photo

Fabrice Benhamouda

fr - en
1101 Kitchawan Road
fabrice.benhamouda (at) normalesup.org
Yorktown Heights, NY 10598
USA

Je suis actuellement en postdoc dans le Cryptography Research Group à IBM T. J. Watson Research Center. Auparavant, j'étais en thèse dans l'équipe de Cryptographie CASCADE à l'ENS, sous la direction de Michel Abdalla et David Pointcheval.

Publications

  • Articles de conférences

    • On the Robustness of Non-Interactive Multi-Party Computation.
      Fabrice Benhamouda, Hugo Krawczyk, and Tal Rabin.
      In Crypto'2017. [BibTeX]
      BibTeX:
      @inproceedings{C:BenKraRab17,
        author = {Fabrice Benhamouda and Hugo Krawczyk and Tal Rabin},
        title = {On the Robustness of Non-Interactive Multi-Party Computation},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2017},
        note = {To appear}
      }
      
    • Private Multiplication over Finite Fields.
      Sonia Belaïd, Fabrice Benhamouda, Alain Passelègue, Emmanuel Prouff, Adrian Thillard, and Damien Vergnaud.
      In Crypto'2017. [BibTeX]
      BibTeX:
      @inproceedings{C:BBPPTV17,
        author = {Sonia Belaïd and Fabrice Benhamouda and Alain Passelègue and Emmanuel Prouff and Adrian Thillard and Damien Vergnaud},
        title = {Private Multiplication over Finite Fields},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2017},
        note = {To appear}
      }
      
    • CCA-Secure Inner-Product Functional Encryption from Projective Hash Functions.
      Fabrice Benhamouda, Florian Bourse, and Helger Lipmaa.
      In PKC'2017. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{PKC:BenBouLip17,
        author = {Fabrice Benhamouda and Florian Bourse and Helger Lipmaa},
        title = {CCA-Secure Inner-Product Functional Encryption from Projective Hash Functions},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2017},
        volume = {10175},
        pages = {36--66},
        url = {https://eprint.iacr.org/2017/038},
        doi = {http://doi.org/10.1007/978-3-662-54388-7_2}
      }
      
    • Removing Erasures with Explainable Hash Proof Systems.
      Michel Abdalla, Fabrice Benhamouda, and David Pointcheval.
      In PKC'2017. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{PKC:AbdBenPoi17,
        author = {Michel Abdalla and Fabrice Benhamouda and David Pointcheval},
        title = {Removing Erasures with Explainable Hash Proof Systems},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2017},
        volume = {10174},
        pages = {151--174},
        url = {https://eprint.iacr.org/2014/125},
        doi = {http://doi.org/10.1007/978-3-662-54365-8_7}
      }
      
    • Optimization of Bootstrapping in Circuits.
      Fabrice Benhamouda, Tancrède Lepoint, Claire Mathieu, and Hang Zhou.
      In SODA'2017. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{SODA:BLMZ17,
        author = {Fabrice Benhamouda and Tancrède Lepoint and Claire Mathieu and Hang Zhou},
        title = {Optimization of Bootstrapping in Circuits},
        booktitle = {SODA},
        year = {2017},
        url = {https://eprint.iacr.org/2016/785},
        doi = {http://doi.org/10.1137/1.9781611974782.160}
      }
      
    • Randomness Complexity of Private Circuits for Multiplication.
      Sonia Belaïd, Fabrice Benhamouda, Alain Passelègue, Emmanuel Prouff, Adrian Thillard, and Damien Vergnaud.
      In Eurocrypt'2016. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{EC:BBPPTV16,
        author = {Sonia Belaïd and Fabrice Benhamouda and Alain Passelègue and Emmanuel Prouff and Adrian Thillard and Damien Vergnaud},
        title = {Randomness Complexity of Private Circuits for Multiplication},
        booktitle = {Eurocrypt},
        publisher = {Springer},
        year = {2016},
        volume = {9666},
        pages = {616--648},
        url = {https://eprint.iacr.org/2016/211},
        doi = {http://doi.org/10.1007/978-3-662-49896-5_22}
      }
      
