Team tanc

Members
Overall Objectives
Scientific Foundations
Application Domains
Software
Contracts and Grants with Industry
Other Grants and Activities
Bibliography
Inria / Raweb 2004
Project: tanc

# Bibliography

## Major publications by the team in recent years

[1]
A. Enge.
Computing Discrete Logarithms in High-Genus Hyperelliptic Jacobians in Provably Subexponential Time, in: Math. Comp., 2002, vol. 71, no 238, p. 729–742.
[2]
A. Enge.
Elliptic Curves and Their Applications to Cryptography — An Introduction, Kluwer Academic Publishers, 1999.
[3]
A. Enge, P. Gaudry.
A general framework for subexponential discrete logarithm algorithms, in: Acta Arith., 2002, vol. CII, no 1, p. 83–103.
[4]
A. Enge, F. Morain.
Comparing Invariants for Class Fields of Imaginary Quadratic Fields, in: Algorithmic Number Theory, C. Fieker, D. R. Kohel (editors), Lecture Notes in Comput. Sci., 5th International Symposium, ANTS-V, Sydney, Australia, July 2002, Proceedings, Springer-Verlag, 2002, vol. 2369, p. 252–266.
[5]
M. Fouquet, P. Gaudry, R. Harley.
An extension of Satoh's algorithm and its implementation, in: J. Ramanujan Math. Soc., 2000, vol. 15, no 4, p. 281–318.
[6]
P. Gaudry, N. Gürel.
An extension of Kedlaya's point counting algorithm to superelliptic curves, in: Advances in Cryptology – ASIACRYPT 2001, C. Boyd (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2001, vol. 2248, p. 480–494.
[7]
P. Gaudry.
Algorithmique des courbes hyperelliptiques et applications à la cryptologie, Thèse, École polytechnique, December 2000.
[8]
P. Gaudry, R. Harley.
Counting points on hyperelliptic curves over finite fields, in: Algorithmic Number Theory, W. Bosma (editor), Lecture Notes in Comput. Sci., 4th International Symposium, ANTS-IV, Leiden, The Netherlands, July 2000, Proceedings, Springer Verlag, 2000, vol. 1838, p. 313–332.
[9]
P. Gaudry, F. Hess, N. Smart.
Constructive and destructive facets of Weil descent on elliptic curves, in: J. of Cryptology, 2002, vol. 15, p. 19–46.
[10]
F. Morain.
Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques, in: J. Théor. Nombres Bordeaux, 1995, vol. 7, p. 255–282.
[11]
E. Thomé.
Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm, in: J. Symbolic Comput., July 2002, vol. 33, no 5, p. 757–775.

## Publications of the year

#### Articles in refereed journals and book chapters

[12]
R. Dupont, A. Enge, F. Morain.
Building curves with small MOV exponent over prime finite fields, in: J. of Cryptology, to appear, 2004,
[13]
F. Morain.
La primalité en temps polynomial [d'après Adleman, Huang ; Agrawal, Kayal, Saxena], in: Astérisque, Séminaire Bourbaki. Vol. 2002/2003, 2004, no 294, p. Exp. No. 917, 205–230.

#### Publications in Conferences and Workshops

[14]
A. Basiri, A. Enge, J.-C. Faugère, N. Gürel.
Implementing the Arithmetic of ${C}_{3,4}$ Curves, in: Algorithmic Number Theory — ANTS-VI, Berlin, D. Buell (editor), Lecture Notes in Computer Science, Springer-Verlag, 2004, vol. 3076, p. 87–101.
[15]
A. Bostan, P. Gaudry, E. Schost.
Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves, in: Finite Fields and Applications, 7th International Conference, Fq7, G. Mullen, A. Poli, H. Stichtenoth (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 2948, p. 40–58.
[16]
J. Franke, T. Kleinjung, F. Morain, T. Wirth.
Proving the primality of very large numbers with fastECPP, in: Algorithmic Number Theory, D. Buell (editor), Lecture Notes in Comput. Sci., 6th International Symposium, ANTS-VI, Burlington, VT, USA, June 2004, Proceedings, Springer-Verlag, 2004, vol. 3076, p. 194–207.
[17]
P. Gaudry.
Chapter 7: Hyperelliptic curves and the HCDLP, in: Advances in Elliptic Curve Cryptography, I. Blake, G. Seroussi, N. Smart (editors), London Mathematical Society Lecture Note Series, In press, Cambridge University Press, 2004.
[18]
P. Gaudry, E. Schost.
A low memory parallel version of Matsuo, Chao and Tsujii's algorithm, in: ANTS-VI, D. Buell (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 3076, p. 208–222.
[19]
P. Gaudry, E. Schost.
Construction of Secure Random Curves of Genus 2 over Prime Fields, in: Advances in Cryptology – EUROCRYPT 2004, C. Cachin, J. Camenisch (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 3027, p. 239–256.

