FGb: A library for computing Gröbner bases

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6327 LNCS, Issue , 2010, Pages 84-87

  Faugère, Jean Charles ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOSYSTEMS; FINITE FIELDS; HIGH-QUALITY IMPLEMENTATION; STATE-OF-THE-ART ALGORITHMS;

CRYPTOGRAPHY;

EID: 78149261517     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-15582-6_17     Document Type: Conference Paper

References (13)

1. Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Innsbruck (1965)
2. Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44-60. Springer, Heidelberg (2003)
3. Faugère, J.-C., Lachartre, S.: Parallel Gaussian Elimination for Gröbner bases computations in finite fields. In: Moreno-Maza, M., Roch, J.L. (eds.) ACM Proceedings of The International Workshop on Parallel and Symbolic Computation (PASCO), LIG, pp. 1-10. ACM, New York (July 2010)
4. Faugère, J.-C., Levy-dit-Vehel, F., Perret, L.: Cryptanalysis of Minrank. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 280-296. Springer, Heidelberg (2008)
5. Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic Cryptanalysis of McEliece Variants with Compact Keys. In: Eurocrypt 2010. LNCS, vol. 6110, pp. 279-298. Springer, Heidelberg (2010)
6. Faugère, J.-C., Rahmany, S.: Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases. In: ISSAC 2009: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp. 151-158. ACM, New York (2009)
7. Faugère, J.C.: FGb library for comptuing Gröbner bases, http://www-salsa.lip6.fr/~jcf/Software/FGb/
8. Faugère, J.-C., Perret, L.: Cryptanalysis of 2R- schemes. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 357-372. Springer, Heidelberg (2006)
9. Faugère, J.-C., Perret, L.: Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 30-47. Springer, Heidelberg (2006)
10. Faugère, J.C.: A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra 139(1-3), 61-88 (1999)
11. Faugère, J.C.: A new efficient algorithm for computing Gröbner bases without reduction to zero F5. In: Mora, T. (ed.) Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp. 75-83. ACM Press, New York (July 2002)
12. Faugère, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient Computation of Zero-Dimensional Gröbner Basis by Change of Ordering 16(4), 329-344 (October 1993)
13. Lecerf, G.: Kronecker Magma package for solving polynomial systems by means of geometric resolutions, http://www.math.uvsq.fr/~lecerf/software/