Bibliography
Major publications by the team in recent years
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1E. Bayer-Fluckiger, J.-P. Cerri, J. Chaubert.
Euclidean minima and central division algebras, in: International Journal of Number Theory, 2009, vol. 5, no 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, no 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, no 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, no 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, no 1, pp. 24–41. -
10D. Lubicz, D. Robert.
Computing isogenies between abelian varieties, in: Compositio Mathematica, 09 2012, vol. 148, no 05, pp. 1483–1515.
http://dx.doi.org/10.1112/S0010437X12000243
Doctoral Dissertations and Habilitation Theses
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11E. Milio.
Computing modular polynomials in dimension 2, université de bordeaux, December 2015.
https://tel.archives-ouvertes.fr/tel-01240690
Articles in International Peer-Reviewed Journals
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12K. 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 -
13H. Cohen.
Exact counting of number fields with given quadratic resolvent, in: Mathematics of Computation, 2015, vol. 84, no 294, pp. 1933-1951.
https://hal.archives-ouvertes.fr/hal-01027417 -
14H. Cohen, S. Rubinstein-Salzedo, F. Thorne.
Identitites for Field Extensions Generalizing the Ohno–Nakagawa Relations, in: Compositio Mathematica, 2015, vol. 151, no 11, pp. 2059-2075.
https://hal.inria.fr/hal-01109980 -
15R. Cosset, D. Robert.
Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves, in: Mathematics of Computation, 2015, vol. 84, no 294, pp. 1953-1975, Accepté pour publication à Mathematics of Computations. [ DOI : 10.1090/S0025-5718-2014-02899-8 ]
https://hal.archives-ouvertes.fr/hal-00578991 -
16J.-M. Couveignes, T. Ezome.
Computing functions on Jacobians and their quotients, in: The London Mathematical Society Journal of Computations and Mathematics, October 2015, vol. 18, no 1, pp. 555-577.
https://hal.archives-ouvertes.fr/hal-01088933 -
17A. Enge.
Bilinear pairings on elliptic curves, in: L'Enseignement Mathématique, 2015, vol. 61, no 2, pp. 209–241.
https://hal.inria.fr/hal-00767404 -
18D. 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 -
19D. Lubicz, D. Robert.
Computing separable isogenies in quasi-optimal time, in: LMS Journal of Computation and Mathematics, 2015, vol. 18, no 1, pp. 198-216. [ DOI : 10.1112/S146115701400045X ]
https://hal.archives-ouvertes.fr/hal-00954895 -
20E. Milio.
A quasi-linear time algorithm for computing modular polynomials in dimension 2, in: LMS Journal of Computation and Mathematics, 2015, vol. 18, pp. 603-632.
https://hal.archives-ouvertes.fr/hal-01080462 -
21A. Page.
Computing arithmetic Kleinian groups, in: Mathematics of Computation, 2015, vol. 84, no 295, pp. 2361-2390.
https://hal.archives-ouvertes.fr/hal-00703043
International Conferences with Proceedings
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22G. Castagnos, F. Laguillaumie.
Linearly Homomorphic Encryption from DDH, in: The Cryptographer's Track at the RSA Conference 2015, San Francisco, United States, Topics in Cryptology –- CT-RSA 2015, April 2015, no 9048. [ DOI : 10.1007/978-3-319-16715-2_26 ]
https://hal.archives-ouvertes.fr/hal-01213284 -
23F. Johansson.
Efficient implementation of elementary functions in the medium-precision range, in: 22nd IEEE Symposium on Computer Arithmetic (ARITH22), Lyon, France, June 2015. [ DOI : 10.1109/ARITH.2015.16 ]
https://hal.archives-ouvertes.fr/hal-01079834
Patents
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24G. Zemor, L. Juan, J.-M. Camus, M. Perret, J.-M. Couveignes.
Method and device for protecting the integrity of data transmitted over a network, April 2015, no US 9,009,839 B2.
https://hal.archives-ouvertes.fr/hal-01213785
Other Publications
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25J. Brau, N. Jones.
Elliptic curves with 2-torsion contained in the 3-torsion field, January 2015, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01111744 -
26S. Ionica, E. Thomé.
Isogeny graphs with maximal real multiplication, January 2015, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-00967742 -
27P. Kılıçer, M. Streng.
The CM class number one problem for curves of genus 2, December 2015, working paper or preprint.
https://hal.inria.fr/hal-01248630 -
28P. Lezowski.
On some Euclidean properties of matrix algebras, March 2015, 39 pages, some corrections and improvements, especially in Section 7.
https://hal.archives-ouvertes.fr/hal-01135202 -
29D. Lubicz, D. Robert.
Arithmetic on Abelian and Kummer Varieties, September 2015, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01057467
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30K. 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. -
31H. 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. -
32A. Enge.
Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
http://tel.archives-ouvertes.fr/tel-00382535/en/