Publications de Pierrick Gaudry

Revues avec comité de lecture

  • An extension of Satoh's algorithm and its implementation, M. Fouquet, P. Gaudry and R. Harley. J. Ramanujan Math. Soc. 15 (2000), 281-318.
  • Constructive and destructive facets of Weil descent on elliptic curves, P. Gaudry, F. Hess and N. Smart. J. of Cryptology 15 (2002), 19-46.
  • A general framework for subexponential discrete logarithm algorithms, A. Enge and P. Gaudry. Acta Arith. 102 (2002), 83-103.
  • Counting points in medium characteristic using Kedlaya's algorithm, P. Gaudry and N. Gürel. Experimental Math. 12 (2003), 395--402.
  • Modular equations for hyperelliptic curves, P. Gaudry and É. Schost. Math. Comp. 74 (2005), 429--454. L'équation modulaire qui y est mentionnée peut être téléchargée ici.
  • Evaluation properties of symmetric polynomials, P. Gaudry, N. M. Thiéry and É. Schost. To appear in Internat. J. Algebra Comput.

    • Actes de colloques avec comité de lecture

  • Speeding up the discrete log computation on curves with automorphisms, I. Duursma, P. Gaudry and F. Morain, Advances in Cryptology, Asiacrypt'99, Springer-Verlag, LNCS 1716, 103-121, 1999. © Springer-Verlag
  • An algorithm for solving the discrete log problem on hyperelliptic curves, P. Gaudry, Advances in Cryptology, Eurocrypt'2000, Springer-Verlag, LNCS 1807, 19-34, 2000. © Springer-Verlag. Le preprint correspondant avait pour titre: A variant of the Adleman-DeMarrais-Huang algorithm and its application to small genera.
  • Counting points on hyperelliptic curves over finite fields, P. Gaudry and R. Harley. ANTS-IV, Springer-Verlag, LNCS 1838, 313-332, 2000. © Springer-Verlag
  • Finding secure curves with the Satoh-FGH algorithm and an early-abort strategy, M. Fouquet, P. Gaudry and R. Harley. Advances in Cryptology, Eurocrypt'2001, Springer-Verlag, LNCS 2045, 14-29, 2001. © Springer-Verlag.
  • On the invariants of the quotients of the Jacobian of a curve of genus 2, P. Gaudry et É. Schost. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer-Verlag, LNCS 2227, 373-386, 2001. © Springer-Verlag.
  • An extension of Kedlaya's algorithm to superelliptic curves, P. Gaudry and N. Gurel. Advances in Cryptology, Asiacrypt'2001, Springer-Verlag, LNCS 2248, 480-494, 2001. © Springer-Verlag.
  • A comparison and a combination of SST and AGM algorithms for counting points of elliptic curves in characteristic 2, P. Gaudry. Advances in Cryptology, Asiacrypt'2002, Springer-Verlag, LNCS 2501, 311-327, 2002. © Springer-Verlag.
  • Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves , A. Bostan, P. Gaudry and É. Schost. Proceedings of Fq7, Springer-Verlag LNCS 2948, 40--58, 2004, © Springer-Verlag.
  • Construction of secure random curves of genus 2 over prime fields , P. Gaudry and É. Schost. Advances in Cryptology, Eurocrypt 2004, Springer-Verlag, LNCS 3027, 239-256, 2004. © Springer-Verlag.
  • A low-memory parallel version of Matsuo, Chao and Tsujii's algorithm , P. Gaudry and É. Schost. Proceedings of ANTS 6, Springer-Verlag LNCS 3076, 208-222, 2004, © Springer-Verlag.

    • Prépublications

  • Index calculus for abelian varieties and the elliptic curve discrete logarithm problem , P. Gaudry. Preprint, 12 pages.
  • Some remarks on the elliptic curve discrete logarithm, P. Gaudry. Note informelle, 7 pages. SLP.mag est un programme Magma contenant les formules de cette note. example.mag illustre son utilisation.
  • Linear recurrences with polynomial coefficients and application to integer factorization and Cartier-Manin operator, A. Bostan, P. Gaudry and É. Schost. Preprint, 29 pages.
  • A double large prime variation for small genus hyperelliptic index calculus, P. Gaudry, N. Thériault and E. Thomé. Preprint, 14 pages.
  • The p-adic CM-method for genus 2, P. Gaudry, T. Houtmann, D. Kohel, C. Ritzenthaler and A. Weng. Preprint, 24 pages.

    • Exposés

  • Transparents de l'exposé fait à Durham, le 28 juin 2000: "Counting points on genus 2 curves over finite fields".
  • Transparents de l'exposé fait à ECC, le 4 octobre 2000: "Hyperelliptic discrete logarithms".
  • Transparents de l'exposé fait à ECC, le 31 octobre 2001: "Algorithms for counting points on curves".
  • Transparents de l'exposé fait à ECC, le 20 septembre 2004: "Discrete logarithm in elliptic curves over extension fields of small degree".

    • Thèse

  • "Algorithmique des courbes hyperelliptiques et applications à la cryptologie", thèse de doctorat de l'École polytechnique, décembre 2000. Version ps.gz ou dvi.gz .