Christophe Petit


Thank you for visiting my research home page!


My main research interests are in algorithmic number theory and cryptography. I'm also very interested in (computational) graph theory and group theory.
The topics covered in my previous work could be categorized as follows:
Rubik's for cryptographers, Factoring in matrix groups, hash functions from Cayley graphs
Elliptic curves in cryptography
Multivariate polynomial equations over finite fields, Gröbner bases
Cryptographic primitives and protocols
Side-channel and fault attacks and countermeaures
Master thesis on epileptic seizure detection

A full list of publications, preprints and talks is available here.



Cryptography is used every day by everybody in applications such as electronic mail or smart cards.

The security of cryptographic applications often ultimately relies on the hardness of some mathematical problems.
A scheme is proved secure if some computational problem is difficult. Formulated the other way around, breaking the scheme would imply a solution for the problem. Popular "hard" problems include integer factorization, the discrete logarithm problem over finite fields and the discrete logarithm problem over elliptic curves.

Part of my research in the last years has focused on solving another "potentially hard" mathematical problem, namely the problem of constructing short factorizations in non-Abelian groups. This problem is relevant to cryptography, but it also relates to the well-known Rubik's cube and to long-standing conjectures in graph theory and group theory. See why and how on this page.

I have also worked on solving multivariate polynomial equations over finite fields with Gröbner basis methods. My first motivation for this work was a connection with the above problem, but it also lead to a very important cryptanalysis progress on the elliptic curve discrete logarithm problem over finite fields of small characteristic. See more on this work on this page and this page.

Once a mathematical problem has been established by the community as "potentially difficult", cryptographers' work is to build elementary functionalities (called primitives) and complex protocols out of it, pretty much like a Lego game. Part of my work has been in that direction, too. See this page to discover it.

Finally, it is of no use to build secure cryptographic protocols if the secret keys they use are not appropriately protected. It has long been known that physical measurements like power consumption or electromagnetic radiations during computation may leak information that eventually reveals secret keys. See this page for my work on physical attacks and countermeasures.