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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 1, pp. 24–41.
• 10D. Lubicz, D. Robert.
  
  Computing isogenies between abelian varieties, in: Compositio Mathematica, 09 2012, vol. 148, n^o 05, pp. 1483–1515.
  
  http://dx.doi.org/10.1112/S0010437X12000243

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11N. Mascot.
  
  Computing modular Galois representations, Universite de Bordeaux, July 2014.
  
  https://hal.archives-ouvertes.fr/tel-01110658
• 12A. Page.
  
  Explicit methods for arithmetic groups, Université de Bordeaux, July 2014.
  
  https://tel.archives-ouvertes.fr/tel-01111509

Articles in International Peer-Reviewed Journals

• 13K. 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
• 14J.-P. Cerri, J. Chaubert, P. Lezowski.
  
  Totally indefinite Euclidean quaternion fields, in: Acta Arithmetica, 2014, vol. 165, n^o 2, pp. 181-200.
  
  https://hal.archives-ouvertes.fr/hal-01016614
• 15H. Cohen.
  
  Exact counting of $D_{\ell }$ number fields with given quadratic resolvent, in: Mathematics of Computation, 2014, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01027417
• 16H. Cohen, F. Thorne.
  
  Dirichlet series associated to cubic fields with given quadratic resolvent, in: Michigan Mathematical Journal, 2014, vol. 63, pp. 253-273.
  
  https://hal.inria.fr/hal-00854662
• 17R. Cosset, D. Robert.
  
  Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves, in: Mathematics of Computation, November 2014, 23 p, forthcoming. [ DOI : 10.1090/S0025-5718-2014-02899-8 ]
  
  https://hal.archives-ouvertes.fr/hal-00578991
• 18J.-M. Couveignes, R. Lercier.
  
  The geometry of some parameterizations and encodings, in: Advances in mathematics of communications, December 2014, vol. 8, n^o 4, 22 p. [ DOI : 10.3934/amc.2014.8.437 ]
  
  https://hal.archives-ouvertes.fr/hal-00870112
• 19A. Enge, F. Morain.
  
  Generalised Weber Functions, in: Acta Arithmetica, 2014, vol. 164, n^o 4, pp. 309-341. [ DOI : 10.4064/aa164-4-1 ]
  
  https://hal.inria.fr/inria-00385608
• 20A. Enge, E. Thomé.
  
  Computing class polynomials for abelian surfaces, in: Experimental Mathematics, 2014, vol. 23, pp. 129-145. [ DOI : 10.1080/10586458.2013.878675 ]
  
  https://hal.inria.fr/hal-00823745
• 21P. Lezowski.
  
  Computation of the Euclidean minimum of algebraic number fields, in: Mathematics of Computation, 2014, vol. 83, pp. 1397-1426, 30 pages, shorter version, with many typos fixed. [ DOI : 10.1090/S0025-5718-2013-02746-9 ]
  
  https://hal.archives-ouvertes.fr/hal-00632997
• 22D. 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
• 23A. Page.
  
  Computing arithmetic Kleinian groups, in: Mathematics of Computation, 2014, 29 p, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-00703043

International Conferences with Proceedings

• 24A. Enge, J. Milan.
  
  Implementing cryptographic pairings at standard security levels, in: Security, Privacy, and Applied Cryptography Engineering, Pune, India, R. S. Chakraborty, V. Matyas, P. Schaumont (editors), Lecture Notes in Computer Science, Springer, October 2014, vol. 8804, pp. 28-46. [ DOI : 10.1007/978-3-319-12060-7_3 ]
  
  https://hal.inria.fr/hal-01034213
• 25A. Page.
  
  An algorithm for the principal ideal problem in indefinite quaternion algebras, in: ANTS XI, GyeongJu, South Korea, August 2014.
  
  https://hal.archives-ouvertes.fr/hal-00996346

Other Publications

• 26H. Cohen, S. Rubinstein-Salzedo, F. Thorne.
  
  Identitites for Field Extensions Generalizing the Ohno–Nakagawa Relations, 2015.
  
  https://hal.inria.fr/hal-01109980
• 27J.-M. Couveignes, T. Ezome.
  
  Computing functions on Jacobians and their quotients, November 2014.
  
  https://hal.archives-ouvertes.fr/hal-01088933
• 28A. Enge.
  
  Bilinear pairings on elliptic curves, February 2014.
  
  https://hal.inria.fr/hal-00767404
• 29B. Julio.
  
  Selmer groups of elliptic curves in degree $p$ extensions, 2014.
  
  https://hal.archives-ouvertes.fr/hal-01111745
• 30B. Julio, J. Nathan.
  
  Elliptic curves with 2-torsion contained in the 3-torsion field, January 2015.
  
  https://hal.archives-ouvertes.fr/hal-01111744
• 31D. Lubicz, D. Robert.
  
  Arithmetic on Abelian and Kummer Varieties, June 2014.
  
  https://hal.archives-ouvertes.fr/hal-01057467
• 32D. Lubicz, D. Robert.
  
  Computing separable isogenies in quasi-optimal time, February 2014, Accepted for publication at LMS Journal of Computation and Mathematics.
  
  https://hal.archives-ouvertes.fr/hal-00954895
• 33N. Mascot.
  
  Tables of modular Galois representations, 2014.
  
  https://hal.archives-ouvertes.fr/hal-01110252
• 34E. Milio.
  
  A quasi-linear algorithm for computing modular polynomials in dimension 2, November 2014.
  
  https://hal.archives-ouvertes.fr/hal-01080462

References in notes

• 35K. 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.
• 36H. 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.
• 37A. Enge.
  
  Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
  
  http://tel.archives-ouvertes.fr/tel-00382535/en/
• 38P. Lezowski.
  
  Computation of the Euclidean minimum of algebraic number fields, 2011, To appear in Mathematics of Computation, 30 pages.
  
  http://hal.archives-ouvertes.fr/hal-00632997
• 39N. Mascot.
  
  Computing modular Galois representations, in: Rendiconti del Circolo Matematico di Palermo, December 2013, vol. 62, n^o 3, pp. 451-476. [ DOI : 10.1007/s12215-013-0136-4 ]
  
  https://hal.archives-ouvertes.fr/hal-00776606