Research

Research Publications

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

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

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

Gaetan Bisson. “Computing endomorphism rings of elliptic curves under the GRH.” In: Journal of Mathematical Cryptology 5.2 (Apr. 2012), pages 101–113. DOI: 10.1515/jmc.2011.008.

Gaetan Bisson and Andrew V. Sutherland. “A low-memory algorithm for finding short product representations in finite groups.” In: Designs, Codes and Cryptography 63.1 (Apr. 2012), pages 1–13. DOI: 10.1007/s10623-011-9527-8.

Gaetan Bisson. “Endomorphism Rings in Cryptography.” PhD Thesis. Eindhoven University of Technology, Netherlands & Institut National Polytechnique de Lorraine, France, July 2011. ISBN: 90-386-2519-7. DOI: 10.6100/IR714676.

Gaetan Bisson, Romain Cosset, and Damien Robert. AVIsogenies. A library for computing isogenies between abelian varieties. Registered software IDDN.FR.001.440011.000.R.P.2010.000.10000. Dec. 2010. URL: http://avisogenies.gforge.inria.fr/.

Gaetan Bisson and Andrew V. Sutherland. “Computing the endomorphism ring of an ordinary elliptic curve over a finite field.” In: Journal of Number Theory 131.5 (May 2011): Elliptic Curve Cryptography. Edited by Neal Koblitz and Victor S. Miller, pages 815–831. DOI: 10.1016/j.jnt.2009.11.003.

Gaetan Bisson and Takakazu Satoh. “More discriminants with the Brezing-Weng method.” In: Progress in Cryptology — INDOCRYPT 2008. Edited by Dipanwita R. Chowdhury, Vincent Rijmen, and Abhijit Das. Volume 5365. Lecture Notes in Computer Science. Springer, Dec. 2008, pages 389–399. DOI: 10.1007/978-3-540-89754-5˙30.

Selected Talks

Gaetan Bisson. “Isogeny Graphs and Endomorphism Rings of Ordinary Abelian Varieties.” Invited talk at the conference on L-functions and algebraic varieties. Poncelet Scientific Center, Higher School of Economics, Russia, Feb. 6, 2018.

Gaetan Bisson. “On Polarized Class Groups of Orders in Quartic CM-Fields.” Invited talk at the conference on Effective moduli spaces and applications to cryptography. IRMAR, University of Rennes, France, June 12, 2014.

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

Gaetan Bisson. “Computing Endomorphism Rings of Abelian Varieties.” Invited talk at the Workshop on Elliptic Curve Cryptography — ECC 2011. LORIA, University of Nancy, France, Sept. 19, 2011.