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