Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

1A. Greuet.

Optimisation polynomiale et variétés polaires : théorie, algorithmes, et implantations, Université de Versailles-Saint Quentin en Yvelines, December 2013.

http://hal.inria.fr/tel-00922805
2L. Huot.

Résolution de systèmes polynomiaux et cryptologie sur les courbes elliptiques, Université Pierre et Marie Curie - Paris VI, December 2013.

http://hal.inria.fr/tel-00925271

Articles in International Peer-Reviewed Journals

3M. Albrecht, C. Cid, J.-C. Faugère, R. Fitzpatrick, L. Perret.

On the Complexity of the BKW Algorithm on LWE, in: Designs, Codes and Cryptography, July 2013. [ DOI : 10.1007%2Fs10623-013-9864-x ]

http://hal.inria.fr/hal-00921517
4M. Bardet, J.-C. Faugère, B. Salvy, P.-J. Spaenlehauer.

On the Complexity of Solving Quadratic Boolean Systems, in: Journal of Complexity, February 2013, vol. 29, n^o 1, pp. 53-75. [ DOI : 10.1016/j.jco.2012.07.001 ]

http://hal.inria.fr/hal-00655745
5J. Berthomieu, G. Lecerf, G. Quintin.

Polynomial root finding over local rings and application to error correcting codes, in: Applicable Algebra in Engineering, Communication and Computing, December 2013, vol. 24, n^o 6, pp. 413-443. [ DOI : 10.1007/s00200-013-0200-5 ]

http://hal.inria.fr/hal-00642075
6L. Bettale, J.-C. Faugère, L. Perret.

Cryptanalysis of HFE, Multi-HFE and Variants for Odd and Even Characteristic, in: Designs, Codes and Cryptography, 2013, vol. 69, n^o 1, pp. 1 - 52. [ DOI : 10.1007/s10623-012-9617-2 ]

http://hal.inria.fr/hal-00776072
7X. Chen, D. Wang.

Formalization and Specification of Geometric Knowledge Objects, in: Mathematics in Computer Science, 2013, vol. 7, n^o 4. [ DOI : 10.1007/s11786-013-0167-4 ]

http://hal.inria.fr/hal-00913400
8C. Eder.

An analysis of inhomogeneous signature-based Gröbner basis computations, in: Journal of Symbolic Computation, 2013, vol. 59, pp. 21–35. [ DOI : 10.1016/j.jsc.2013.08.001 ]

http://hal.inria.fr/hal-00930286
9C. Eder.

Improving incremental signature-based Gröbner basis algorithms, in: ACM Communications in Computer Algebra, 2013, vol. 47, n^o 1, pp. 1-13. [ DOI : 10.1145/2503697.2503699 ]

http://hal.inria.fr/hal-00930293
10I. Emiris, E. Tsigaridas, G. Tzoumas.

Exact Voronoi diagram of smooth convex pseudo-circles: General predicates, and implementation for ellipses, in: Computer Aided Geometric Design, 2013. [ DOI : 10.1016/j.cagd.2013.06.005 ]

http://hal.inria.fr/hal-00843033
11J.-C. Faugère, P. Gaudry, L. Huot, G. Renault.

Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm, in: Journal of Cryptology, May 2013, pp. 1-40, 40 pages. [ DOI : 10.1007/s00145-013-9158-5 ]

http://hal.inria.fr/hal-00700555
12J.-C. Faugère, V. Gauthier-Umana, A. Otmani, L. Perret, J.-P. Tillich.

A Distinguisher for High Rate McEliece Cryptosystems, in: IEEE Transactions on Information Theory, June 2013, vol. 59, n^o 10, pp. 6830-6844. [ DOI : 10.1109/TIT.2013.2272036 ]

http://hal.inria.fr/hal-00776068
13J.-C. Faugère, M. Safey El Din, P.-J. Spaenlehauer.

On the Complexity of the Generalized MinRank Problem, in: Journal of Symbolic Computation, March 2013, vol. 55, pp. 30-58. [ DOI : 10.1016/j.jsc.2013.03.004 ]

http://hal.inria.fr/hal-00654094
14A. Ghosh, E. Tsigaridas, B. Mourrain, R. Deriche.

A polynomial approach for extracting the extrema of a spherical function and its application in diffusion MRI, in: Medical Image Analysis, July 2013, vol. 17, n^o 5, pp. 503-514. [ DOI : 10.1016/j.media.2013.03.004 ]

http://hal.inria.fr/hal-00815120
15K. A. Hansen, R. Ibsen-Jensen, V. V. Podolskii, E. Tsigaridas.