    • Easing Coppersmith Methods Using Analytic Combinatorics: Applications to Public-Key Cryptography with Weak Pseudorandomness.
      Fabrice Benhamouda, Céline Chevalier, Adrian Thillard, and Damien Vergnaud.
      In PKC'2016. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{PKC:BCTV16,
        author = {Fabrice Benhamouda and Céline Chevalier and Adrian Thillard and Damien Vergnaud},
        title = {Easing Coppersmith Methods Using Analytic Combinatorics: Applications to Public-Key Cryptography with Weak Pseudorandomness},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2016},
        volume = {9615},
        pages = {36--66},
        url = {https://eprint.iacr.org/2016/007},
        doi = {http://doi.org/10.1007/978-3-662-49387-8_3}
      }
      
    • Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security.
      Michel Abdalla, Fabrice Benhamouda, and Alain Passelègue.
      In Asiacrypt'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{AC:AbdBenPas15,
        author = {Michel Abdalla and Fabrice Benhamouda and Alain Passelègue},
        title = {Multilinear and Aggregate Pseudorandom Functions: New Constructions and Improved Security},
        booktitle = {Asiacrypt},
        publisher = {Springer},
        year = {2015},
        url = {https://eprint.iacr.org/2015/867},
        doi = {http://doi.org/10.1007/978-3-662-48797-6_5}
      }
      
    • Implicit Zero-Knowledge Arguments and Applications to the Malicious Setting.
      Fabrice Benhamouda, Geoffroy Couteau, David Pointcheval, and Hoeteck Wee.
      In Crypto'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{C:BCPW15,
        author = {Fabrice Benhamouda and Geoffroy Couteau and David Pointcheval and Hoeteck Wee},
        title = {Implicit Zero-Knowledge Arguments and Applications to the Malicious Setting},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2015},
        volume = {9216},
        pages = {107--129},
        url = {http://eprint.iacr.org/2015/246},
        doi = {http://doi.org/10.1007/978-3-662-48000-7_6}
      }
      
    • An Algebraic Framework for Pseudorandom Functions and Applications to Related-Key Security.
      Michel Abdalla, Fabrice Benhamouda, and Alain Passelègue.
      In Crypto'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{C:AbdBenPas15,
        author = {Michel Abdalla and Fabrice Benhamouda and Alain Passelègue},
        title = {An Algebraic Framework for Pseudorandom Functions and Applications to Related-Key Security},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2015},
        volume = {9215},
        pages = {388--409},
        url = {http://eprint.iacr.org/2015/554},
        doi = {http://doi.org/10.1007/978-3-662-47989-6_19}
      }
      
    • Security of the J-PAKE Password-Authenticated Key Exchange Protocol.
      Michel Abdalla, Fabrice Benhamouda, and Philip MacKenzie.
      In SP'2015. [BibTeX] [DOI] [PDF]
      BibTeX:
      @inproceedings{SP:AbdBenMac15,
        author = {Michel Abdalla and Fabrice Benhamouda and Philip MacKenzie},
        title = {Security of the J-PAKE Password-Authenticated Key Exchange Protocol},
        booktitle = {SP},
        publisher = {IEEE},
        year = {2015},
        pages = {571--587},
        doi = {http://doi.org/10.1109/SP.2015.41}
      }
      
    • Disjunctions for Hash Proof Systems: New Constructions and Applications.
      Michel Abdalla, Fabrice Benhamouda, and David Pointcheval.
      In Eurocrypt'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{EC:AbdBenPoi15,
        author = {Michel Abdalla and Fabrice Benhamouda and David Pointcheval},
        title = {Disjunctions for Hash Proof Systems: New Constructions and Applications},
        booktitle = {Eurocrypt},
        publisher = {Springer},
        year = {2015},
        volume = {9057},
        pages = {69--100},
        url = {https://eprint.iacr.org/2014/483},
        doi = {http://doi.org/10.1007/978-3-662-46803-6_3}
      }
      
