The research activities of the ECO group covers a large spectrum at the interface of computer algebra, coding theory and cryptography, with motivations ranging from the theoretical foundations to the practical applications of these domains. The originality of our approach is to combine various aspects of computer science and mathematics. In particular, we are interested in:

• Algebra to understand and to describe the underlying structure of the objects
• Combinatorics to analyse their properties
• Arithmetic to efficiently solve computational problems
• Softwares to turn our theoretical results into effective solutions
• Complexity theory, to assess the efficiency of the algorithms and the security of cryptosystems

More precisely, our current works include the following problems:

• Computer Algebra: efficient algorithms in linear algebra, sparse or in-place polynomial arithmetic, finite field arithmetic, verified computing
• Cryptography: public-key cryptography, elliptic curves, side-channel attacks and countermeasures, design and proofs of protocols, advanced cryptography, multi-party computation, post-quantum crypto
• Error Correcting Codes: algebraic decoding algorithms, bounds on parameters, fault tolerant linear algebra