Bibliography

Major publications by the team in recent years

1P. Aubry, D. Lazard, M. Moreno-Maza.

On the theories of triangular sets, in: Journal of Symbilic Computation, 1999, vol. 28, p. 105-124.
2P. Aubry, F. Rouillier, M. Safey El Din.

Real Solving for Positive Dimensional Systems, in: Journal of Symbolic Computation, 2002, vol. 34, n^o 6, p. 543–560.
3J.-C. Faugère.

A new efficient algorithm for computing Gröbner bases without reduction to zero $F_{5}$ , in: International Symposium on Symbolic and Algebraic Computation Symposium - ISSAC 2002, Villeneuve d'Ascq, France, Jul 2002.
4J.-C. Faugère.

A New Efficient Algorithm for Computing Gröbner bases ( $F_{4}$ ), in: Journal of Pure and Applied Algebra, June 1999, vol. 139, n^o 1-3, p. 61-88.
5J.-C. Faugère, A. Joux.

Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases, in: CRYPTO 2003, 2003, p. 44-60.
6D. Lazard, F. Rouillier.

Solving parametric polynomial systems, in: Journal of Symbolic Computation, 2007, vol. 42, p. 636-667.
7M. Safey El Din, E. Schost.

Polar varieties and computation of one point in each connected component of a smooth real algebraic set, in: International Symposium on Symbolic and Algebraic Computation 2003 - ISSAC'2003, Philadelphie, USA, J. Sendra (editor), ACM Press, aug 2003, p. 224-231.
8D. Wang.

Elimination Methods, Springer-Verlag, Wien New York, 2001.

Publications of the year

Doctoral Dissertations and Habilitation Theses

9L. Bettale.

Cryptanalyse algébrique : outils et applications, Université Paris 6, 2011.
10Y. Liang.

Approximate Gröbner Bases, Université Paris 6 and Beihang University, 2011.
11W. Niu.

Analyse Qualitative des Systèmes Biologiques par des Méthodes Algébriques, Université Paris 6, 2011.

Articles in International Peer-Reviewed Journal

12X. Chen, D. Wang.

Management of Geometric Knowledge in Textbooks, in: Data and Knowledge Engineering, 2011, p. 1–15, In press.

http://dx.doi.org/10.1016/j.datak.2011.10.004
13J.-C. Faugère, Y. Liang.

Artificial discontinuities of single-parametric Gröbner bases, in: Journal of Symbolic Computation, 2011, vol. 46, n^o 4, p. 459 – 466. [ DOI : 10.1016/j.jsc.2010.11.001 ]

http://www-salsa.lip6.fr/~jcf/Papers/JSC_LP10.pdf
14J.-C. Faugère, Y. Liang.

Pivoting in Extended Rings for Computing Approximate Gröbner Bases, in: Mathematics in Computer Science, 2011, vol. 5, p. 179-194. [ DOI : 10.1007/s11786-011-0089-y ]

http://www-salsa.lip6.fr/~jcf/Papers/MCS2011.pdf
15J.-C. Faugère, D. Lubicz, D. Robert.

Computing modular correspondences for abelian varieties, in: Journal Of Algebra, 2011, vol. 343, n^o 1, p. 248 - 277. [ DOI : 10.1016/j.jalgebra.2011.06.031 ]

http://www-salsa.lip6.fr/~jcf/Papers/JAlgebra2011.pdf
16J.-C. Faugère, M. Safey El Din, P.-J. Spaenlehauer.

Gröbner Bases of Bihomogeneous Ideals Generated by Polynomials of Bidegree (1,1): Algorithms and Complexity, in: Journal of Symbolic Computation, 2011, vol. 46, n^o 4, p. 406–437, Available online 4 November 2010. [ DOI : 10.1016/j.jsc.2010.10.014 ]

http://www-salsa.lip6.fr/~jcf/Papers/JSC_FSS10.pdf
17A. Galligo, A. Poteaux.