    • Public-Key Encryption Indistinguishable Under Plaintext-Checkable Attacks.
      Michel Abdalla, Fabrice Benhamouda, and David Pointcheval.
      In PKC'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{PKC:AbdBenPoi15,
        author = {Michel Abdalla and Fabrice Benhamouda and David Pointcheval},
        title = {Public-Key Encryption Indistinguishable Under Plaintext-Checkable Attacks},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2015},
        volume = {9020},
        url = {https://eprint.iacr.org/2014/609},
        doi = {http://doi.org/10.1007/978-3-662-46447-2_15}
      }
      
    • Efficient Zero-Knowledge Proofs for Commitments from Learning With Errors over Rings.
      Fabrice Benhamouda, Stephan Krenn, Vadim Lyubashevsky, and Krzysztof Pietrzak.
      In ESORICS'2015. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{ESORICS:BKLP15,
        author = {Fabrice Benhamouda and Stephan Krenn and Vadim Lyubashevsky and Krzysztof Pietrzak},
        title = {Efficient Zero-Knowledge Proofs for Commitments from Learning With Errors over Rings},
        booktitle = {ESORICS},
        publisher = {Springer},
        year = {2015},
        volume = {9326},
        pages = {305--325},
        url = {https://eprint.iacr.org/2014/889},
        doi = {http://doi.org/10.1007/978-3-319-24174-6_16}
      }
      
    • Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures.
      Fabrice Benhamouda, Jan Camenisch, Stephan Krenn, Vadim Lyubashevsky, and Gregory Neven.
      In Asiacrypt'2014. [BibTeX] [DOI] [PDF]
      BibTeX:
      @inproceedings{AC:BCKLN14,
        author = {Fabrice Benhamouda and Jan Camenisch and Stephan Krenn and Vadim Lyubashevsky and Gregory Neven},
        title = {Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures},
        booktitle = {Asiacrypt},
        publisher = {Springer},
        year = {2014},
        volume = {8873},
        pages = {551--572},
        doi = {http://doi.org/10.1007/978-3-662-44371-2_5}
      }
      
    • Related-Key Security for Pseudorandom Functions Beyond the Linear Barrier.
      Michel Abdalla, Fabrice Benhamouda, Alain Passelègue, and Kenneth G. Paterson.
      In Crypto'2014. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{C:ABPP14,
        author = {Michel Abdalla and Fabrice Benhamouda and Alain Passelègue and Kenneth G. Paterson},
        title = {Related-Key Security for Pseudorandom Functions Beyond the Linear Barrier},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2014},
        volume = {8616},
        pages = {77--94},
        url = {https://eprint.iacr.org/2014/488},
        doi = {http://doi.org/10.1007/978-3-662-44371-2_5}
      }
      
    • SPHF-Friendly Non-Interactive Commitments.
      Michel Abdalla, Fabrice Benhamouda, Olivier Blazy, Céline Chevalier, and David Pointcheval.
      In Asiacrypt'2013. [BibTeX] [DOI] [URL]
      BibTeX:
      @inproceedings{AC:ABBCP13,
        author = {Michel Abdalla and Fabrice Benhamouda and Olivier Blazy and Céline Chevalier and David Pointcheval},
        title = {SPHF-Friendly Non-Interactive Commitments},
        booktitle = {Asiacrypt},
        publisher = {Springer},
        year = {2013},
        volume = {8269},
        pages = {214--234},
        url = {https://eprint.iacr.org/2013/588},
        doi = {http://doi.org/10.1007/978-3-642-42033-7}
      }
      
    • New Techniques for SPHFs and Efficient One-Round PAKE Protocols.
      Fabrice Benhamouda, Olivier Blazy, Céline Chevalier, David Pointcheval, and Damien Vergnaud.
      In Crypto'2013. [BibTeX] [DOI] [URL] [PDF]
      BibTeX:
      @inproceedings{C:BBCPV13,
        author = {Fabrice Benhamouda and Olivier Blazy and Céline Chevalier and David Pointcheval and Damien Vergnaud},
        title = {New Techniques for SPHFs and Efficient One-Round PAKE Protocols},
        booktitle = {Crypto},
        publisher = {Springer},
        year = {2013},
        volume = {8042},
        pages = {449--475},
        note = {Full versions in IACR Eprint 2013/034 and 2013/341},
        url = {https://eprint.iacr.org/2015/188},
        doi = {http://doi.org/10.1007/978-3-642-40041-4}
      }
      
