About

I am a DGA researcher at the Institut de Recherche Mathématique de Rennes (IRMAR, UMR CNRS 6625), Université de Rennes, working on algorithms in number theory and arithmetic geometry, with applications to cryptography.

My research interests include:

• Elliptic and small genus curves: point counting, isogenies, complex multiplication
• Invariant theory and moduli of curves — invariants, models, stable reduction types
• Cryptography, discrete logarithm (Number Field Sieve, Function Field Sieve)

News

April 2026With Jean-Marc Couveignes, our paper Elliptic Butterflies is now published in the Journal of Complexity (2026) — also on arXiv:2510.27375.

April 2026I am a member of the organising committee of the Post-Quantum Cryptography workshop, held as part of the European Cyber Week 2026 in Rennes.

March 2026With Thomas Bouchet, Jeroen Sijsling, and Christophe Ritzenthaler, we posted an updated version of Functionality for isomorphism classes of curves and hypersurfaces, now including results from Thomas's PhD thesis — see arXiv:2102.04372 (v2).

Publications

A continuously up-to-date list is maintained on arXiv and HAL. Selected papers below — see the full list sorted by year for everything else.

Recent papers (2016–2026)

• Reduction of Plane Quartics and Cayley Octads, with R. van Bommel, J. Docking, V. Dokchitser, and E. Lorenzo García. Foundations of Computational Mathematics, 26:1425–1496, 2026. DOI arXiv:2309.17381
• Reduction of Plane Quartics and Dixmier–Ohno Invariants, with R. van Bommel, J. Docking, and E. Lorenzo García. Research in Number Theory, 11:41, 2025. DOI arXiv:2401.13902
• Stable models of plane quartics with hyperelliptic reduction, with E. Lorenzo García and C. Ritzenthaler. Contemporary Mathematics, 770:223–237, 2021. DOI arXiv:1906.00795
• Reduction type of smooth plane quartics, with Q. Liu, E. Lorenzo García, and C. Ritzenthaler. Algebra & Number Theory, 15(6):1429–1468, 2021. DOI arXiv:1803.05816
• Reconstructing Plane Quartics from Their Invariants, with C. Ritzenthaler and J. Sijsling. Discrete & Computational Geometry, 63(1):73–113, 2020. DOI arXiv:1606.05594
• Distributions of Traces of Frobenius for Smooth Plane Curves over Finite Fields, with C. Ritzenthaler, F. Rovetta, J. Sijsling, and B. Smith. Experimental Mathematics, 28(1):39–48, 2019. DOI arXiv:1510.05601
• Grøstl Distinguishing Attack: A New Rebound Attack of an AES-like Permutation, with V. Cauchois and C. Gomez. IACR Transactions on Symmetric Cryptology, 2017(3):1–23, 2017. DOI ePrint 2017/508
• Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group, with C. Ritzenthaler and J. Sijsling. Mathematics of Computation, 85(300):2011–2045, 2016. DOI arXiv:1301.0695

Books & chapters

• Number Field Sieve for DLP, with A. Joux. In Encyclopedia of Cryptography and Security (2nd ed.), pages 867–873. Springer, 2011. DOI
• Point Counting on Elliptic and Hyperelliptic Curves, with D. Lubicz and F. Vercauteren. Chapter 17 in Handbook of Elliptic and Hyperelliptic Curve Cryptography, H. Cohen and G. Frey, eds., pages 407–449. Chapman & Hall/CRC, 2006 (2nd ed. 2012). DOI

Manuscripts

• Contributions à l'arithmétique de la cryptographie. Habilitation à diriger des recherches, Université d'Aix-Marseille II, November 2004. HAL tel-01101947
• Algorithmique des courbes elliptiques dans les corps finis. PhD thesis, École Polytechnique, June 1997. HAL tel-01101949

Software

• G3Cayley

  With R. van Bommel, V. Dokchitser, J. Docking, and E. Lorenzo García. Stable reduction type of a genus 3 curve. Magma, 2023.

  GitHub
• Hyperelliptic

  With C. Ritzenthaler and J. Sijsling. A Magma repository for reconstruction and isomorphisms of hyperelliptic curves. Now included by default in the Magma distribution (since v2.26). 2020.

  GitHub
• Quartic

  With C. Ritzenthaler and J. Sijsling. A Magma package for calculating with smooth plane quartic curves. Now included by default in the Magma distribution (since v2.26). 2020.

  GitHub
• Isocar2g1

  With X. Caruso and E. Eid. Elliptic curve isogenies in characteristic two. Magma, 2020.

  GitHub
• G3Twists v1.1

  With C. Ritzenthaler. Reconstruction of genus 3 curves from their invariants. Now included by default in the Magma distribution (since v2.20). 2013.

  Download (gz)
• GaloisTest v1.1

  With J.-M. Couveignes and T. Ezome. A faster pseudo-primality test. Magma, 2012.

  Download (tgz)
• G2Twists v1.1

  With C. Ritzenthaler. Reconstruction of genus 2 curves from their invariants and twists over a finite field. Now included by default in the Magma distribution (since v2.15).

  Download (tgz)
• EllBasis v1.1

  With J.-M. Couveignes. Elliptic bases for finite fields. Magma, 2008.

  Download (tgz)
• ZEN

  With F. Chabaud. Toolbox for finite extensions of finite rings. C, 1996.

  SourceForge

PhD Students

• Joris Dannemann. Approches cryptographiques basées sur une algorithmique elliptique rapide. Université de Rennes, in progress. With J.-M. Couveignes.
• Thomas Bouchet. Géométrie des courbes : une approche explicite par les invariants. Université Côte d'Azur, 2025. With C. Ritzenthaler. theses.fr Website
• Elie Eid. Sur le calcul d'isogénies par résolution d'équations différentielles p-adiques. Université de Rennes 1, 2021. With X. Caruso. theses.fr Website
• Romain Basson. Arithmétique des espaces de modules des courbes hyperelliptiques de genre 3 en caractéristique positive. Université de Rennes 1, 2015. With S. Duquesne. theses.fr Website
• Jean-Gabriel Kammerer. Analyse de nouvelles primitives cryptographiques pour les schémas Diffie-Hellman. Université de Rennes 1, 2013. theses.fr
• Clément Dunand. Autour de la cryptographie à base de tores algébriques. Université de Rennes 1, 2010. theses.fr Website
• Thomas Sirvent. Courbes elliptiques et applications cryptographiques à la diffusion numérique sécurisée. Université de Rennes 1, 2008. With L. Mahé. theses.fr

Teaching

• 2023 – 2026 : Elliptic curve algorithms — M2, Master Mathématiques de l'information, Cryptographie.

  Algorithmique des courbes elliptiques, with F. Narbonne. Lecture notes, Master de Mathématiques et Applications, Université de Rennes, February 2024.

  PDF F. Narbonne

Links

• ORCID
• arXiv
• HAL
• Google Scholar
• GitHub
• Univ. Rennes profile