Computing monodromy via continuation methods on random Riemann surfaces, in: Theoretical Computer Science, 2011, vol. 412, n^o 16, p. 1492–1507, Symbolic and Numerical Algorithms. [ DOI : 10.1016/j.tcs.2010.11.047 ]

http://www.sciencedirect.com/science/article/B6V1G-51MDSJP-5/2/798a2d9fedcde3f52382391e770e1a5a
18A. Greuet, G. Guo, M. Safey El Din, L. Zhi.

Global optimization of polynomials restricted to a smooth variety using sums of squares, in: Journal of Symbolic Computation, 2011, p. 1–19, to appear.

http://www-salsa.lip6.fr/~safey/Articles/sos_vcg_final.pdf
19A. Hashemi, D. Lazard.

Sharper complexity bounds for zero-dimensional Gröbner bases and polynomial system solving, in: International Journal of Algebra and Computation (IJAC), 2011, vol. 21, p. 703–713.

http://dx.doi.org/10.1142/S0218196711006364
20H. Hong, M. Safey El Din.

Variant Quantifier Elimination, in: Journal of Symbolic Computation, 2011, p. 1–24, to appear.

http://www-salsa.lip6.fr/~safey/Articles/vqe_jsc_final.pdf
21Y. Huang, D. Wang.

Computing Intersection and Self-intersection Loci of Parametrized Surfaces Using Regular Systems and Gröbner Bases, in: Computer Aided Geometric Design, 2011, vol. 28, n^o 9, p. 566–581.

http://dx.doi.org/10.1016/j.cagd.2011.09.002
22X. Li, C. Mou, W. Niu, D. Wang.

Stability Analysis for Discrete Biological Models Using Algebraic Methods, in: Mathematics in Computer Science, 2011, vol. 5, n^o 3, p. 247–262.

http://dx.doi.org/10.1007/s11786-011-0096-z
23D. Lin, J.-C. Faugère, L. Perret, T. Wang.

On enumeration of polynomial equivalence classes and their application to MPKC, in: Finite Fields and Their Applications, 2011, p. 1–20. [ DOI : doi:10.1016/j.ffa.2011.09.001 ]

http://www-salsa.lip6.fr/~jcf/Papers/FFA2011.pdf
24A. Poteaux, M. Rybowicz.

Complexity bounds for the rational Newton-Puiseux algorithm over finite fields, in: Applicable Algebra in Engineering, Communication and Computing, 2011, vol. 22, p. 187–217.

http://dx.doi.org/10.1007/s00200-011-0144-6
25M. Safey El Din, E. Schost.

A Baby Steps/Giant Steps Probabilistic Algorithm for Computing Roadmaps in Smooth Bounded Real Hypersurface, in: Discrete and Computational Geometry, 2011, vol. 45, n^o 1, p. 181–220. [ DOI : 10.1007/s00454-009-9239-2 ]

http://www-salsa.lip6.fr/~safey/Articles/SaSc09.pdf
26D. Wang.

Algebraic Analysis of Stability and Bifurcation for Nonlinear Flight Dynamics, in: The Aeronautical Journal, 2011, vol. 115, n^o 1168, p. 345–349.
27T. Zhao, D. Wang, H. Hong.

Solution Formulas for Cubic Equations Without or With Constraints, in: Journal of Symbolic Computation, 2011, vol. 46, n^o 8, p. 904–918.

http://dx.doi.org/10.1016/j.jsc.2011.02.001

Articles in National Peer-Reviewed Journal

28X. Li, D. Wang.

Simple Decomposition of Polynomial Sets over Finite Fields (in Chinese), in: Journal of Systems Science and Mathematical Sciences, 2011, p. 1–13, In press.

International Conferences with Proceedings

29M. Albrecht, C. Cid, T. Dulien, J.-C. Faugère, L. Perret.

