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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

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Differential privacy Floating-point arithmetic Decision problems Correlation electromagnetic analysis Linearly homomorphic encryption Algebraic Coding Theory Algèbre linéaire exacte Cofactorization Calcul formel Algorithmes Computer Algebra Class group cryptography Algorithm Efficient arithmetic Database query evaluation and containment Mixed-radix number system Decoding failure probability analysis Complexity Relaxed algorithm Cryptographic primitives Collision Attacks RSA Computation on polynomials Algorithms and containers Correct rounding Benchmarking Conditional independence structures Cryptography based on class groups of an imaginary quadratic field Exact linear algebra Design pattern Bivariate polynomial systems Complexity theory Arithmétique modulaire Simultaneous rational function reconstruction Design of algorithms Information-theoretic cryptography Dual pairing vector spaces Algebraic algorithms Kolmogorov complexity Twisted Edwards curve Arithmétique en place Cryptographic accumulators Arithmetic circuits Coding and cryptography days 2014 Online algorithm Cryptosystem Algèbre linéaire Control flow divergence Dataflow Parallelism Cauchy matrices Arithmetic Triangular set Class groups of quadratic fields Complexity Analysis Information inequalities Finite fields Communication complexity Digital arithmetic Montgomery curve Scalar multiplication Bases d'approximant Asymptotics CADO-NFS Double-base representation Arithmétique polynomiale Codes correcteurs d'erreurs Side-channel attacks Polynomial multiplication Covering systems of congruences Bornes combinatoires Elliptic curve method Chinese remainder codes Bootstrapping Coding theory Expander mixing lemma Polynomial root finding SIMD Cutting Strategy Randomized algorithms Deterministic algorithm Clustering Algorithms Polynomial Modular Number System Computer algebra Certification Circuits arithmétiques Analyse Domain Specific Language Discrete circle Communication compelxity Supersingular isogeny Diffie-Hellman Class Groups Multi-party computation Digital Signatures Arithmetic complexity Class groups of quadratic imaginary number fields Digital straight segment recognition Computations on polynomials Cauchy interpolation with poles Algorithme Correlation Electromagnetic Analysis