Christophe Petit

Research Interests

My main research interests are in **Cryptography** and related topics, mostly at the intersection of Mathematics and Computer Science.

Cryptography is used every day in applications such as electronic mail or smart cards, so its practical importance cannot be overstated. At the same time, it crucially relies on beautiful mathematics.

In a large part of my work I study **"hard" mathematics problems** used in cryptography, and I **design algorithms** to solve them. This work allows to understand the exact security of cryptographic protocols, and in particular to decide on key sizes. At the same time, it involves tools from number theory, group theory, algebraic geometry and many other mathematics areas.

In another important part of my work I build new **cryptographic primitives and protocols** based on these mathematics problems. I have in particular worked on **cryptographic hash functions**, **zero-knowledge proofs of knowledge** and **group signatures**. I am particularly interested in **post-quantum cryptography**, namely cryptography protocols that will remain secure even when large scale quantum computers will be built.

Finally, a last part of my work is dedicated to **physical attacks** against cryptographic implementations, including side-channel and fault attacks, and how to prevent them.

Some mathematics problems that I work on, like the **elliptic curve discrete logarithm problem**, are used in TLS, a major cryptography protocol suites used to secure http connections. Other problems that I work on, including **polynomial systems**, **isogeny problems**, and **non Abelian group problems**, could become the basis of the next generation of protocols due to their potential post-quantum resistance.

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