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
• 3X. Caruso, J. L. Borgne.
  
  A new faster algorithm for factoring skew polynomials over finite fields, in: J. Symbolic Comput., 2018, vol. 79, pp. 411–443.
• 4X. Caruso, D. Roe, T. Vaccon.
  
  Tracking $p$-adic precision, in: LMS J. Comput. Math., 2014, vol. 17, pp. 274–294.
• 5G. Castagnos, F. Laguillaumie, I. Tucker.
  
  Practical Fully Secure Unrestricted Inner Product Functional Encryption modulo p, in: Advances in Cryptology – ASIACRYPT 2018, Part II, T. Peyrin, S. Galbraith (editors), Lecture Notes in Computer Science, International Association for Cryptologic Research, 2018, vol. 11273, pp. 733–764.
• 6H. Cohen, F. Strömberg.
  
  Modular Forms: A Classical Approach, Graduate Studies in Mathematics, American Mathematical Society, 2017, vol. 179.
  
  http://bookstore.ams.org/gsm-179/
• 7J.-M. Couveignes, B. Edixhoven.
  
  Computational aspects of modular forms and Galois representations, Princeton University Press, 2011.
• 8A. 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.
• 9A. Enge, W. Hart, F. Johansson.
  
  Short addition sequences for theta functions, in: Journal of Integer Sequences, 2018, vol. 18, n^o 2, pp. 1–34.
• 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

• 11G. Castagnos.
  
  Cryptography based on quadratic fields: cryptanalyses, primitives and protocols, Université de Bordeaux, November 2019, Habilitation à diriger des recherches.
  
  https://tel.archives-ouvertes.fr/tel-02403707

Articles in International Peer-Reviewed Journals

• 12R. Barbulescu, J. Ray.
  
  Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's p-rationality conjecture, in: Journal de Théorie des Nombres de Bordeaux, 2019, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01534050
• 13A. Bartel, A. Page.
  
  Group representations in the homology of 3-manifolds, in: Commentarii Mathematici Helvetici, March 2019, https://arxiv.org/abs/1605.04866. [ DOI : 10.4171/CMH/455 ]
  
  https://hal.inria.fr/hal-01671748
• 14K. Belabas, D. Bernardi, B. Perrin-Riou.
  
  La constante de Manin et le degré modulaire d'une courbe elliptique, in: Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres, 2019, n^o 2, pp. 81-103.
  
  https://hal.archives-ouvertes.fr/hal-01766202
• 15J.-P. Cerri, P. Lezowski.
  
  Computation of Euclidean minima in totally definite quaternion fields, in: International Journal of Number Theory, 2019, vol. 15, n^o 1, pp. 43–66.
  
  https://hal.archives-ouvertes.fr/hal-01447059
• 16S. Ionica, E. Thomé.
  
  Isogeny graphs with maximal real multiplication, in: Journal of Number Theory, February 2020, vol. 207, pp. 385-422, https://arxiv.org/abs/1407.6672. [ DOI : 10.1016/j.jnt.2019.06.019 ]
  
  https://hal.archives-ouvertes.fr/hal-00967742
• 17F. Johansson, I. V. Blagouchine.
  
  Computing Stieltjes constants using complex integration, in: Mathematics of Computation, 2019, vol. 88, n^o 318, https://arxiv.org/abs/1804.01679.
  
  https://hal.inria.fr/hal-01758620
• 18A. Riffaut.
  
  Equations with powers of singular moduli, in: International Journal of Number Theory, 2019, vol. 15, n^o 3, pp. 445-468. [ DOI : 10.1142/S1793042119500234 ]
  
  https://hal.archives-ouvertes.fr/hal-01630363

International Conferences with Proceedings

• 19X. Caruso, T. Vaccon, T. Verron.
  
  Gröbner bases over Tate algebras, in: ISSAC, Beijing, China, July 2019, https://arxiv.org/abs/1901.09574. [ DOI : 10.1145/3326229.3326257 ]
  
  https://hal.archives-ouvertes.fr/hal-01995881
• 20G. Castagnos, D. Catalano, F. Laguillaumie, F. Savasta, I. Tucker.
  
  Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations, in: CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, United States, Advances in Cryptology – CRYPTO 2019, August 2019, vol. LNCS, n^o 11694, pp. 191-221. [ DOI : 10.1007/978-3-030-26954-8_7 ]
  
  https://hal.archives-ouvertes.fr/hal-02281931

Scientific Books (or Scientific Book chapters)

• 22X. Caruso.
  
  An introduction to p-adic period rings, in: An introduction to p-adic Hodge theory, 2019, https://arxiv.org/abs/1908.08424, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-02268787
• 23H. Cohen.
  
  An Introduction to Modular Forms, in: Notes from the International School on Computational Number Theory, I. Inam, E. Büyükaşık (editors), Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2019, pp. 3-62, https://arxiv.org/abs/1809.10907.
  
  https://hal.inria.fr/hal-01883058
• 24H. Cohen.
  
  Computational Number Theory in Relation with L-Functions, in: Notes from the International School on Computational Number Theory, I. Inam, E. Büyükaşık (editors), Tutorials, Schools, and Workshops in the Mathematical Sciences, Birkhäuser, 2019, pp. 171-266, https://arxiv.org/abs/1809.10904. [ DOI : 10.1007/978-3-030-12558-5_3 ]
  
  https://hal.inria.fr/hal-01883052
• 25H. Cohen.
  
  Expansions at Cusps and Petersson Products in Pari/GP, in: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider, P. Paule (editors), Texts & Monographs in Symbolic Computation, Springer, 2019, https://arxiv.org/abs/1809.10908.
  
  https://hal.inria.fr/hal-01883070
• 26F. Johansson.
  
  Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms, in: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider, P. Paule (editors), Texts & Monographs in Symbolic Computation, Springer, 2019, pp. 269-293, https://arxiv.org/abs/1806.06725.
  
  https://hal.inria.fr/hal-01817952

Other Publications

• 27R. Barbulescu, N. El Mrabet, L. Ghammam.
  
  A taxonomy of pairings, their security, their complexity, May 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02129868
• 28R. Barbulescu, S. Shinde.
  
  A classification of ECM-friendly families using modular curves, February 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01822144
• 29X. Caruso.
  
  Residues of skew rational functions and linearized Goppa codes, August 2019, https://arxiv.org/abs/1908.08430 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02268790
• 30J.-M. Couveignes.
  
  Enumerating number fields, November 2019, https://arxiv.org/abs/1907.13617 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02375397
• 31J. Kieffer.
  
  Degree and height estimates for modular equations on PEL Shimura varieties, January 2020, https://arxiv.org/abs/2001.04138 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02436057
• 32J. Kieffer, A. Page, D. Robert.
  
  Computing isogenies from modular equations between Jacobians of genus 2 curves, January 2020, https://arxiv.org/abs/2001.04137 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02436133
• 33C. Maire, A. Page.
  
  Codes from unit groups of division algebras over number fields, 2019, https://arxiv.org/abs/1804.07108 - working paper or preprint.
  
  https://hal.inria.fr/hal-01770396
• 34C. Martindale.
  
  Hilbert Modular Polynomials, January 2019, working paper or preprint.
  
  https://hal.inria.fr/hal-01990298
• 35E. Milio, D. Robert.
  
  Modular polynomials on Hilbert surfaces, June 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01520262

References in notes

• 36K. 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.
• 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.
• 38A. Enge.
  
  Courbes algébriques et cryptologie, Université Denis Diderot, Paris 7, 2007, Habilitation à diriger des recherches.
  
  http://tel.archives-ouvertes.fr/tel-00382535/en/