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Bibliography

Major publications by the team in recent years
  • 1E. Bayer-Fluckiger, J.-P. Cerri, J. Chaubert.

    Euclidean minima and central division algebras, in: International Journal of Number Theory, 2009, vol. 5, no 7, pp. 1155–1168.

    http://www.worldscinet.com/ijnt/05/0507/S1793042109002614.html
  • 2K. Belabas, M. Bhargava, C. Pomerance.

    Error estimates for the Davenport-Heilbronn theorems, in: Duke Mathematical Journal, 2010, vol. 153, no 1, pp. 173–210.

    http://projecteuclid.org/euclid.dmj/1272480934
  • 3J. Belding, R. Bröker, A. Enge, K. Lauter.

    Computing Hilbert class polynomials, in: Algorithmic Number Theory — ANTS-VIII, Berlin, A. van der Poorten, A. Stein (editors), Lecture Notes in Computer Science, Springer-Verlag, 2007, vol. 5011.

    http://hal.inria.fr/inria-00246115
  • 4J.-P. Cerri.

    Euclidean minima of totally real number fields: algorithmic determination, in: Math. Comp., 2007, vol. 76, no 259, pp. 1547–1575.

    http://www.ams.org/journals/mcom/2007-76-259/S0025-5718-07-01932-1/
  • 5H. Cohen.

    Number Theory I: Tools and Diophantine Equations; II: Analytic and Modern Tool, Graduate Texts in Mathematics, Springer-Verlag, New York, 2007, vol. 239/240.
  • 6H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.

    Handbook of Elliptic and Hyperelliptic Curve Cryptography, Discrete mathematics and its applications, Chapman & Hall, Boca Raton, 2006.
  • 7J.-M. Couveignes, B. Edixhoven.

    Computational aspects of modular forms and Galois representations, Princeton University Press, 2011.
  • 8A. Enge.

    The complexity of class polynomial computation via floating point approximations, in: Mathematics of Computation, 2009, vol. 78, no 266, pp. 1089–1107.

    http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02200-X/home.html
  • 9A. Enge, P. Gaudry, E. Thomé.

    An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, in: Journal of Cryptology, 2011, vol. 24, no 1, pp. 24–41.
  • 10D. Lubicz, D. Robert.

    Computing isogenies between abelian varieties, in: Compositio Mathematica, 09 2012, vol. 148, no 05, pp. 1483–1515.

    http://dx.doi.org/10.1112/S0010437X12000243
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 12K. Belabas, E. Friedman.

    Computing the residue of the Dedekind zeta function, in: Mathematics of Computation, 2015, vol. 84, pp. 357-369, 16 pages.

    https://hal.inria.fr/hal-00916654
  • 13H. Cohen.

    Exact counting of Dℓ number fields with given quadratic resolvent, in: Mathematics of Computation, 2015, vol. 84, no 294, pp. 1933-1951.

    https://hal.archives-ouvertes.fr/hal-01027417
  • 14H. Cohen, S. Rubinstein-Salzedo, F. Thorne.

    Identitites for Field Extensions Generalizing the Ohno–Nakagawa Relations, in: Compositio Mathematica, 2015, vol. 151, no 11, pp. 2059-2075.

    https://hal.inria.fr/hal-01109980
  • 15R. Cosset, D. Robert.

    Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves, in: Mathematics of Computation, 2015, vol. 84, no 294, pp. 1953-1975, Accepté pour publication à Mathematics of Computations. [ DOI : 10.1090/S0025-5718-2014-02899-8 ]

    https://hal.archives-ouvertes.fr/hal-00578991
  • 16J.-M. Couveignes, T. Ezome.

    Computing functions on Jacobians and their quotients, in: The London Mathematical Society Journal of Computations and Mathematics, October 2015, vol. 18, no 1, pp. 555-577.

    https://hal.archives-ouvertes.fr/hal-01088933
  • 17A. Enge.

    Bilinear pairings on elliptic curves, in: L'Enseignement Mathématique, 2015, vol. 61, no 2, pp. 209–241.

    https://hal.inria.fr/hal-00767404
  • 18D. Lubicz, D. Robert.

    A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties, in: Journal of Symbolic Computation, 2015, vol. 67, pp. 68-92. [ DOI : 10.1016/j.jsc.2014.08.001 ]

    https://hal.inria.fr/hal-00806923
  • 19D. Lubicz, D. Robert.

    Computing separable isogenies in quasi-optimal time, in: LMS Journal of Computation and Mathematics, 2015, vol. 18, no 1, pp. 198-216. [ DOI : 10.1112/S146115701400045X ]

    https://hal.archives-ouvertes.fr/hal-00954895
  • 20E. Milio.

    A quasi-linear time algorithm for computing modular polynomials in dimension 2, in: LMS Journal of Computation and Mathematics, 2015, vol. 18, pp. 603-632.

    https://hal.archives-ouvertes.fr/hal-01080462
  • 21A. Page.

    Computing arithmetic Kleinian groups, in: Mathematics of Computation, 2015, vol. 84, no 295, pp. 2361-2390.

    https://hal.archives-ouvertes.fr/hal-00703043

International Conferences with Proceedings

  • 22G. Castagnos, F. Laguillaumie.

    Linearly Homomorphic Encryption from DDH, in: The Cryptographer's Track at the RSA Conference 2015, San Francisco, United States, Topics in Cryptology –- CT-RSA 2015, April 2015, no 9048. [ DOI : 10.1007/978-3-319-16715-2_26 ]

    https://hal.archives-ouvertes.fr/hal-01213284
  • 23F. Johansson.

    Efficient implementation of elementary functions in the medium-precision range, in: 22nd IEEE Symposium on Computer Arithmetic (ARITH22), Lyon, France, June 2015. [ DOI : 10.1109/ARITH.2015.16 ]

    https://hal.archives-ouvertes.fr/hal-01079834

Patents

Other Publications

References in notes
  • 30K. Belabas.

    L'algorithmique de la théorie algébrique des nombres, in: Théorie algorithmique des nombres et équations diophantiennes, N. Berline, A. Plagne, C. Sabbah (editors), 2005, pp. 85–155.
  • 31H. Cohen, P. Stevenhagen.

    Computational class field theory, in: Algorithmic Number Theory — Lattices, Number Fields, Curves and Cryptography, J. Buhler, P. Stevenhagen (editors), MSRI Publications, Cambridge University Press, 2008, vol. 44.
  • 32A. Enge.

    Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.

    http://tel.archives-ouvertes.fr/tel-00382535/en/


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