Students

  • Ph.D.
    • Aude Le Gluher, Ph.D. started in Sep. 2018.
      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.
    • Aude Le Gluher, Feb.-July 2018.
      Geometric algorithms for computing Riemann-Roch spaces.
    • Léo Barré, Feb.-Aug. 2018.
      Cube attacks and cube testers for the cryptanalysis of Trivium.

Journal papers

  • A polyhedral method for sparse systems with many positive solutions.
    With Frédéric Bihan and Francisco Santos.
    To appear in the SIAM Journal on Applied Algebra and Geometry.
    arXiv.
  • Improved Complexity Bounds for Counting Points on Hyperelliptic Curves.
    With Simon Abelard and Pierrick Gaudry.
    To appear in Foundations of Computational Mathematics.
    arXiv.
  • 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] Magma Code

Articles in conference proceedings

  • Counting points on genus-3 hyperelliptic curves with explicit real multiplication.
    With Simon Abelard and Pierrick Gaudry.
    Proceedings of the 13th Algorithmic Number Theory Symposium (ANTS-XIII).
    Held in Madison, USA, 2018.

    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.

    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 Magma Code

Preprints

  • A Fast Randomized Geometric Algorithm for Computing Riemann-Roch Spaces.
    With Aude Le Gluher. arXiv.

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].

Talks in workshops and conferences

  • Critical points computations on smooth varieties: degree and complexity bounds. ISSAC 2016. Waterloo, Ontario, Canada. July 20-22, 2016.
  • Computing small certificates of inconsistency of quadratic fewnomial systems. ISSAC 2016. Waterloo, Ontario, Canada. July 20-22, 2016.
  • Sparse polynomial systems with many positive solutions from bipartite simplicial complexes.
    • Workshop on Algebra, Geometry and Proofs in Symbolic Computation. Fields Institute, Toronto, Canada. December 7-16, 2015.
  • A quadratically convergent algorithm for Structured Low-Rank Approximation.
    • ICIAM 2015, Workshop on hybrid methodologies for symbolic-numeric computations, Beijing, China, August 10-13, 2015.
    • RAIM 2013. Institut Henri Poincaré, Paris, France. November 18-20, 2013.
    • Numerical methods and computations. CIRM, Luminy, France. October 28-31, 2013.
  • Exact solutions in structured low-rank approximation.
    • SIAM Conference on Applied Algebraic Geometry. Daejeon, Korea, August 3-7, 2015. Minisymposium on ML Degree and Critical Points.
    • SLRA workshop. Grenoble, France. June, 1, 2015.
  • Sparse Gröbner bases: the unmixed case.
    • SIAM Conference on Applied Algebraic Geometry. Daejeon, Korea, August 3-7, 2015. Minisymposium on Algorithms and Complexity in Polynomial Systems.
    • Conference on Effective Moduli Spaces and Applications to Cryptology. Rennes, France. June, 12, 2014.
  • Gröbner bases and bilinear systems.
    DLP 2014. Ascona, Switzerland. May, 06, 2014.
  • Solving Determinantal and Quadratic Boolean Systems. Applications to Algebraic Cryptanalysis.
    Journées C2 2014, Invited talk. Grenoble, France. March, 26, 2014.
    slides[pdf]
  • Critical Points and Gröbner Bases: the Mixed Case.
    • Workshop on Gröbner Bases, Resultants and Linear Algebra. RISC, Hagenberg, Austria. September 3-6, 2013.
    • SIAM Conference on Applied Algebraic Geometry. Fort Collins, CO, USA. August 1-4, 2013. Mini-Symposium on Algorithms in Real Algebraic Geometry.
  • Critical Points and Gröbner Bases: the Unmixed Case.
    ISSAC 2012. Grenoble, France. July 22-25, 2012.
  • On the Complexity of Solving Boolean Quadratic Systems.
    SIAM Conference on Applied Algebraic Geometry. Raleigh, NC, USA. October 6-9, 2011. Mini-Symposium on Algebraic Complexity.
  • Gröbner bases of Structured Systems and their Applications in Cryptology.
    MAYA Workshop 2011. Bochum, Germany. July 28-29, 2011.
    slides[pdf]
  • Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology.
    ISSAC 2010. Munich, Germany. July 25-28, 2010.
    slides[pdf]
  • Algebraic Cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
    PKC 2010. Paris, France. May 26-28, 2010.
    slides[pdf]
  • Algebraic-Differential Cryptanalysis of DES.
    Weworc 2009. Graz, Austria. July 7-9, 2009.
    summary[pdf] slides[pdf]