I am pursuing a PhD thesis at INRIA CARAMBA; my advisors are Emmanuel Thomé and Pierre-Jean Spaenlehauer. My work is at the interface between post-quantum isogeny-based cryptography and computer algebra: I build algorithms for handling Drinfeld modules, often with the aim of applying them to cryptography.

Numbers evolved into monolithic and magnificent structures, that were polished by countless brilliant mathematicians. How can one manipulate and appropriate those structures? Using explicit computations. Through examples, one can get a firm grasp on objects. This is the root of intuition, that grows into conjectures, and theorems.

Computer algebra is one of the best tools used by mathematicians to build examples. Algorithms work in concert with the more fundamental branches in mathematics, and they embody some experimental sides of our science. Gauß, Euler, Legendre, all had fantastic computing abilities, mastering both the abstract and algorithmic aspects of mathematics. This double-ability was certainly instrumental to their work.

Besides this, number theory turned out to be essential in public-key cryptography, which is itself critical for privacy and individual freedoms, two of the most important human rights. By being at the intersection of computer sciences, mathematics and human rights, cryptography also embodies humanistic values. I am more than hopeful that my personal interest in mathematics will serve the purpose of contributing to cryptography and its use.

My goal is to write reliable and efficient algorithms, that will serve in cryptography or in mathematical research, and my area of expertise is that of Drinfeld modules. Drinfeld modules were introduced in 1974 to create an explicit class field theory for function fields, in which rank two Drinfeld modules — and their theory of complex multiplication — play the role of elliptic curves. The motivation for Drinfeld modules in cryptography comes from the fact that algorithms tend to be faster in function fields than in number fields.

Our first result was to derive a “Drinfeld-analogue” of the following action: the class group of a quadratic imaginary number field K/ℚ acts simply transitively on the set of isomorphism classes of ordinary elliptic curves whose complex multiplication is given by K/ℚ. In our case, this action is realized in terms of isogenies of Drinfeld modules, and we can efficiently compute it. Surprisingly, the algorithm holds into six lines; we implemented it, ran it, and gave an explicit computation. See the preprint. We are now focusing on new cryptography applications of Drinfeld modules and new algorithms.

Finally, programming is very important for me; I am also the main author of the first (upcoming) SageMath-integrated library for Drinfeld modules; see the Software section.