F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases

Journal of Symbolic Computation

Volumn 45, Issue 12, 2010, Pages 1442-1458

  Eder, Christian ^a   Perry, John ^b  

^a University of Koblenz Landau   (Germany)

^b UNIVERSITY OF SOUTHERN MISSISSIPPI   (United States)

Author keywords

Buchberger's criteria; F5; Reduced Gr bner bases

Indexed keywords

EID: 77957280869     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2010.06.019     Document Type: Article

References (17)

1. Albrecht, M., Perry, J., 2008. Sage implementation of Faugère's F5 algorithm. Sage library. http://bitbucket.org/malb/algebraic_attacks/src/tip/f5.py.
2. Becker T., Weispfenning V., Kredel H. Gröbner Bases: A Computational Approach to Commutative Algebra 1993, Springer-Verlag, New York, Inc., New York.
3. Buchberger, B., 1965. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalem Polynomideal (an algorithm for finding the basis elements in the residue class ring modulo a zero dimensional polynomial ideal). Ph.D. Thesis, Mathematical Institute, University of Innsbruck, Austria (English translation published in the Journal of Symbolic Computation (2006) 475-511).
4. Caboara M., Traverso C. Efficient algorithms for module operation. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation 1998, 147-157. ACM Press.
5. Eder, C., Perry, J., 2008. Singular implementation of Faugère's F5 algorithm. Singular library. http://www.math.usm.edu/perry/Research/f5_library.lib.
6. Faugère J.-C. A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra 1999, 139(1-3):61-88.
7. Faugère, J.-C., 2002. A new efficient algorithm for computing Gröbner bases without reduction to zero F5. In: International Symposium on Symbolic and Algebraic Computation Symposium, ISSAC 2002, Villeneuve d'Ascq, France. pp. 75-82, revised version downloaded from http://fgbrs.lip6.fr/jcf/Publications/index.html.
8. Faugère, J.-C., 2005. Cryptochallenge 11 is broken or an efficient attack of the C* cryptosystem. Tech. rep., LIP6/Universitè Paris.
9. Gebauer R., Möller H. On an installation of Buchberger's algorithm. Journal of Symbolic Computation 1988, 6:275-286.
10. Greuel G.-M., Pfister G. A SINGULAR Introduction to Commutative Algebra 2008, Springer. second ed.
11. Greuel, G.-M., Pfister, G., Schönemann, H., 2009. Singular 3-1-0. A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern, http://www.singular.uni-kl.de.
12. Lazard D. Gröbner bases, Gaussian elimination, and resolution of systems of algebraic equations. LNCS 1983, vol. 162:146-156. Springer. J.A. van Hulzen (Ed.).
13. Möller H., Mora F., Traverso C. Gröbner bases computation using syzygies. Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery 1992, 320-328. ACM Press. P.S. Wang (Ed.).
14. Mora T. Solving Polynomial Equation Systems II: Macaulay's paradigm and Gröbner technology. Encyclopedia of Mathematics and its Applications 2005, vol.~99. Cambridge University Press, Cambridge.
15. Stegers, T., 2006. Faugère's F5 Algorithm Revisited. Diplom. Thesis, Technische Universität Darmstadt, Germany.
16. Stein, W., 2008. Sage: Open Source Mathematical Software (Version 3.1.1). The Sage Group, http://www.sagemath.org.
17. Yap C.K. Fundamental Problems of Algorithmic Algebra 2000, Oxford University Press, Oxford.