Joint project-team with INRIA Nancy, LORIA (CNRS) and Université de Lorraine
The CARAMBA team has four main research themes:
- Mathematical objects. Several kinds of mathematical objects are commonly encountered in our research. Some basic ones are truly ubiquitous: integers, finite fields, polynomials, real and complex numbers. We also work with more structured objects such as number fields, algebraic curves, or polynomial systems. In this first research axis, we study these mathematical objects mostly for their own sake. Our expertise in computational mathematics and computer algebra allows us to contribute to the general algorithmic toolbox that makes these mathematical objects easy to work with in practice: computations with these objects must be effective and fast. A sizeable portion of our work in this domain is realized in the form of software projects, which are developed over long periods of time.
- Secret-key cryptology. We work on the formalization of various statistical cryptanalysis techniques. Our typical cryptanalysis targets are the most recently proposed cipher primitives such as the NIST lightweight AEAD ciphers, as well as others at various stages of their development. We are also interested in the automation of cryptanalysis (for example in the search of differential trails), as well as the design of new symmetric primitives that fulfill the combined goals of security, speed, and minimal use of resources. Most of our expertise is in classical cryptanalysis, but we also work on quantum algorithms. We focus on quantum algorithms that are the most distinct from classical algorithms, like the algorithms for the hidden subgroup problem, and on quantum variants of our classical cryptanalyses.
- Public-key cryptology. Our team has been studying the mathematical building blocks of public-key cryptography for a long time. More specifically, we have a long-established record on the study of the public-key cryptographic primitives based on integer factorization and finite field discrete logarithm, as well as on algebraic curves, abelian varieties, and their applications in cryptography. Most of the time we study them from a classical (non quantum) angle. We work in particular on the Number Field Sieve algorithm and its variants, and on the software implementation cado-nfs. We also work on cryptographic aspects of algebraic curves and abelian varieties, and some aspects of pairing-based cryptography.
- Implications in computer security and the real world. The questions that we address in our last research axis are less problem-centered than above, and rather revolve around how the different building blocks that we work with can be assembled, and whether this leads to impactful results in computer security. In particular we have been working since 2016 on electronic voting, and our most visible work in this domain is Belenios, which is a protocol with a complete specification, a free software implementation, and a free-of-charge web platform that anyone can use to setup their own elections. We also work on the implications of our crypanalysis results for computer security, for example concerning the understanding of the necessary evolution of key sizes for RSA-based public key cryptography.
The Caramba project-team and its predessor project-team called Caramel acknowledge the support of the following grants:
- ANR CADO (2007-2010): Number field sieve: distribution, optimization.
- ANR CHIC (2009-2012): Hyperelliptic Curves Isogenies, point Counting.
- ANR CATREL (2013-2016): Sieve Algorithms: Theoretical Advances, and Effective Resolution of the Discrete Logarithm Problem.
- ANR KLEPTOMANIAC (2022-2025): Key Length Estimates: Practical and Theoretical Optimizations and Modern Approaches on NFS Instances for Accurate Costs
- PEPR Cybersécurité, CRYPTANALYSE project (2023-2028).