I am pursuing a PhD thesis at INRIA CARAMBA; my advisors are Emmanuel Thomé and Pierre-Jean Spaenlehauer, and my work focusses on post-quantum cryptography (isogeny-based), algorithmic number theory, especially Drinfeld modules.

Numbers evolved into monolithic and magnificent structures, that were polished by countless brilliant mathematicians: Galois theory, Langlands program, number and function fields. How can one actually manipulate abstract structures? Using explicit computations is a way. Through examples and explicit constructions, it is possible to get a grasp on objects, to access the innermost reaches of their structure. This is the root of intuition, that grows into conjectures, and theorems.

In this regard, computer algebra is one of the best tools used by mathematicians to build examples. Algorithms work beautifully in concert with the more fundamental branches in mathematics, and they sometimes embody the experimental side of our science. They often work by expressing algebraic structures in terms of hidden geometric laws. 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. This discipline is both meaningful and fundamentally useful; by being at the intersection of computer sciences, mathematics and human rights, cryptography 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. My area of expertise is that of Drinfeld modules, which are arithmetic constructs from the theory of function fields. They were introduced 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.

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: hash functions, or verifiable delay functions.

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.