Bibliography
Major publications by the team in recent years
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1R. 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 -
2R. 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 -
3A. Enge, P. Gaudry, E. Thomé.
An 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 -
4P. Gaudry, É. Schost.
Genus 2 point counting over prime fields, in: Journal of Symbolic Computation, 2012, vol. 47, no 4, pp. 368-400. [ DOI : 10.1016/j.jsc.2011.09.003 ]
http://hal.inria.fr/inria-00542650 -
5T. 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 -
6D. Lubicz, D. Robert.
Computing isogenies between Abelian Varieties, in: Compositio Mathematica, September 2012, vol. 148, no 05, pp. 1483–1515. [ DOI : 10.1112/S0010437X12000243 ]
http://hal.inria.fr/hal-00446062
Articles in International Peer-Reviewed Journals
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7S. Bai, R. Brent, E. Thomé.
Root optimization of polynomials in the number field sieve, in: Mathematics of Computation, 2014, forthcoming.
https://hal.inria.fr/hal-00919367 -
8C. Bouvier, P. Zimmermann.
Division-Free Binary-to-Decimal Conversion, in: IEEE Transactions on Computers, August 2014, vol. 63, no 8, pp. 1895-1901. [ DOI : 10.1109/TC.2014.2315621 ]
https://hal.inria.fr/hal-00864293 -
9R. 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 -
10A. 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 -
11E. Gioan, S. Burckel, E. Thomé.
Computation with No Memory, and Rearrangeable Multicast Networks, in: Discrete Mathematics and Theoretical Computer Science, February 2014, vol. 16, no 1, pp. 121-142.
http://hal-lirmm.ccsd.cnrs.fr/lirmm-00959964 -
12G. Ottaviani, P.-J. Spaenlehauer, B. Sturmfels.
Exact Solutions in Structured Low-Rank Approximation, in: SIAM Journal on Matrix Analysis and Applications, 2014, vol. 4, pp. 1521-1542.
https://hal.archives-ouvertes.fr/hal-00953702 -
13É. Schost, P.-J. Spaenlehauer.
A Quadratically Convergent Algorithm for Structured Low-Rank Approximation, in: Foundations of Computational Mathematics, 2015, forthcoming.
https://hal.archives-ouvertes.fr/hal-00953684 -
14P.-J. Spaenlehauer.
On the Complexity of Computing Critical Points with Gröbner Bases, in: SIAM Journal on Optimization, 2014, vol. 24, no 3, pp. 1382-1401, 25 pages.
https://hal.archives-ouvertes.fr/hal-01017032
International Conferences with Proceedings
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15R. Barbulescu, C. Bouvier, J. Detrey, P. Gaudry, H. Jeljeli, E. Thomé, M. Videau, P. Zimmermann.
Discrete logarithm in GF( ) 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 -
16R. Barbulescu, P. Gaudry, A. Guillevic, F. Morain.
Improving NFS for the discrete logarithm problem in non-prime finite fields, in: Eurocrypt 2015, Sofia, Bulgaria, M. Fischlin, E. Oswald (editors), Eurocrypt 2015, 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, April 2015, 27 p.
https://hal.inria.fr/hal-01112879 -
18V. 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 -
19J.-C. Faugère, P. Gaudry, L. Huot, G. Renault.
Sub-cubic Change of Ordering for Gröner Basis: A Probabilistic Approach, in: ISSAC '14 - Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, Kobe, Japan, ISSAC '14, ACM, July 2014, pp. 170–177. [ DOI : 10.1145/2608628.2608669 ]
https://hal.inria.fr/hal-01064551 -
20J.-C. Faugère, P.-J. Spaenlehauer, J. Svartz.
Sparse Gröbner Bases: the Unmixed Case, in: ISSAC 2014, Kobe, Japan, July 2014, 20 pages, Corollary 6.1 has been corrected. [ DOI : 10.1145/2608628.2608663 ]
https://hal.archives-ouvertes.fr/hal-00953501 -
21H. Jeljeli.
Accelerating Iterative SpMV for Discrete Logarithm Problem Using GPUs, in: International Workshop on the Arithmetic of Finite Fields WAIFI 2014, Gebze, Turkey, September 2014.
https://hal.inria.fr/hal-00734975 -
22H. Jeljeli.
Resolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures, in: Euro-Par 2014 Parallel Processing, Porto, Portugal, August 2014.
https://hal.inria.fr/hal-00946895
Internal Reports
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23V. Cortier, D. Galindo, S. Glondu, M. Izabachène.
Election Verifiability for Helios under Weaker Trust Assumptions, June 2014, no RR-8555, 20 p.
https://hal.inria.fr/hal-01011294
Other Publications
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24S. Bai, C. Bouvier, A. Kruppa, P. Zimmermann.
Better polynomials for GNFS, September 2014.
https://hal.inria.fr/hal-01089507 -
25R. Barbulescu, P. Gaudry, A. Guillevic, F. Morain.
Improvements to the number field sieve for non-prime finite fields, November 2014.
https://hal.inria.fr/hal-01052449 -
26S. Covanov, E. Thomé.
Fast arithmetic for faster integer multiplication, January 2015.
https://hal.inria.fr/hal-01108166 -
27N. Coxon.
Montgomery's method of polynomial selection for the number field sieve, December 2014.
https://hal.inria.fr/hal-01097069 -
28J. Detrey.
FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve, May 2014.
https://hal.inria.fr/hal-01002419 -
29S. Ionica, E. Thomé.
Isogeny graphs with maximal real multiplication, March 2014.
https://hal.archives-ouvertes.fr/hal-00967742 -
30M. Massierer.
Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves, December 2014.
https://hal.inria.fr/hal-01097362
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31Agence 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/ -
32N. Koblitz.
Hyperelliptic cryptosystems, in: J. Cryptology, 1989, vol. 1, pp. 139–150.