Publications of Pierrick Gaudry
Refereed journal papers
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.
The modular equation of degree 3 and genus 2 can be downloaded
here.
Evaluation properties of symmetric
polynomials, P. Gaudry, N. M. Thiéry and É. Schost. To appear
in Internat. J. Algebra Comput.
Referred conference proceedings
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.
The title of the corresponding
preprint was:
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.
Preprints
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. Informal note, 7 pages. SLP.mag
is a Magma code with the formulae of this note. example.mag illustrates its use.
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.
Talks
Slides of the talk at Durham, June
28, 2000: "Counting points on genus 2 curves over finite fields".
Slides of the talk at ECC, October 4, 2000:
"Hyperelliptic discrete logarithms".
Slides of the talk at ECC, October
31, 2001: "Algorithms for counting points on curves".
Slides of the talk at ECC, September
20, 2004: "Discrete logarithm in elliptic
curves over extension fields of small degree".
Thesis
"Algorithmique des courbes hyperelliptiques et applications
à la cryptologie", thèse de doctorat de l'École
polytechnique, December 2000. Available in ps.gz or dvi.gz .