FGb/Gb libraryGb is a program (191 420 lines of C++) for computing Grobner bases, implement ”standard” algoritms. FGb (206 052 lines of C) ia an efficient program written in C for solving polynomial systems. The purpose of the FGb library is twofold. First of all, the main goal is to provide efficient implementations of state-of-the-art algorithms for computing Gröbner bases: actually, from a research point of view, it is mandatory to have such an implementation to demonstrate the practical efficiency of new algorithms. Secondly, in conjunction with other software, the FGb library has been used in various applications (Robotic, Signal Theory, Biology, Computational Geometry, . . . ) and more recently to a wide range of problems in Cryptology (for instance, FGb was explicitly used in [2, 8, 9, 4, 5] to break several cryptosystems)

References in zbMATH (referenced in 224 articles , 1 standard article )

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  1. Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef: The number of realizations of a Laman graph (2018)
  2. Faugère, Jean-Charles; Wallet, Alexandre: The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic (2018)
  3. Greenwood, Torin: Asymptotics of bivariate analytic functions with algebraic singularities (2018)
  4. Horáček, Jan; Kreuzer, Martin: 3BA: a border bases solver with a SAT extension (2018)
  5. Jiang, Yunfeng; Zhang, Yang: Algebraic geometry and Bethe ansatz. I: The quotient ring for BAE (2018)
  6. Naldi, Simone: Solving rank-constrained semidefinite programs in exact arithmetic (2018)
  7. Rodriguez, Jose Israel; Tang, Xiaoxian: A probabilistic algorithm for computing data-discriminants of likelihood equations (2017)
  8. Didier Henrion, Simone Naldi, Mohab Safey El Din: SPECTRA -a Maple library for solving linear matrix inequalities in exact arithmetic (2016) arXiv
  9. Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre: Structural cryptanalysis of McEliece schemes with compact keys (2016)
  10. Faugère, Jean-Charles; Safey El Din, Mohab; Verron, Thibaut: On the complexity of computing Gröbner bases for weighted homogeneous systems (2016)
  11. Henrion, Didier; Naldi, Simone; El Din, Mohab Safey: Exact algorithms for linear matrix inequalities (2016)
  12. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Real root finding for determinants of linear matrices (2016)
  13. Naldi, Simone: Solving rank-constrained semidefinite programs in exact arithmetic (2016)
  14. Trébuchet, Philippe; Mourrain, Bernard; Bucero, Marta Abril: Border basis for polynomial system solving and optimization (2016)
  15. Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo: Degeneracy loci and polynomial equation solving (2015)
  16. Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno: On the complexity of the $F_5$ Gröbner basis algorithm (2015)
  17. Cox, David A.; Little, John; O’Shea, Donal: Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra (2015)
  18. Chiu, Yi-Hao; Hong, Wei-Chih; Chou, Li-Ping; Ding, Jintai; Yang, Bo-Yin; Cheng, Chen-Mou: A practical attack on patched MIFARE Classic (2014)
  19. Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël: Using symmetries in the index calculus for elliptic curves discrete logarithm (2014)
  20. Faugère, Jean-Charles; Huot, Louise; Joux, Antoine; Renault, Guénaël; Vitse, Vanessa: Symmetrized summation polynomials: using small order torsion points to speed up elliptic curve index calculus (2014)

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Further publications can be found at: http://www-polsys.lip6.fr/~jcf/Publications/index.html