    • Tighter Reductions for Forward-Secure Signature Schemes.
      Michel Abdalla, Fabrice Ben Hamouda, and David Pointcheval.
      In PKC'2013. [BibTeX] [DOI] [URL] [PDF]
      BibTeX:
      @inproceedings{PKC:AbdBenPoi13,
        author = {Michel Abdalla and Ben Hamouda, Fabrice and David Pointcheval},
        title = {Tighter Reductions for Forward-Secure Signature Schemes},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2013},
        volume = {7778},
        pages = {292--311},
        note = {Full version available from the web page of the authors},
        url = {https://eprint.iacr.org/2015/196},
        doi = {http://doi.org/10.1007/978-3-642-36362-7_19}
      }
      
    • Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages.
      Fabrice Ben Hamouda, Olivier Blazy, Céline Chevalier, David Pointcheval, and Damien Vergnaud.
      In PKC'2013. [BibTeX] [DOI] [URL] [PDF]
      BibTeX:
      @inproceedings{PKC:BBCPV13,
        author = {Ben Hamouda, Fabrice and Olivier Blazy and Céline Chevalier and David Pointcheval and Damien Vergnaud},
        title = {Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages},
        booktitle = {PKC},
        publisher = {Springer},
        year = {2013},
        volume = {7778},
        pages = {272--291},
        note = {Full version available from the web page of the authors or from https://eprint.iacr.org/2012/284},
        url = {https://eprint.iacr.org/2012/284},
        doi = {http://doi.org/10.1007/978-3-642-36362-7_18}
      }
      
  • Articles journaux

    • Efficient Cryptosystems From 2^k-th Power Residue Symbols.
      Fabrice Benhamouda, Javier Herranz, Marc Joye, and Benoît Libert.
      [BibTeX] [DOI] [URL]
      BibTeX:
      @article{JC:BHJL16,
        author = {Fabrice Benhamouda and Javier Herranz and Marc Joye and Benoît Libert},
        title = {Efficient Cryptosystems From 2^k-th Power Residue Symbols},
        journal = {Journal of Cryptology},
        publisher = {Springer},
        year = {2016},
        url = {https://eprint.iacr.org/2013/435},
        doi = {http://doi.org/10.1007/s00145-016-9229-5}
      }
      
    • A New Framework for Privacy-Preserving Aggregation of Time-Series Data.
      Fabrice Benhamouda, Marc Joye, and Benoît Libert.
      [BibTeX] [DOI] [URL]
      BibTeX:
      @article{TISSEC:BenJoyLib16,
        author = {Fabrice Benhamouda and Marc Joye and Benoît Libert},
        title = {A New Framework for Privacy-Preserving Aggregation of Time-Series Data},
        journal = {ACM TISSEC},
        publisher = {ACM},
        year = {2016},
        volume = {18},
        number = {3},
        pages = {10:1--10:21},
        url = {https://hal.inria.fr/hal-01181321},
        doi = {http://doi.org/10.1145/2873069}
      }
      
    • Public-Key Encryption Indistinguishable Under Plaintext-Checkable Attacks.
      Michel Abdalla, Fabrice Benhamouda, and David Pointcheval.
      [BibTeX] [DOI] [URL]
      BibTeX:
      @article{IETITS:AbdBenPoi16,
        author = {Michel Abdalla and Fabrice Benhamouda and David Pointcheval},
        title = {Public-Key Encryption Indistinguishable Under Plaintext-Checkable Attacks},
        journal = {IET Information Security},
        year = {2016},
        volume = {10},
        number = {6},
        pages = {288--303},
        note = {Full version of PKC:AbdBenPoi15},
        url = {https://eprint.iacr.org/2014/609},
        doi = {http://doi.org/10.1049/iet-ifs.2015.0500}
      }
      
  • Autres

    • Diverse modules and zero-knowledge.
      Fabrice Benhamouda. Supervisors: Michel Abdalla and David Pointcheval.
      PhD thesis. Defense: Friday, July 1, 2016. [Abstract] [BibTeX] [PDF]
      Abstract:

      Smooth (or universal) projective hash functions were first introduced by Cramer and Shoup, at Eurocrypt'02, as a tool to construct efficient encryption schemes, indistinguishable under chosen-ciphertext attacks. Since then, they have found many other applications, including password-authenticated key exchange, oblivious transfer, blind signatures, and zero-knowledge arguments. They can be seen as implicit proofs of membership for certain languages. An important question is to characterize which languages they can handle.

