Research

Research Publications

Razvan Barbulescu and Gaetan Bisson. Regev’s attack on hyperelliptic cryptosystems. IACR Cryptology ePrint archive, reference 2024/2004. 2024. URL: https://eprint.iacr.org/2024/2004

Samir Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, and Stefano Rini. Empirical Risk Minimization with Relative Entropy Regularization. IEEE Transactions on Information Theory, volume 70.7, pages 5122–5161. 2024. DOI: 10.1109/TIT.2024.3365728

Alp Bassa, Gaetan Bisson, and Roger Oyono. Iterative constructions of irreducible polynomials from isogenies. Finite Fields and their Applications, volume 97, reference 102429. 2024. DOI: 10.1016/j.ffa.2024.102429

Samir Perlaza, Iñaki Esnaola, Gaetan Bisson, and H. Vincent Poor. On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation. IEEE International Symposium on Information Theory — ISIT 2023, pages 328–333. 2023. DOI: 10.1109/ISIT54713.2023.10206506

Gaetan Bisson and Roger Oyono. On the vaccination threshold for Covid-19 in French Polynesia. Pacific Health, volume 5. 2022. DOI: 10.24135/pacifichealth.v5i.59

Samir Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, and Stefano Rini. Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis. IEEE International Symposium on Information Theory — ISIT 2022, pages 684–689. 2022. DOI: 10.1109/ISIT50566.2022.9834273

Gaetan Bisson and Mehdi Tibouchi. Constructing Permutation Rational Functions From Isogenies. SIAM Journal on Discrete Mathematics, volume 32.3, pages 1741–1749. 2018. DOI: 10.1137/17M1135736

Gaetan Bisson and Mehdi Tibouchi. 同種写像を用いた置換有理関数の生成手法. IEICE Symposium on Cryptography and Information Security — SCIS 2017, reference 3B2-3. 2017.

Gaetan Bisson and Marco Streng. On polarised class groups of orders in quartic CM-fields. Mathematical Research Letters, volume 24.2, pages 247–270. 2017. DOI: 10.4310/MRL.2017.v24.n2.a1

Gaetan Bisson. Computing endomorphism rings of abelian varieties of dimension two. Mathematics of Computation, volume 84.294, pages 1977–1989. 2015. DOI: 10.1090/S0025-5718-2015-02938-X

Gaetan Bisson. Computing endomorphism rings of elliptic curves under the GRH. Journal of Mathematical Cryptology, volume 5.2, pages 101–114. 2012. DOI: 10.1515/jmc.2011.008

Gaetan Bisson and Andrew V. Sutherland. A low-memory algorithm for finding short product representations in finite groups. Designs, Codes and Cryptography, volume 63, pages 1–13. 2012. DOI: 10.1007/s10623-011-9527-8

Gaetan Bisson and Andrew V. Sutherland. Computing the endomorphism ring of an ordinary elliptic curve over a finite field. Journal of Number Theory, volume 131.5, pages 815–831. 2011. DOI: 10.1016/j.jnt.2009.11.003

Gaetan Bisson and Takakazu Satoh. More discriminants with the Brezing-Weng method. Progress in Cryptology — INDOCRYPT 2008, Springer LNCS, volume 5365, pages 389–399. 2008. DOI: 10.1007/978-3-540-89754-5_30

Computer Software

Gaetan Bisson, Romain Cosset, and Damien Robert. AVIsogenies, a library for computing isogenies between abelian varieties. 2010. URL: https://gitlab.inria.fr/roberdam/avisogenies/

Academic Manuscripts

Gaetan Bisson. Contributions aux aspects effectifs des variétés abéliennes et à leurs applications. Habilitation thesis, University of French Polynesia. 2023.

Gaetan Bisson. Endomorphism Rings in Cryptography. Doctoral thesis, Eindhoven University of Technology & Institut National Polytechnique de Lorraine. 2011. ISBN: 90-3862-519-7 DOI: 10.6100/IR714676

Editorial Activities

Gaetan Bisson, Philippe Lebacque, and Roger Oyono. Actes du colloque international «Géométrie algébrique, Théorie des nombres et Applications» (GTA 2021). Publications mathématiques de Besançon, volume 2024. ISBN: 2-38549-112-5

Stéphane Ballet, Gaetan Bisson, and Irene Bouw. Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics, volume 770. 2021. ISBN: 14-7045-426-2 DOI: 10.1090/conm/770

Stéphane Ballet, Gaetan Bisson, Roger Oyono, Renate Scheidler, and Nicolas Thériault. Special issue on GEOCRYPT 2013. Advances in Mathematics of Communications, volume 8.4. 2014. ISSN: 1930-5346

Invited Talks

Gaetan Bisson. Constructing irreducible polynomials using isogenies. Computations and their uses in number theory. CIRM, University of Marseille, France. 1 March 2023.

Gaetan Bisson. Isogeny Graphs and Endomorphism Rings of Ordinary Abelian Varieties. Conference on L-functions and algebraic varieties. Poncelet Scientific Center, Higher School of Economics, Russia. 6 February 2018.

Gaetan Bisson. On Polarized Class Groups of Orders in Quartic CM-Fields. Conference on Effective moduli spaces and applications to cryptography. IRMAR, University of Rennes, France. 12 June 2014.

Gaetan Bisson. On Polarized Class Groups of Orders in Quartic CM-Fields. Conference on Theoretical and Practical Aspects of the Discrete Logarithm Problem — DLP 2014. Centro Stefano Franscini, ETH Zürich, Switzerland. 7 May 2014.

Gaetan Bisson. Computing Endomorphism Rings of Abelian Varieties. Workshop on Elliptic Curve Cryptography — ECC 2011. LORIA, University of Nancy, France. 19 September 2011.

Student Supervision

Keva Djambaé, PhD Candidate, University of French Polynesia. 2024. (With David Kohel.)

Stefano Marseglia, postdoctoral researcher, University of French Polynesia. 2024.

Emiliano Torti, postdoctoral researcher, University of French Polynesia. 2023–2025.
(With Alexander Rahm.)

Marama Simoneau, L3 Candidate, ENSAE Paris. 2023.

Hugo Nartz, PhD Candidate, University of French Polynesia. 2022. (With Alexander Rahm.)

Nathan Chiche, M2 Candidate, Sorbonne University. 2022.

Garry Terii, M1 Candidate, University of Lyon. 2016.