Abstract
FGb is a high-performance, portable, C library for computing Gröbner bases over the integers and over finite fields. FGb provides high quality implementations of state-of-the-art algorithms (F 4 and F 5) for computing Gröbner bases. Currently, it is one of the best implementation of these algorithms, in terms of both speed and robustness. For instance, FGb has been used to break several cryptosystems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Innsbruck (1965)
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)
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)
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)
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)
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)
Faugère, J.C.: FGb library for comptuing Gröbner bases, http://www-salsa.lip6.fr/~jcf/Software/FGb/
Faugère, J.-C., Perret, L.: Cryptanalysis of 2R– schemes. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 357–372. Springer, Heidelberg (2006)
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)
Faugère, J.C.: A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra 139(1-3), 61–88 (1999)
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)
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)
Lecerf, G.: Kronecker Magma package for solving polynomial systems by means of geometric resolutions, http://www.math.uvsq.fr/~lecerf/software/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Faugère, JC. (2010). FGb: A Library for Computing Gröbner Bases. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-15582-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
Online ISBN: 978-3-642-15582-6
eBook Packages: Computer ScienceComputer Science (R0)