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

Articles in International Peer-Reviewed Journals

• 11J.-P. Cerri, J. Chaubert, P. Lezowski.
  Euclidean totally definite quaternion fields over the rational field and over quadratic number fields, in: International Journal of Number Theory, January 2013, vol. 9, n^o 3, pp. 653-673. [ DOI : 10.1142/S1793042112501540 ]
  http://hal.inria.fr/hal-00738164
• 12J.-M. Couveignes, R. Lercier.
  Fast construction of irreducible polynomials over finite fields, in: Israël Journal of Mathematics, 2013, vol. 194, n^o 1, pp. 77-105, This text reports on a talk given at Lorentz center in Leiden during the recent workshop on it Counting points on varieties. [ DOI : 10.1007/s11856-012-0070-8 ]
  http://hal.inria.fr/hal-00456456
• 13A. Enge, R. Schertz.
  Singular values of multiple eta-quotients for ramified primes, in: LMS Journal of Computation and Mathematics, 2013, vol. 16, pp. 407-418. [ DOI : 10.1112/S146115701300020X ]
  http://hal.inria.fr/hal-00768375
• 14A. Enge, E. Thomé.
  Computing class polynomials for abelian surfaces, in: Experimental Mathematics, 2014, Accepted for publication.
  http://hal.inria.fr/hal-00823745
• 15N. 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 ]
  http://hal.inria.fr/hal-00776606

International Conferences with Proceedings

• 16A. Angelakis, P. Stevenhagen.
  Imaginary quadratic fields with isomorphic abelian Galois groups, in: ANTS X - Tenth Algorithmic Number Theory Symposium, San Diego, United States, E. W. Howe, K. S. Kedlaya (editors), Mathematical Sciences Publisher, November 2013, vol. 1, pp. 21-39. [ DOI : 10.2140/obs.2013.1.21 ]
  http://hal.inria.fr/hal-00751883
• 17H. Cohen.
  Haberland's formula and numerical computation of Petersson scalar products, in: ANTS X, San Diego, United States, E. W. Howe, K. S. Kedlaya (editors), The Open Book Series, Mathematical Sciences Publisher, 2013, vol. 1, pp. 249-270. [ DOI : 10.2140/obs.2013.1.249 ]
  http://hal.inria.fr/hal-00854440
• 18K. Lauter, D. Robert.
  Improved CRT Algorithm for Class Polynomials in Genus 2, in: ANTS X - Algorithmic Number Theory 2012, San Diego, United States, E. W. Howe, K. S. Kedlaya (editors), The Open Book Series, Mathematical Sciences Publisher, November 2013, vol. 1, pp. 437-461. [ DOI : 10.2140/obs.2013.1.437 ]
  http://hal.inria.fr/hal-00734450

Scientific Books (or Scientific Book chapters)

• 19K. Belabas, F. Beukers, P. Gaudry, W. Mccallum, B. Poonen, S. Siksek, M. Stoll, M. Watkins.
  Explicit methods in number theory. Rational points and Diophantine equations, SMF, 2013, xxi + 179 p.
  http://hal.inria.fr/hal-00932377
• 20J.-M. Couveignes, P. Boalch, P. Dèbes, D. Bertrand.
  Geometric and differential Galois theories, Société Mathématique de France, 2013, 240 p.
  http://hal.inria.fr/hal-00694296
• 21A. Enge.
  Elliptic curve cryptographic systems, in: Handbook of Finite Fields, G. L. Mullen, D. Panario (editors), Discrete Mathematics and Its Applications, Chapman and Hall/CRC, 2013, pp. 784-796.
  http://hal.inria.fr/hal-00764963

Other Publications

• 22K. Belabas, E. Friedman.
  Computing the residue of the Dedekind zeta function, 2013, 16 p.
  http://hal.inria.fr/hal-00916654
• 23H. Cohen, F. Thorne.
  Dirichlet series associated to cubic fields with given quadratic resolvent, 2013, 16 pages, submitted. Revised version: includes counts of S_3-sextic fields.
  http://hal.inria.fr/hal-00854662
• 24H. Cohen, F. Thorne.
  Dirichlet series associated to quartic fields with given resolvent, 2013, 36 pages, submitted, comments welcome.
  http://hal.inria.fr/hal-00854664
• 25R. Cosset, D. Robert.
  Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves, 2013, Accepté pour publication à Mathematics of Computations.
  http://hal.inria.fr/hal-00578991
• 26J.-M. Couveignes, R. Lercier.
  The geometry of some parameterizations and encodings, 2013.
  http://hal.inria.fr/hal-00870112
• 27A. Enge.
  Bilinear pairings on elliptic curves, January 2013.
  http://hal.inria.fr/hal-00767404
• 28A. Enge, F. Morain.
  Generalised Weber Functions, 2013.
  http://hal.inria.fr/inria-00385608
• 29D. Lubicz, D. Robert.
  A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties, 2013.
  http://hal.inria.fr/hal-00806923
• 30A. Page.
  Computing arithmetic Kleinian groups, 2013, Revisions according to the comments of the referee.
  http://hal.inria.fr/hal-00703043

References in notes

• 31E. Bach.
  Improved approximations for Euler products, in: Number theory (Halifax, NS, 1994), Amer. Math. Soc., 1995, pp. 13–28.
• 32K. 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.
• 33K. Belabas, F. Diaz y Diaz, E. Friedman.
  Small generators of the ideal class group, in: Mathematics of Computation, 2008, vol. 77, n^o 262, pp. 1185–1197.
  http://www.ams.org/journals/mcom/2008-77-262/S0025-5718-07-02003-0/home.html
• 34J.-P. Cerri.
  Spectres euclidiens et inhomogènes des corps de nombres, IECN, Université Henri Poincaré, Nancy, 2005.
  http://tel.archives-ouvertes.fr/tel-00011151/en/
• 35J.-P. Cerri.
  Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1, in: J. Reine Angew. Math., 2006, vol. 592, pp. 49–62.
• 36D. Charles, E. Goren, K. Lauter.
  Cryptographic Hash Functions from Expander Graphs, in: Journal of Cryptology, 2009, vol. 22, n^o 1, pp. 93–113.
• 37H. 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.
• 38R. Dupont.
  Moyenne arithmetico-geometrique, suites de Borchardt et applications, Ecole polytechnique, Palaiseau, 2006.
• 39A. Enge.
  Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
  http://tel.archives-ouvertes.fr/tel-00382535/en/
• 40A. Enge.
  Elliptic Curves and Their Applications to Cryptography — An Introduction, Kluwer Academic Publishers, 1999.
• 41P. Lezowski.
  Computation of the Euclidean minimum of algebraic number fields, 2011, 30 p, To appear.
  http://hal.archives-ouvertes.fr/hal-00632997
• 42D. Lubicz, D. Robert.
  Efficient pairing computation with theta functions, in: Algorithmic Number Theory — ANTS-IX, G. Hanrot, F. Morain, E. Thomé (editors), Lecture Notes in Comput. Sci., Springer–Verlag, 07 2010, vol. 6197. [ DOI : 10.1007/978-3-642-14518-6_21 ]
  http://www.normalesup.org/~robert/pro/publications/articles/pairings.pdf
• 43A. Rostovtsev, A. Stolbunov.
  Public-key cryptosystem based on isogenies, 2006, Preprint, Cryptology ePrint Archive 2006/145.
  http://eprint.iacr.org/2006/145/