Team Lfant
Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Contracts and Grants with Industry
Other Grants and Activities
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years

[1]
K. 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, p. 85–155.
[2]
K. Belabas, F. Diaz y Diaz, E. Friedman.
Small generators of the ideal class group, in: Mathematics of Computation, 2008, vol. 77, no 262, p. 1185–1197.
[3]
J. 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.
[4]
J.-P. Cerri.
Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1, in: J. Reine Angew. Math., 2006, vol. 592, p. 49–62.
[5]
J.-P. Cerri.
Euclidean minima of totally real number fields: algorithmic determination, in: Math. Comp., 2007, vol. 76, no 259, p. 1547–1575.
[6]
H. 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.
[7]
H. 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.
[8]
H. 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.
[9]
A. Enge.
Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007
http://tel.archives-ouvertes.fr/tel-00382535/en/, Habilitation à diriger des recherches.
[10]
A. Enge, P. Gaudry.
An L(1/3 + $ \varepsilon$ ) algorithm for the discrete logarithm problem for low degree curves, in: Advances in Cryptology — Eurocrypt 2007, Berlin, M. Naor (editor), Lecture Notes in Computer Science, Springer-Verlag, 2007, vol. 4515, p. 367–382.

Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
A. Morra.
Comptage asymptotique et algorithmique d'extensions cubiques relatives, University of Bordeaux, 2009, Ph. D. Thesis.

Articles in International Peer-Reviewed Journal

[12]
E. Bayer-Fluckiger, J.-P. Cerri, J. Chaubert.
Euclidean minima and central division algebras, in: International Journal of Number Theory, 2009, vol. 5, no 7, p. 1155–1168
http://hal.archives-ouvertes.fr/hal-00282364/en/.
[13]
K. Belabas, M. van Hoeij, J. Klüners, A. Steel.
Factoring polynomials over global fields, in: J. Théor. Nombres Bordeaux, 2009, vol. 21, no 1, p. 15–39
http://jtnb.cedram.org/item?id=JTNB_2009__21_1_15_0.
[14]
K. Belabas, R. Layla.
L'analyse logique des probabilites selon Waismann, in: Cahiers de Philosophie du Langage, 2009, vol. 6, p. 235-260
http://hal.archives-ouvertes.fr/hal-00377355/en/.
[15]
H. Cohen, F. Pazuki.
Elementary 3-descent with a 3-isogeny, in: Acta Arithmetica, 2009, vol. 140, p. 369–404.
[16]
A. Enge.
Computing modular polynomials in quasi-linear time, in: Mathematics of Computation, 2009, vol. 78, no 267, p. 1809-1824
http://hal.inria.fr/inria-00143084/en/.
[17]
A. Enge.
The complexity of class polynomial computation via floating point approximations, in: Mathematics of Computation, 2009, vol. 78, no 266, p. 1089-1107
http://hal.inria.fr/inria-00001040/en/.

Articles in Non Peer-Reviewed Journal

[18]
A. Enge.
Komplexe Multiplikation: von numerisch bis symbolisch, in: Computeralgebra-Rundbrief GI_DMV_DAMM, 2009, vol. 45, p. 13-17
http://hal.inria.fr/inria-00429093/en/.

Internal Reports

[19]
J. Boxall, A. Enge.
Some security aspects of pairing-based cryptography, Pace, 2009, no deliverable L1.2
https://pace.rd.francetelecom.com/public/livrables/wp1-algorithmique-et-theorie-des-pairings/PACE_WP1_L1_2_v1_0.pdf/view, Technical report.
[20]
J. Boxall, A. Enge, F. Laguillaumie.
Bilinear pairings on elliptic curves, Pace, 2009, no deliverable L1.1
https://pace.rd.francetelecom.com/public/livrables/wp1-algorithmique-et-theorie-des-pairings/PACE_WP1_L1_1_v1_0.pdf/view, Technical report.

Other Publications

[21]
K. Belabas, M. Bhargava, C. Pomerance.
Error estimates for the Davenport-Heilbronn theorems, 2009
http://hal.archives-ouvertes.fr/hal-00413888/en/, to appear in Duke Mathematical Journal.
[22]
K. Belabas, E. Fouvry.
Discriminants cubiques et progressions arithmétiques, 2009
http://hal.archives-ouvertes.fr/hal-00442277/en/, to appear in International Journal of Number Theory.
[23]
J.-F. Biasse.
Improvements in the computation of ideal class groups of imaginary quadratic number fields, 2009
http://hal.inria.fr/inria-00397408/en/, to appear in Advances in Mathematics of Communications.
[24]
J.-F. Biasse.
An L(1/3) algorithm for ideal class group and regulator computation in certain number fields, 2009
http://hal.inria.fr/inria-00440223/en/, preprint.
[25]
J.-P. Cerri.
New examples in number theory, 2009, submitted.
[26]
H. Cohen, A. Morra.
Counting cubic extensions with given quadratic resolvent, 2009, submitted.
[27]
A. Enge, P. Gaudry, E. Thomé.
An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, 2009
http://hal.inria.fr/inria-00383941/en/, to appear in Journal of Cryptology.
[28]
A. Enge, F. Morain.
Generalised Weber Functions. I, 2009
http://hal.inria.fr/inria-00385608/en/, preprint.
[29]
J. Milan.
Factoring Small Integers: An Experimental Comparison, 2009
http://hal.inria.fr/inria-00188645/en/, preprint.
[30]
A. Morra.
An algorithm to compute relative cubic fields, 2009, submitted.

References in notes

[31]
J.-P. Cerri.
Spectres euclidiens et inhomogènes des corps de nombres, IECN, Université Henri Poincaré, Nancy, 2005
http://tel.archives-ouvertes.fr/tel-00011151/en/, Thèse de doctorat.
[32]
D. X. Charles, E. Z. Goren, K. E. Lauter.
Cryptographic Hash Functions from Expander Graphs, in: Journal of Cryptology, 2009, vol. 22, no 1, p. 93–113.
[33]
A. Enge.
Elliptic Curves and Their Applications to Cryptography — An Introduction, Kluwer Academic Publishers, 1999.
[34]
A. Enge, P. Gaudry.
An L(1/3 + $ \varepsilon$ ) algorithm for the discrete logarithm problem for low degree curves, in: Advances in Cryptology — Eurocrypt 2007, Berlin, M. Naor (editor), Lecture Notes in Computer Science, Springer-Verlag, 2007, vol. 4515, p. 379–393
http://hal.inria.fr/inria-00135324.
[35]
A. Enge, F. Morain.
SEA in genus 1: 2500 decimal digits, December 2006
http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0612&L=NMBRTHRY&P=R125&I=-3, Posting to the Number Theory List.
[36]
M. Jacobson.
Subexponential Class Group Computation in Quadratic Orders, Technische Universität Darmstadt, 1999, Ph. D. Thesis.
[37]
A. Rostovtsev, A. Stolbunov.
Public-key cryptosystem based on isogenies, 2006
http://eprint.iacr.org/2006/145/, Preprint, Cryptology ePrint Archive 2006/145.

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