Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. - Jean-Charles Faugère; Mohab Safey El Din; Pierre-Jean Spaenlehauer (ISSAC, 2010)

Algebraic Cryptanalysis of the PKC'2009 Algebraic Surface Cryptosystem. - Jean-Charles Faugère; Pierre-Jean Spaenlehauer (Public Key Cryptography, 2010)

Gröbner Bases of Bihomogeneous Ideals generated by Polynomials of Bidegree (1,1): Algorithms and Complexity - Jean-Charles Faugère; Mohab Safey El Din; Pierre-Jean Spaenlehauer (CoRR, 2010)

Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1, 1): Algorithms and complexity. - Jean-Charles Faugère; Mohab Safey El Din; Pierre-Jean Spaenlehauer (J. Symb. Comput., 2011)

Critical points and Gröbner bases: the unmixed case. - Jean-Charles Faugère; Mohab Safey El Din; Pierre-Jean Spaenlehauer (ISSAC, 2012)

Solving multi-homogeneous and determinantal systems: algorithms, complexity, applications. (Résolution de systèmes multi-homogènes et déterminantiels : algorithmes, complexité, applications). - Pierre-Jean Spaenlehauer (2012)

Newton-like iteration for determinantal systems and structured low rank approximation. - Éric Schost; Pierre-Jean Spaenlehauer (ACM Commun. Comput. Algebra, 2013)

Algebraic Methods for Structured Low-Rank Approximation. - Giorgio Ottaviani; Pierre-Jean Spaenlehauer; Bernd Sturmfels (CoRR, 2013)

Complexity Bounds for Computing Critical Points with Gröbner Bases Algorithms: the Mixed Case. - Pierre-Jean Spaenlehauer (CoRR, 2013)

On the complexity of solving quadratic Boolean systems. - Magali Bardet; Jean-Charles Faugère; Bruno Salvy; Pierre-Jean Spaenlehauer (J. Complex., 2013)

On the complexity of the generalized MinRank problem. - Jean-Charles Faugère; Mohab Safey El Din; Pierre-Jean Spaenlehauer (J. Symb. Comput., 2013)

Sparse Gröbner bases: the unmixed case. - Jean-Charles Faugère; Pierre-Jean Spaenlehauer; Jules Svartz (ISSAC, 2014)

On the Complexity of Computing Critical Points with Gröbner Bases. - Pierre-Jean Spaenlehauer (SIAM J. Optim., 2014)

Exact Solutions in Structured Low-Rank Approximation. - Giorgio Ottaviani; Pierre-Jean Spaenlehauer; Bernd Sturmfels (SIAM J. Matrix Anal. Appl., 2014)

Sparse Gröbner bases: algorithms and complexity. - Jean-Charles Faugère; Pierre-Jean Spaenlehauer; Jules Svartz (ACM Commun. Comput. Algebra, 2015)

Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes. - Frédéric Bihan; Pierre-Jean Spaenlehauer (CoRR, 2015)

Critical Point Computations on Smooth Varieties: Degree and Complexity Bounds. - Mohab Safey El Din; Pierre-Jean Spaenlehauer (ISSAC, 2016)

Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems. - Jean-Charles Faugère; Pierre-Jean Spaenlehauer; Jules Svartz (ISSAC, 2016)

A Quadratically Convergent Algorithm for Structured Low-Rank Approximation. - Éric Schost; Pierre-Jean Spaenlehauer (Found. Comput. Math., 2016)

Counting points on genus-3 hyperelliptic curves with explicit real multiplication. - Simon Abelard; Pierrick Gaudry; Pierre-Jean Spaenlehauer (CoRR, 2018)

A Polyhedral Method for Sparse Systems with Many Positive Solutions. - Frédéric Bihan; Francisco Santos; Pierre-Jean Spaenlehauer (SIAM J. Appl. Algebra Geom., 2018)

Improved Complexity Bounds for Counting Points on Hyperelliptic Curves. - Simon Abelard; Pierrick Gaudry; Pierre-Jean Spaenlehauer (Found. Comput. Math., 2019)

Refined Analysis of the Asymptotic Complexity of the Number Field Sieve. - Aude Le Gluher; Pierre-Jean Spaenlehauer; Emmanuel Thomé (IACR Cryptol. ePrint Arch., 2020)

A fast randomized geometric algorithm for computing Riemann-Roch spaces. - Aude Le Gluher; Pierre-Jean Spaenlehauer (Math. Comput., 2020)

Hard Homogeneous Spaces from the Class Field Theory of Imaginary Hyperelliptic Function Fields. - Antoine Leudière; Pierre-Jean Spaenlehauer (IACR Cryptol. ePrint Arch., 2022)

Dimension results for extremal-generic polynomial systems over complete toric varieties. - Matías R. Bender; Pierre-Jean Spaenlehauer (CoRR, 2023)

Computing a group action from the class field theory of imaginary hyperelliptic function fields. - Antoine Leudière; Pierre-Jean Spaenlehauer (J. Symb. Comput., 2024)

Fast Algebraic Algorithms for Arithmetic Geometry and Polynomial Systems. - Pierre-Jean Spaenlehauer (2025)

Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces. - Pierrick Gaudry; Julien Soumier; Pierre-Jean Spaenlehauer (IACR Cryptol. ePrint Arch., 2025)

Computing Isomorphisms between Products of Supersingular Elliptic Curves. - Pierrick Gaudry; Julien Soumier; Pierre-Jean Spaenlehauer (CoRR, 2025)