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 211 articles , 1 standard article )

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  1. Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre: Structural cryptanalysis of McEliece schemes with compact keys (2016)
  2. Faugère, Jean-Charles; Safey El Din, Mohab; Verron, Thibaut: On the complexity of computing Gröbner bases for weighted homogeneous systems (2016)
  3. Henrion, Didier; Naldi, Simone; El Din, Mohab Safey: Exact algorithms for linear matrix inequalities (2016)
  4. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Real root finding for determinants of linear matrices (2016)
  5. Trébuchet, Philippe; Mourrain, Bernard; Bucero, Marta Abril: Border basis for polynomial system solving and optimization (2016)
  6. Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo: Degeneracy loci and polynomial equation solving (2015)
  7. Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno: On the complexity of the $F_5$ Gröbner basis algorithm (2015)
  8. Cox, David A.; Little, John; O’Shea, Donal: Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra (2015)
  9. 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)
  10. Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël: Using symmetries in the index calculus for elliptic curves discrete logarithm (2014)
  11. 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)
  12. Ferčec, Brigita; Giné, Jaume; Mencinger, Matej; Oliveira, Regilene: The center problem for a $1:-4$ resonant quadratic system (2014)
  13. Greuet, Aurélien; El Din, Mohab Safey: Probabilistic algorithm for polynomial optimization over a real algebraic set (2014)
  14. Storjohann, Arne; Yang, Shiyun: Linear independence oracles and applications to rectangular and low rank linear systems (2014)
  15. Sun, Yao; Wang, Dingkang: The implementation and complexity analysis of the branch Gröbner bases algorithm over Boolean polynomial rings (2014)
  16. van der Hoeven, Joris: Overview of the Mathemagix type system (2014)
  17. Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno; Spaenlehauer, Pierre-Jean: On the complexity of solving quadratic Boolean systems (2013)
  18. Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic: Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic (2013)
  19. Ferčec, Brigita; Giné, Jaume; Liu, Yirong; Romanovski, Valery G.: Integrability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities (2013)
  20. Gao, Shuhong; Heindl, Raymond: Multivariate public key cryptosystems from Diophantine equations (2013)

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