Patience of Matrix Games, in: Discrete Applied Mathematics, 2013. [ DOI : 10.1016/j.dam.2013.05.008 ]

http://hal.inria.fr/hal-00843052
16H. Hong, D. Wang, J. Yang.

A Framework for Improving Uniformity of Parameterizations of Curves, in: Science China Information Sciences, 2013, vol. 56, n^o 10. [ DOI : 10.1007/s11432-013-4924-4 ]

http://hal.inria.fr/hal-00913394
17G. Jeronimo, D. Perrucci, E. Tsigaridas.

On the minimum of a polynomial function on a basic closed semialgebraic set and applications, in: SIAM Journal on Optimization, 2013, vol. 23, n^o 1, pp. 241–255.

http://hal.inria.fr/hal-00776280
18M. Jin, X. Li, D. Wang.

A new algorithmic scheme for computing characteristic sets, in: Journal of Symbolic Computation, 2013, vol. 50, pp. 431-449. [ DOI : 10.1016/j.jsc.2012.04.004 ]

http://hal.inria.fr/hal-00793120
19C. Mou, D. Wang, X. Li.

Decomposing polynomial sets into simple sets over finite fields: The positive-dimensional case, in: Theoretical Computer Science, January 2013, vol. 468, pp. 102-113. [ DOI : 10.1016/j.tcs.2012.11.009 ]

http://hal.inria.fr/hal-00765840
20J. Yang, D. Wang, H. Hong.

Improving Angular Speed Uniformity by Reparameterization, in: Computer Aided Geometric Design, 2013, vol. 30, n^o 7, pp. 636-652. [ DOI : 10.1016/j.cagd.2013.04.001 ]

http://hal.inria.fr/hal-00913378

Invited Conferences

21M. Safey El Din.

Critical Point Methods and Effective Real Algebraic Geometry: New Results and Trends, in: ISSAC 2013 - 38th International Symposium on Symbolic and Algebraic Computation, Boston, United States, M. Kauers (editor), 2013, pp. 5-6. [ DOI : 10.1145/2465506.2465928 ]

http://hal.inria.fr/hal-00922718
22D. Wang.

Automation of Geometry - Theorem Proving, Diagram Generation, and Knowledge Management, in: ADG 2012 - 9th International Workshop Automated Deduction in Geometry, Edinburgh, United Kingdom, T. Ida, J. Fleuriot (editors), Lecture Notes in Computer Science, Springer, 2013, vol. 7993, pp. 31-32. [ DOI : 10.1007/978-3-642-40672-0_2 ]

http://hal.inria.fr/hal-00913433

International Conferences with Proceedings

23M. Albrecht, J.-C. Faugère, R. Fitzpatrick, L. Perret.

Lazy Modulus Switching for the BKW Algorithm on LWE, in: Public-Key Cryptography - PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Buenos Aires, Argentina, Springer, March 2014.

http://hal.inria.fr/hal-00925187
24M. Albrecht, J.-C. Faugère, R. Fitzpatrick, L. Perret, Y. Todo, K. Xagawa.

Practical Cryptanalysis of a Public-Key Encryption Scheme Based on New Multivariate Quadratic Assumptions, in: PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Buenos Aires, Argentina, Springer, March 2014.

http://hal.inria.fr/hal-00932382
25G. Barbu, A. Battistelllo, G. Dabosville, C. Giraud, G. Renault, S. Renner, R. Zeitoun.

Combined Attack on CRT-RSA. Why Public Verification Must Not Be Public?, in: PKC 2013 - Public-Key Cryptography, Nara, Japan, K. Kurosawa, G. Hanaoka (editors), Lecture Notes in Computer Science, Springer, 2013, vol. 7778, pp. 1-17. [ DOI : 10.1007/978-3-642-36362-7_13 ]

http://hal.inria.fr/hal-00777788
26J. Bi, J.-S. Coron, J.-C. Faugère, P. Q. Nguyen, G. Renault, R. Zeitoun.

Rounding and Chaining LLL: Finding Faster Small Roots of Univariate Polynomial Congruences, in: PKC 2014 - 17th IACR International Conference on Practice and Theory of Public-Key Cryptography, Buenos Aires, Argentina, Springer, 2014.

http://hal.inria.fr/hal-00926902
27C. Eder, B. H. Roune.