#### Miscellaneous

[20]
A. Basiri, A. Enge, J.-C. Faugère, N. Gürel.
The Arithmetic of Jacobian Groups of Superelliptic Cubics, To appear in Math. Comp., 2004.
[21]
A. Enge, R. Schertz.
Constructing Elliptic Curves from Modular Curves of Positive Genus, To appear in Journal de Théorie des Nombres de Bordeaux; available at http://www.lix.polytechnique.fr/Labo/Andreas.Enge/vorabdrucke/cm.ps.gz, 2004.
[22]
A. Enge, R. Schertz.
Modular Curves of Composite Level, To appear in Acta Arithmetica, available at http://www.lix.polytechnique.fr/Labo/Andreas.Enge/vorabdrucke/modular.ps.gz, 2004.
[23]
P. Gaudry.
Index calculus for abelian varieties and the elliptic curve discrete logarithm problem, Cryptology ePrint Archive: Report 2004/073, 2004.
[24]
P. Gaudry, É. Schost.
Modular equations for hyperelliptic curves, To appear in Math. Comp., 2004.
[25]
F. Morain.
Computing the cardinality of CM elliptic curves using torsion points, Submitted, October 2004.

## References in notes

[26]
O. Chevassut, P.-A. Fouque, P. Gaudry, D. Pointcheval.
The 'Twist-AUgmented' approach to authenticated key exchange, Preprint, 2004, 2004.
[27]
R. Dupont.
Fast evaluation of modular functions using Newton iterations and the AGM, In preparation, 2004.
[28]
R. Dupont, A. Enge.
Provably Secure Non-Interactive Key Distribution Based on Pairings, in: WCC 2003 — Proceedings of the International Workshop on Coding and Cryptography, D. Augot, P. Charpin, G. Kabatianski (editors), To appear in Discrete Applied Mathematics, École Supérieure et d'Application des Transmissions, 2003, p. 165–174.
[29]
A. Enge, F. Morain.
Comparing Invariants for Class Fields of Imaginary Quadratic Fields, in: Algorithmic Number Theory, C. Fieker, D. R. Kohel (editors), Lecture Notes in Comput. Sci., 5th International Symposium, ANTS-V, Sydney, Australia, July 2002, Proceedings, Springer-Verlag, 2002, vol. 2369, p. 252–266.
[30]
A. Enge, F. Morain.
Fast decomposition of polynomials with known Galois group, in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, T. Høholdt, A. Poli (editors), Lecture Notes in Comput. Sci., 15th International Symposium, AAECC-15, Toulouse, France, May 2003, Proceedings, Springer-Verlag, 2003, vol. 2643, p. 254–264.
[31]
P. Gaudry, N. Gürel.
Counting points in medium characteristic using Kedlaya's algorithm, in: Experiment. Math., 2003, vol. 12, no 4, p. 395–402,
http://www.expmath.org/expmath/volumes/12/12.html.
[32]
P. Gaudry.
A comparison and a combination of SST and AGM algorithms for counting points of elliptic curves in characteristic 2, in: Advances in Cryptology – ASIACRYPT 2002, Y. Zheng (editor), Lecture Notes in Comput. Sci., Springer–Verlag, 2002, vol. 2501, p. 311–327.
[33]
P. Gaudry, T. Houtmann, D. Kohel, C. Ritzenthaler, A. Weng.
The p-adic CM-method for genus 2, In preparation, 2004.
[34]
P. Gaudry, N. Thériault, E. Thomé.
A double large prime variation for small genus hyperelliptic index calculus, Preprint, 2004.
[35]
F. Morain.
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm, In preparation, December 2004.