Bibliography

Major publications by the team in recent years

• 1R. Barbulescu, P. Gaudry, A. Joux, E. Thomé.
  
  A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic, in: Eurocrypt 2014, Copenhagen, Denmark, P. Q. Nguyen, E. Oswald (editors), Springer, May 2014, vol. 8441, pp. 1-16. [ DOI : 10.1007/978-3-642-55220-5_1 ]
  
  https://hal.inria.fr/hal-00835446
• 2R. Brent, P. Zimmermann.
  
  Modern Computer Arithmetic, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2010, vol. 18, 221 p.
  
  http://hal.inria.fr/inria-00424347
• 3R. 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
• 4A. Enge, P. Gaudry, E. Thomé.
  
  An $L(1/3)$ Discrete Logarithm Algorithm for Low Degree Curves, in: Journal of Cryptology, 2011, vol. 24, pp. 24-41. [ DOI : 10.1007/s00145-010-9057-y ]
  
  http://hal.inria.fr/inria-00383941
• 5P. Gaudry, É. Schost.
  
  Genus 2 point counting over prime fields, in: Journal of Symbolic Computation, 2012, vol. 47, n^o 4, pp. 368-400. [ DOI : 10.1016/j.jsc.2011.09.003 ]
  
  http://hal.inria.fr/inria-00542650
• 6T. Kleinjung, K. Aoki, J. Franke, A. K. Lenstra, E. Thomé, J. W. Bos, P. Gaudry, A. Kruppa, P. L. Montgomery, D. A. Osvik, H. Te Riele, A. Timofeev, P. Zimmermann.
  
  Factorization of a 768-bit RSA modulus, in: CRYPTO 2010, Santa Barbara, United States, T. Rabin (editor), Lecture Notes in Computer Science, Springer Verlag, 2010, vol. 6223, pp. 333-350.
  
  http://link.springer.com/chapter/10.1007/978-3-642-14623-7_18
• 7D. Lubicz, D. Robert.
  
  Computing isogenies between Abelian Varieties, in: Compositio Mathematica, September 2012, vol. 148, n^o 05, pp. 1483–1515. [ DOI : 10.1112/S0010437X12000243 ]
  
  http://hal.inria.fr/hal-00446062

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 8C. Bouvier.
  
  Algorithms for integer factorization and discrete logarithms computation, Université de Lorraine, June 2015.
  
  https://tel.archives-ouvertes.fr/tel-01167281
• 9H. Jeljeli.
  
  Hardware and Software Accelerators for Sparse Linear Algebra over Finite Fields, Université de Lorraine, July 2015.
  
  https://tel.archives-ouvertes.fr/tel-01178931

Articles in International Peer-Reviewed Journals

• 10S. Bai, C. Bouvier, A. Kruppa, P. Zimmermann.
  
  Better polynomials for GNFS, in: Mathematics of Computation / Mathematics of Computation, December 2015, 12 p.
  
  https://hal.inria.fr/hal-01089507
• 11R. Barbulescu.
  
  Selecting polynomials for the Function Field Sieve, in: Mathematics of Computation, March 2015, S0025-5718-2015-02940-8.
  
  https://hal.inria.fr/hal-00798386
• 12R. Cosset, D. Robert.
  
  Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves, in: Mathematics of Computation, 2015, vol. 84, n^o 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
• 13S. Galbraith, P. Gaudry.
  
  Recent progress on the elliptic curve discrete logarithm problem, in: Designs, Codes and Cryptography, 2015. [ DOI : 10.1007/s10623-015-0146-7 ]
  
  https://hal.inria.fr/hal-01215623
• 14É. Schost, P.-J. Spaenlehauer.
  
  A Quadratically Convergent Algorithm for Structured Low-Rank Approximation, in: Foundations of Computational Mathematics, March 2015, pp. 1-36.
  
  https://hal.archives-ouvertes.fr/hal-00953684

International Conferences with Proceedings

• 16R. Barbulescu, P. Gaudry, A. Guillevic, F. Morain.
  
  Improving NFS for the discrete logarithm problem in non-prime finite fields, in: Eurocrypt 2015, 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, M. Fischlin, E. Oswald (editors), April 2015, 27 p.
  
  https://hal.inria.fr/hal-01112879

National Conferences with Proceedings

• 18H. Labrande.
  
  Crack me, I'm famous!: Cracking weak passphrases using freely available sources, in: SSTIC 2015, Rennes, France, June 2015.
  
  https://hal.inria.fr/hal-01238600

Other Publications

• 19F. Bihan, P.-J. Spaenlehauer.
  
  Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes, October 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01217547
• 20S. Covanov, E. Thomé.
  
  Fast arithmetic for faster integer multiplication, January 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01108166
• 21J.-G. Dumas, E. Kaltofen, E. Thomé.
  
  Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices, July 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01171249
• 22S. Ionica, E. Thomé.
  
  Isogeny graphs with maximal real multiplication, January 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-00967742
• 23H. Labrande.
  
  Computing Jacobi's $\theta$ in quasi-linear time, November 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01227699

References in notes

• 24Agence nationale de la sécurité des systèmes d'information.
  
  Référentiel général de sécurité, annexe B1, 2013.
  
  http://www.ssi.gouv.fr/fr/reglementation-ssi/referentiel-general-de-securite/
• 25R. Barbulescu, C. Bouvier, J. Detrey, P. Gaudry, H. Jeljeli, E. Thomé, M. Videau, P. Zimmermann.
  
  Discrete logarithm in GF($2^{809}$) with FFS, in: PKC 2014 - International Conference on Practice and Theory of Public-Key Cryptography, Buenos Aires, Argentina, H. Krawczyk (editor), LNCS, Springer, 2014. [ DOI : 10.1007/978-3-642-54631-0_13 ]
  
  https://hal.inria.fr/hal-00818124
• 26R. Barbulescu, P. Gaudry, A. Joux, E. Thomé.
  
  A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic, in: Eurocrypt 2014, Copenhagen, Denmark, P. Q. Nguyen, E. Oswald (editors), Springer, May 2014, vol. 8441, pp. 1-16. [ DOI : 10.1007/978-3-642-55220-5_1 ]
  
  https://hal.inria.fr/hal-00835446
• 27V. Cortier, D. Galindo, S. Glondu, M. Izabachène.
  
  Election Verifiability for Helios under Weaker Trust Assumptions, in: Proceedings of the 19th European Symposium on Research in Computer Security (ESORICS'14), Wroclaw, Poland, September 2014.
  
  https://hal.inria.fr/hal-01080292
• 28N. Koblitz.
  
  Hyperelliptic cryptosystems, in: J. Cryptology, 1989, vol. 1, pp. 139–150.