.
    Distinguished Student Author Award.
    [pdf]
  • Algebraic cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
    With Jean-Charles Faugère.
    Proceedings of the 13th International Conference on Practice and Theory in Public Key Cryptography (PKC 2010).
    Held in Paris, France.
    [pdf] slides

Unpublished work

  • Sparse polynomial systems with many positive solutions from bipartite simplicial complexes.
    With Frédéric Bihan. arXiv. Unpublished work. Most of the results have been strengthened in this paper.
  • Computing the rho constant.
    With Jérémie Detrey and Paul Zimmermann. Unpublished work. Short note on the computation of the density of integer numbers such that the number of distinct prime factors has the same parity as the number prime factors counted with multiplicity. Note (pdf).

Ph.D. thesis

  • Solving multi-homogeneous and determinantal systems.
    Algorithms - Complexity - Applications.
    Supervisors: Jean-Charles Faugère, Mohab Safey El Din.
    PolSys project-team (INRIA/UPMC/LIP6).
    Université Pierre et Marie Curie, 2012.
    [pdf]
    [Erratum]

Posters

  • Newton-like iteration for determinantal systems and structured low-rank approximation.
    Éric Schost, Pierre-Jean Spaenlehauer.
    International Symposium on Symbolic and Algebraic Computation 2013 (ISSAC 2013).
    Held in Boston, USA.
    abstract[pdf].