Signature Rewriting in Gröbner Basis Computation, in: ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Boston, United States, M. Kauers (editor), ACM, 2013, pp. 331-338. [ DOI : 10.1145/2465506.2465522 ]

http://hal.inria.fr/hal-00930273
28J.-C. Faugère, L. Huot, A. Joux, G. Renault, V. Vitse.

Symmetrized summation polynomials: using small order torsion points to speed up elliptic curve index calculus, in: EUROCRYPT 2014 - 33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, 2014.

http://hal.inria.fr/hal-00935050
29J.-C. Faugère, M. Safey El Din, T. Verron.

On the Complexity of Computing Gröbner Bases for Quasi-homogeneous Systems, in: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, Boston, United States, ACM, 2013, pp. 189–196. [ DOI : 10.1145/2465506.2465943 ]

http://hal.inria.fr/hal-00780388
30J.-C. Faugère, J. Svartz.

Gröbner Bases of Ideals Invariant under a Commutative Group: the Non-Modular Case, in: IProceedings of the 38th International Symposium on Symbolic and Algebraic Computation, Boston, United States, ACM, 2013, pp. 347-354. [ DOI : 10.1145/2465506.2465944 ]

http://hal.inria.fr/hal-00819337
31Q. Guo, M. Safey El Din, L. Zhi.

Computing rational solutions of linear matrix inequalities, in: ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Boston, United States, 2013.

http://hal.inria.fr/hal-00815174
32V. Pan, E. Tsigaridas.

On the Boolean complexity of real root refinement, in: ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Boston, United States, M. Kauers (editor), ACM, April 2013. [ DOI : 10.1145/2465506.2465938 ]

http://hal.inria.fr/hal-00816214
33J. Yang, D. Wang, H. Hong.

Improving Angular Speed Uniformity by C¹ Piecewise Reparameterization, in: ADG 2012 - 9th International Workshop Automated Deduction in Geometry, Edinburgh, United Kingdom, T. Ida, J. Fleuriot (editors), Lecture Notes in Computer Science, Springer, 2013, vol. 7993, pp. 33-47. [ DOI : 10.1007/978-3-642-40672-0_3 ]

http://hal.inria.fr/hal-00913415

Other Publications

34M. Albrecht, J.-C. Faugère, R. Fitzpatrick, L. Perret.

Practical Cryptanalysis of a Public-Key Encryption Scheme Based on New Multivariate Quadratic Assumptions, January 2014.

http://hal.inria.fr/hal-00918314
35B. Bank, M. Giusti, J. Heintz, M. Safey El Din.

Intrinsic complexity estimates in polynomial optimization, April 2013.

http://hal.inria.fr/hal-00815123
36M. Bardet, J.-C. Faugère, B. Salvy.

On the Complexity of the F5 Gröbner basis Algorithm, December 2013, 20 pages.

http://hal.inria.fr/hal-00915522
37J. Berthomieu.

Decomposition of multihomogeneous polynomials: minimal number of variables, January 2013.

http://hal.inria.fr/hal-00778659
38J. Berthomieu, J.-C. Faugère, L. Perret.

Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials, 2013.

http://hal.inria.fr/hal-00846041
39X. Chen, D. Wang, X. Zhang.

Mathematics, Data and Knowledge, 2013, Special focus of Mathematics in Computer Science, Birkhäuser/Springer, Basel.

http://hal.inria.fr/hal-00913449
40J.-C. Faugère, P. Gaudry, L. Huot, G. Renault.

Polynomial Systems Solving by Fast Linear Algebra, 2013, 27 pages.

http://hal.inria.fr/hal-00816724
41J.-C. Faugère, C. Mou.

Sparse FGLM algorithms, April 2013.

http://hal.inria.fr/hal-00807540
42A. Greuet, M. Safey El Din.

Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set, 2013.

http://hal.inria.fr/hal-00849523
43M. Safey El Din, E. Schost.

A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets, July 2013.

http://hal.inria.fr/hal-00849057
44M. Safey El Din, E. Tsigaridas.

A probabilistic algorithm to compute the real dimension of a semi-algebraic set, 2014, Several typos fixed in Sections 4 and 5. There is an error in Section 5 and thus the complexity result stated does not hold.

http://hal.inria.fr/hal-00808708

Previous |

Home