Algebraic Precomputations in Differential Cryptanalysis, in: Information Security and Cryptology: 6th International Conference, Inscrypt 2010, Revised Selected Papers, X. Lai, M. Yung, D. Lin (editors), Springer Berlin / Heidelberg, October 2011, vol. 6584, p. 387-403. [ DOI : 10.1007/978-3-642-21518-627 ]

http://www-salsa.lip6.fr/~jcf/Papers/INSCRYPT2010.pdf
30M. Albrecht, P. Farshim, K. Paterson, G. Watson.

On Cipher-Dependent Related-Key Attacks in the Ideal Cipher Model, in: Fast Software Encryption 2011, FSE, Lecture Notes in Computer Science, Springer, 2011, p. 1–20.
31M. Albrecht, J.-C. Faugère, P. Farshim, L. Perret.

Polly Cracker, Revisited, in: Advances in Cryptology Asiacrypt 2011, D. Lee, X. Wang (editors), Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2011, vol. 7073, p. 179–196. [ DOI : 10.1007/978-3-642-25385-010 ]

http://www-salsa.lip6.fr/~jcf/Papers/Asia2011.pdf
32F. Armknecht, D. Augot, L. Perret, A. Sadeghi.

On Constructing Homomorphic Encryption Schemes from Coding Theory, in: IMA Int. Conf., 2011, p. 23-40.

http://dx.doi.org/10.1007/978-3-642-25516-8_3
33L. Bettale, J.-C. Faugère, L. Perret.

Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants, in: Public Key Cryptography - PKC 2011, D. Catalano, N. Fazio, R. Gennaro, A. Nicolosi (editors), Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2011, vol. 6571, p. 441–458. [ DOI : 10.1007/978-3-642-19379-827 ]

http://www-salsa.lip6.fr/~jcf/Papers/pkc2011a.pdf
34C. Bouillaguet, J.-C. Faugère, P.-A. Fouque, L. Perret.

Practical Cryptanalysis of the Identification Scheme Based on the Isomorphism of Polynomial with One Secret Problem, in: Public Key Cryptography - PKC 2011, D. Catalano, N. Fazio, R. Gennaro, A. Nicolosi (editors), Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2011, vol. 6571, p. 473-493. [ DOI : 10.1007/978-3-642-19379-829 ]

http://www-salsa.lip6.fr/~jcf/Papers/BFFP11.pdf
35X. Chen, Y. Huang, D. Wang.

On the Design and Implementation of a Geometric Knowledge Base, in: Automated Deduction in Geometry, Berlin Heidelberg, T. Sturm, C. Zengler (editors), Lecture Notes in Artificial Intelligence, Springer-Verlag, 2011, vol. 6301, p. 22–41.

http://dx.doi.org/10.1007/978-3-642-21046-4_2
36J.-C. Faugère, A. Gauthier-Umaña, L. Perret, J.-P. Tillich.

A Distinguisher for High Rate McEliece Cryptosystems, in: Information Theory Workshop (ITW), 2011 IEEE, oct. 2011, p. 282 -286. [ DOI : 10.1109/ITW.2011.6089437 ]

http://www-salsa.lip6.fr/~jcf/Papers/ITW2011.pdf
37J.-C. Faugère, D. Gligoroski, E. Jensen, R. Odegard, L. Perret, S. Johan Knapskog, S. Markovski.

An Ultra-fast and Provably CMA Resistant Digital Signature Scheme, in: The Third International Conference on Trusted Systems - INTRUST 2011, Y. Moti, C. Liqun, Z. Liehuang (editors), Lecture Notes in Computer Science, Springer Verlag, 2011, p. 1–10.
38J.-C. Faugère, C. Mou.

Fast Algorithm for Change of Ordering of Zero-dimensional Gröbner Bases with Sparse Multiplication Matrices, in: Proceedings of the 36th international symposium on Symbolic and algebraic computation, New York, NY, USA, ISSAC '11, ACM, 2011, p. 115–122. [ DOI : 10.1145/1993886.1993908 ]

http://www-salsa.lip6.fr/~jcf/Papers/FM11.pdf
39J.-C. Faugère, L. Perret, C. Petit, G. Renault.

Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Field, in: Proceedings of Eurocrypt 2012, Lecture Notes in Computer Science, Springer Verlag, 2012, p. 1–15.
40C. Goyet, J.-C. Faugère, G. Renault.

Algebraic Side Channel Analysis, in: COSADE'11: The 2nd International Workshop on Constructive Side-Channel Analysis and Secure Design, Fraunhofer SIT, 2011, p. 1–6.
41A. Greuet, M. Safey El Din.

Deciding reachability of the infimum of a multivariate polynomial, in: ISSAC '11: Proceedings of the 2011 international symposium on Symbolic and algebraic computation, New York, NY, USA, ISSAC '11, ACM, 2011, p. 131–138.

http://doi.acm.org/10.1145/1993886.1993910
42T. Zhao, D. Wang, H. Hong, P. Aubry.

Real Solution Formulas of Cubic and Quartic Equations Applied to Generate Dynamic Diagrams with Inequality Constraints, in: SAC 2012: Proceedings of the 27th ACM Symposium on Applied Computing, Riva del Garda/Trento, Italy, ACM Press, March 2012, p. 1–8, In press.

Scientific Books (or Scientific Book chapters)

43Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2011), IEEE Computer Society, Timisoara, Romania, September 2011, p. 1–400.
44D. Wang, C. Mou, X. Li, J. Yang, M. Jin, Y. Huang.

Polynomial Algebra (in Chinese), Higher Education Press, 2011, isbn: 9787040316988.

References in notes

45S. Basu, R. Pollack, M.-F. Roy.

A new algorithm to find a point in every cell defined by a family of polynomials, in: Quantifier elimination and cylindrical algebraic decomposition, Springer-Verlag, 1998.
46B. Buchberger.

“Groebner bases : an algorithmic method in polynomial ideal theory”, Recent trends in multidimensional systems theory, Reider ed. Bose, 1985.
47B. Buchberger, G.-E. Collins, R. Loos.

Computer Algebra Symbolic and Algebraic Computation, second edition, Springer-Verlag, 1982.
48G.-E. Collins.

Quantifier elimination for real closed fields by cylindrical algebraic decomposition, in: Springer Lecture Notes in Computer Science 33, 1975, vol. 33, p. 515-532.
49J.-C. Faugère, P. Gianni, D. Lazard, T. Mora.

Efficient Computation of Zero-Dimensional Gröbner Basis by Change of Ordering, in: Journal of Symbolic Computation, Oct. 1993, vol. 16, n^o 4, p. 329–344.
50J.-C. Faugère, F. Levy-dit-Vehel, L. Perret.

Cryptanalysis of Minrank, in: Advances in Cryptology CRYPTO 2008, Santa-Barbara, USA, D. Wagner (editor), Lecture Notes in Computer Science, Springer-Verlag, 2008, vol. 5157, p. 280–296.
51J.-C. Faugère, L. Perret.

Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects, in: Advances in Cryptology - EUROCRYPT 2006, 25th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Lecture Notes in Computer Science, Springer, 2007, vol. 4004, p. 30-47.
52J.-C. Faugère, D. Lazard.

The Combinatorial Classes of Parallel Manipulators, in: Mechanism and Machine Theory, 1995, vol. 30, p. 765–776.
53J.-C. Faugère, L. Perret.

Cryptanalysis of 2R $^{-}$ Schemes, in: Advances in Cryptology - CRYPTO 2006, 26th Annual International Cryptology Conference, Lecture Notes in Computer Science, Springer, 2007, vol. 4117, p. 357-372.
54P.-A. Fouque, G. Macariorat, L. Perret, J. Stern.

On the Security of the $ℓ$ -IC Signature Scheme, in: Public Key Cryptography, 4th International Workshop on Practice and Theory in Public Key Cryptography, PKC 2008, Lecture Notes in Computer Science, Springer, 2008, vol. 4939, p. 1–17.
55D. Grigor'ev, N. Vorobjov.

