Research activities


My research area lies at the crossroads between algebraic geometry and number theory and finds several applications in information theory (cryptography and coding theory).

In my Ph.D thesis (supervised by Yves Aubry) I addressed the problem of determining the maximum number of rational points on singular curves defined over finite fields. My work is based on notions and tools from commutative algebra, algebraic geometry and combinatorics.

Later, my postdoctoral experience at University of South Florida under the supervision of Jean-François Biasse and Xiang-dong Hou has been an opportunity to broaden my research horizons towards some new and/or more applied topics: post-quantum cryptography (isogeny-based cryptography), algorithmic number theory, permutation polynomials, etc. More specifically, in a joint work with Jean-François Biasse and Michael J. Jacobson, we have recently analyzed the quantum security of an isogeny-based cryptosystem called CSIDH, proposed in 2018 by Castryck et al.

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

In preparation:

  • An application of the Hasse--Weil bound to rational functions over finite fields, with Xiang-dong Hou.

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

pdf slides defense

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

pdf slides


Talks