      In this thesis, we make a step forward towards this goal, by introducing diverse modules. A diverse module is a representation of a language, as a submodule of a larger module, where a module is essentially a vector space over a ring. Any diverse module directly yields a smooth projective hash function for the corresponding language, and almost all the known smooth projective hash functions are constructed this way.

      Diverse modules are also valuable in their own right. Thanks to their algebraic structural properties, we show that they can be easily combined to provide new applications related to zero-knowledge notions, such as implicit zero-knowledge arguments (a lightweight alternative to non-interactive zero-knowledge arguments), and very efficient one-time simulation-sound (quasi-adaptive) non-interactive zero-knowledge arguments for linear languages over cyclic groups.

      BibTeX:
                          @phdthesis{PhD:Benhamouda16,
                          author = {Fabrice Benhamouda},
                          title = {Diverse modules and zero-knowledge},
                          school = {PSL Research University - ENS},
                          year = {2016},
                          month = {July}
                          }
                        
    • Verifier-Based Password-Authenticated Key Exchange: New Models and Constructions.
      Fabrice Benhamouda, and David Pointcheval.
      Cryptology ePrint Archive, Report 2013/833. [BibTeX] [URL]
      BibTeX:
      @misc{EPRINT:BenPoi13b,
        author = {Fabrice Benhamouda and David Pointcheval},
        title = {Verifier-Based Password-Authenticated Key Exchange: New Models and Constructions},
        year = {2013},
        note = {https://eprint.iacr.org/},
        url = {https://eprint.iacr.org/2013/833}
      }
      
    • Trapdoor Smooth Projective Hash Functions.
      Fabrice Benhamouda, and David Pointcheval.
      Cryptology ePrint Archive, Report 2013/341. [BibTeX] [URL]
      BibTeX:
      @misc{EPRINT:BenPoi13a,
        author = {Fabrice Benhamouda and David Pointcheval},
        title = {Trapdoor Smooth Projective Hash Functions},
        year = {2013},
        note = {https://eprint.iacr.org/},
        url = {https://eprint.iacr.org/2013/341}
      }
      
    • New Smooth Projective Hash Functions and One-Round Authenticated Key Exchange.
      Fabrice Benhamouda, Olivier Blazy, Céline Chevalier, David Pointcheval, and Damien Vergnaud.
      Cryptology ePrint Archive, Report 2013/034. [BibTeX] [URL]
      BibTeX:
      @misc{EPRINT:BBCPV13,
        author = {Benhamouda, Fabrice and Olivier Blazy and Céline Chevalier and David Pointcheval and Damien Vergnaud},
        title = {New Smooth Projective Hash Functions and One-Round Authenticated Key Exchange},
        year = {2013},
        note = {https://eprint.iacr.org/},
        url = {https://eprint.iacr.org/2013/034}
      }
      
    • Physical aggregated objects and dependability.
      Fabien Allard, Michel Banâtre, Fabrice Ben Hamouda, Paul Couderc, and Jean-François Verdonck.
      [Abstract] [BibTeX] [URL] [PDF]
      Abstract:

      {This documents deals with dependability issues of aggregated objects and RFID-based systems. It analyses the different categories of issues raised by these objects and proposes some measures to face them. It also provides a state of the art of actual implementations of those solutions with multiple comparisons.}

      BibTeX:
      @techreport{Tech:ABBCV11,
        author = {Fabien Allard and Michel Banâtre and Ben Hamouda, Fabrice and Paul Couderc and Jean-François Verdonck},
        title = {Physical aggregated objects and dependability},
        school = {INRIA},
        year = {2011},
        number = {RR-7512},
        pages = {33},
        url = {http://hal.inria.fr/inria-00556951/en/}
      }
      