Solving Systems of Polynomial Inequalities in Subexponential Time, in: J. Symbolic Comput., 1988, vol. 5, p. 37–64.
56M. Kalkbrenner.

Three contributions to elimination theory, Johannes Kepler University, Linz, 1991.
57D. Lazard.

Resolution of polynomial systems, in: 4th Asian Symposium on Computer Mathematics - ASCM 2000, Chiang Mai, Thailand, Lecture Notes Series on Computing, World Scientific, Dec 2000, vol. 8, p. 1 - 8.
58D. Lazard.

On the specification for solvers of polynomial systems, in: 5th Asian Symposium on Computers Mathematics -ASCM 2001, Lecture Notes Series in Computing, World Scientific, 2001, vol. 9, p. 66-75.
59D. Lazard.

Solving Zero - dimensional algebraic systems, in: Journal of Symbolic Computation, 1992, vol. 13, p. 117-132.
60D. Lazard.

Stewart platforms and Gröbner basis, in: Proceedings of Advances in Robotics Kinematics, Sep 1992, p. 136-142.
61D. Lazard, J.-P. Merlet.

The (true) Stewart platform has 12 configurations, in: Proc. of IEEE Conference on Robotics and Vision, San Diego, 1994.
62T. Matsumoto, H. Imai.

Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption, in: Advances in Cryptology: EUROCRYPT 1988, Lecture Notes in Computer Science, Springer-Verlag, 1988, vol. 330, p. 497–506.
63J. Patarin.

Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of Asymmetric Algorithms, in: Advances in Cryptology: EUROCRYPT 1996, Lecture Notes in Computer Science, Springer-Verlag, 1996, vol. 1070, p. 33-48.
64J.-F. Ritt.

Differential equations from an algebraic standpoint, in: American Mathematical Society Colloquium Publications, 1932, vol. 14.
65F. Rouillier, M.-F. Roy, M. Safey El Din.

Finding at least one point in each connected component of a real algebraic set defined by a single equation, in: Journal of Complexity, 2000, vol. 16, p. 716–750.
66F. Rouillier, M. Safey El Din, E. Schost.

Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study, in: Automated Deduction in Geometry - Third International Workshop ADG 2000, Zurich Switzerland, September 2000, Revised Papers, J. Richter-Gebert, D. Wang (editors), Lecture Notes in Artificial Intelligence, Springer, 2001, n^o 2061, p. 26–40.
67M. Safey El Din, E. Schost.

Properness defects of projection functions and computation of at least one point in each connected component of a real algebraic set, in: Journal of Discrete and Computational Geometry, sep 2004.
68M. Safey El Din, P. Trébuchet.

Strong bihomogeneous Bézout theorem and degree bounds for algebraic optimization, INRIA, 2004, n^o 5071, submitted to Journal of Pure and Applied Algebra.

http://hal.inria.fr/inria-00071512
69E. Schost.

Computing Parametric Geometric Resolutions, in: Applicable Algebra in Engineering, Communication and Computing, 2003, vol. 13, n^o 5, p. 349 - 393.
70D. Wang.

An Elimination Method for Polynomial Systems, in: Journal of Symbolic Computation, 1993, vol. 16, p. 83–114.
71V. Weispfenning.

Canonical comprehensive Gröbner bases, in: Proceedings of the 2002 international symposium on Symbolic and algebraic computation, ACM Press, 2002, p. 270–276.

http://doi.acm.org/10.1145/780506.780541
72V. Weispfenning.

Comprehensive Gröbner bases, in: Journal of Symbolic Computation, 1992, vol. 14, p. 1–29.
73V. Weispfenning.

Solving parametric polynomial equations and inequalities by symbolic algorithms, World Scientific, 1995.
74L. Yang, J. Zhang.

Searching dependency between algebraic equations: an algorithm applied to automated reasoning, in: Artificial intelligence in mathematics, J. Johnson, S. McKee, A. Vella (editors), Oxford University Press, 1994, p. 147–156.

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