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 RiemannRoch spaces.
 Léo Barré, Feb.Aug. 2018.
Cube attacks and cube testers for
the cryptanalysis of Trivium. Cosupervision with Marine
Minier.
Preprints
 Refined analysis of the asymptotic complexity of the Number Field Sieve.
With Aude Le Gluher and Emmanuel Thomé.
arXiv.
Journal papers
 A fast randomized geometric algorithm for computing RiemannRoch
spaces.
With Aude Le Gluher.
Mathematics of Computation, 89:23992433, 2020.
arXiv.
 Improved complexity bounds for counting points on hyperelliptic
curves.
With Simon Abelard and Pierrick Gaudry.
Foundations of Computational Mathematics. 19(3):591621, 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):620645, 2018.
arXiv.
Published version.
 A quadratically convergent algorithm for structured lowrank
approximation.
With Éric Schost.
Foundations of
Computational Mathematics. 16(2):457492, 2016.
arXiv. Maple code.
 Exact solutions in structured lowrank approximation.
With Giorgio Ottaviani and Bernd Sturmfels.
SIAM Journal on Matrix Analysis and Applications. 35(4):15211542, 2014.
[pdf].
 On the complexity of computing critical points with Gröbner bases.
SIAM Journal on Optimization. 24(3):13821401, 2014.
[pdf].

On the complexity of the generalized Minrank problem.
With JeanCharles Faugère, Mohab Safey El Din.
Journal of Symbolic Computation. 55:3058, 2013.
[pdf].

On the complexity of solving quadratic boolean systems.
With Magali Bardet, JeanCharles Faugère, Bruno Salvy.
Journal of Complexity, 29(1):5375, 2013.
[pdf].

Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): algorithms and complexity.
With JeanCharles Faugère, Mohab Safey El Din.
Journal of Symbolic Computation, 46(4):406437, 2011.
[pdf] Magma Code
Articles in conference proceedings
 Counting points on genus3 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 JeanCharles 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 JeanCharles 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 JeanCharles 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 JeanCharles 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 JeanCharles 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
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 multihomogeneous and determinantal systems.
Algorithms  Complexity  Applications.
Supervisors: JeanCharles Faugère, Mohab Safey El Din.
PolSys projectteam (INRIA/UPMC/LIP6).
Université Pierre et Marie Curie, 2012.
[pdf]
[Erratum]
Posters

Newtonlike iteration for determinantal systems and structured lowrank approximation.
Éric Schost, PierreJean 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 2022, 2016.
 Computing small certificates of inconsistency of quadratic
fewnomial systems.
ISSAC 2016. Waterloo, Ontario, Canada. July 2022, 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 716, 2015.

A quadratically convergent algorithm for Structured LowRank Approximation.
 ICIAM 2015, Workshop on hybrid methodologies for symbolicnumeric computations, Beijing, China, August 1013, 2015.
 RAIM 2013. Institut Henri Poincaré, Paris, France. November 1820, 2013.
 Numerical methods and computations. CIRM, Luminy, France. October 2831, 2013.

Exact solutions in structured lowrank approximation.
 SIAM Conference on Applied Algebraic Geometry. Daejeon, Korea,
August 37, 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 37, 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 36, 2013.
 SIAM Conference on Applied Algebraic Geometry. Fort Collins, CO, USA. August 14, 2013. MiniSymposium on Algorithms in Real Algebraic Geometry.
 Critical points and Gröbner bases: the unmixed case.
ISSAC 2012. Grenoble, France. July 2225, 2012.

On the complexity of solving boolean quadratic systems.
SIAM Conference on Applied Algebraic Geometry. Raleigh, NC, USA. October 69, 2011. MiniSymposium on Algebraic Complexity.

Gröbner bases of structured systems and their applications in cryptology.
MAYA Workshop 2011. Bochum, Germany. July 2829, 2011.
slides[pdf]

Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology.
ISSAC 2010. Munich, Germany. July 2528, 2010.
slides[pdf]

Algebraic cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem.
PKC 2010. Paris, France. May 2628, 2010.
slides[pdf]

Algebraicdifferential cryptanalysis of DES.
Weworc 2009. Graz, Austria. July 79, 2009.
summary[pdf] slides[pdf]