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Projets et Stages

  • CryptoBib

    Base de donnée BibTeX pour la Cryptographie
    Maintenue avec Michel Abdalla. Créée par Michel Abdalla.
  • Non-interactive secure multiparty computation and multilinear maps

    Automne 2015 - 3 mois
    Visit to IBM's Thomas J. Watson Research, Cryptography Research Group
  • Aggrégation de données et protection de la vie privée

    Printemps 2012 - 1 mois
    Stage à Technicolor, Rennes
    Encadrants: Marc Joye and Benoît Libert
  • Sécurité exacte des schémas de signature forward-secure

    Été 2012 - 4,5 mois
    Stage dans l'équipe Crypto CASCADE à l'ENS
  • Efficacité et sécurité contre les attaques par canaux auxiliaires des implémentations de RSA

    Été 2011 - 5 mois
    Stage dans l'équipe Cryptography de l'université de Bristol
    Encadrants: Elisabeth Oswald et Dan Page
    (anglais) The Residue Number System (RNS) is a non-classical way to implement multi-precision arithmetic for RSA. Hardware implementations of RSA using RNS have already been proposed, but software implementations seem to have had far less attention. We analyse the time and space efficiency of RNS implementations of RSA on microprocessors and compare it with classical implementations. In addition, we propose an instruction set extension (ISE) designed to accelerate RNS on RISC-style processors. We also investigate two countermeasures, against some side-channel attacks, for RNS implementations of RSA, and we partially extend them to classical implementations.
  • Nooda

    Automne 2010 - projet (ENS)
    Plateforme de communication spontanée
    Projet réalisé avec Ludovic Patey. Idée originale de Ludovic Patey.
  • Objets physiques agrégés
    et sûreté de fonctionnement

    Été 2011 - 3 mois
    Stage dans l'équipe ACES à l'INRIA Rennes
    Physical aggregated objects and dependability.
    Fabien Allard, Michel Banâtre, Fabrice Ben Hamouda, Paul Couderc, and Jean-François Verdonck.
    [Abstract] [BibTeX] [URL] [PDF]
    Abstract:

    {This documents deals with dependability issues of aggregated objects and RFID-based systems. It analyses the different categories of issues raised by these objects and proposes some measures to face them. It also provides a state of the art of actual implementations of those solutions with multiple comparisons.}

    BibTeX:
    @techreport{Tech:ABBCV11,
      author = {Fabien Allard and Michel Banâtre and Ben Hamouda, Fabrice and Paul Couderc and Jean-François Verdonck},
      title = {Physical aggregated objects and dependability},
      school = {INRIA},
      year = {2011},
      number = {RR-7512},
      pages = {33},
      url = {http://hal.inria.fr/inria-00556951/en/}
    }
    
  • Sqwarea

    Printemps 2010 - projet (ENS)
    Jeu multi-joueurs en ligne sur Windows Azure
  • Petit microprocesseur

    Printemps 2010 - projet (ENS)
    Et simulateur de netlists
    projet (en) - rapport (en) - présentation (en)
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Autres

  • P = NP avec des nombres réels ?

    Automne 2009 - présentation (ENS)
    Machines de Blum-Shub-Smale
    Presentation de l'article:
    Lower Bounds Are Not Easier over the Reals: Inside PH.
    H. Fournier, and P. Koiran.
    In Proceedings of the 27th International Colloquium on Automata, Languages and Programming'2000. [BibTeX] [URL]
    BibTeX:
    @inproceedings{fournier2000lower,
      author = {Fournier, H. and Koiran, P.},
      title = {Lower Bounds Are Not Easier over the Reals: Inside PH},
      booktitle = {Proceedings of the 27th International Colloquium on Automata, Languages and Programming},
      year = {2000},
      pages = {832--843},
      url = {http://perso.ens-lyon.fr/pascal.koiran/Publis/lip.99-21.ps}
    }
    
  • Un écoulement quotidien pas si simple

    2005-2006
    Olympiades nationales de Physique
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