Research activities
My research topics are at the intersection of algebraic geometry, number theory and their applications to cryptography and coding theory.
In my Ph.D thesis (defended on July 6, 2016) I focused on some questions about the maximum number of rational points on a singular curve defined over a finite field.
I am also a member of the research project ANR manta: Algebraic Geometry and Coding Theory. Within this context, I am interested in codes built over higher dimensional varieties.
Publications
Here is the list of my publications:
- A note on the security of CSIDH, joint work with Jean-François Biasse and Michael J. Jacobson, Progress in Cryptology – INDOCRYPT 2018. 19th International Conference on Cryptology in India, New Delhi, India, December 9–12, 2018, Proceedings, Security and Cryptology, vol. 11356, Springer, pp. 153--168, 2018.
pdf arXiv - Optimal and maximal singular curves, joint work with Yves Aubry, Arithmetic, geometry, cryptography and coding theory, Contemporary Mathematics 686, pp. 31--43, 2017.
pdf arXiv -
On the maximum number of rational points on singular curves over finite fields, joint work with Yves Aubry, Moscow Math. Journal, Volume 15, Issue 4, October-December 2015, pp. 615--627.
pdf arXiv
Ph.D thesis
Nombre de points rationnels des courbes singulières sur les corps finis
Language: French (sorry!)
Supervisor: Yves Aubry
Defended on July 6, 2016, at Aix-Marseille Université, in Marseille
Master thesis
Domini Almost Dedekind
Language: Italian (sorry again!)
Supervisor: Stefania Gabelli
Defended on July 18 2012 at Università degli Studi di Roma 3, in Rome
Talks
01/08/2019: Un échange de clés dans le monde des calculateurs quantiques, Retraite ANR Manta, Paris, France.
12/11/2018: A note on the security of CSIDH, Indocrypt 2018, New Delhi, India.
19/11/2018: On the security of a recent isogeny-based cryptosystem, Discrete Mathematics Seminar, Department of Mathematics & Statistics, University of South Florida.
03/05/2018: A singular trip through the world of algebraic curves over finite fields, Discrete Mathematics Seminar, Department of Mathematics & Statistics, University of South Florida.
11/20/2016: Curve su campi finiti a singolarità prescritte, Seminario d'Algebra Commutativa, Dipartimento di Matematica e Fisica, Università degli Studi di Roma Tre.
11/05/2015: Courbes optimales et maximales, Séminaire d’Arithmétique et Théorie de l’Information, Institut de Mathématiques de Marseille, Aix-Marseille Université.
- 05/18/2015: Towards maximal singular curves over finite fields, Arithmetics, Geometry, Cryptography and
Coding Theory 2015 (AGCT-2015), CIRM, Marseille.
slides - 02/17/2015: Sur le nombre maximum de points rationnels d’une courbe singulière sur un corps fini, Séminaire Algébrique de l’Institut de Mathématiques de Toulon (IMATH), Université de Toulon.
- 29/01/2015: Sur le nombre maximum de points rationnels d’une courbe singulière sur un corps fini, Séminaire d’Arithmétique et Théorie de l’Information, Institut de Mathématiques de Marseille, Aix-Marseille Université.
- 06/11/2014: Singular curves over finite fields with many rational points, Yet Another Conference on Cryptography 2014 (YACC 2014), Île de Porquerolles, France.
slides - 05/12/2014: Singular curves over finite fields with many rational points, Antalya Algebra Days XVI, Antalya,
Turquie.
slides - 05/14/2013: Courbes avec un nombre fixé de points rationnels, Séminaire Algébrique de l’Institut de Mathématiques de Toulon (IMATH), Université de Toulon