index - Exact Computing

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