A new incremental algorithm for computing Groebner bases

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn , Issue , 2010, Pages 13-19

  Gao, Shuhong ^a   Guan, Yinhua ^a   Volny IV, Frank ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Buchberger's algorithm; Colon ideal; F5 algorithm; Gr bner basis

Indexed keywords

EID: 77956336230     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1837934.1837944     Document Type: Conference Paper

References (17)

1. B. BUCHBERGER, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, PhD thesis, Innsbruck, 1965.
2. B. BUCHBERGER, "A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Basis," In Proc. EUROSAM 79 (1979), vol. 72 of Lect. Notes in Comp. Sei., Springer Verlag, 3-21.
3. B. BUCHBERGER, "Gröbner Bases : an Algorithmic Method in Polynomial Ideal Theory," In Recent trends in multidimensional system theory, Ed. Bose, 1985.
4. J. BUCHMANN, D. CABARCAS, J. DING, M. S. E. MOHAMED, "Flexible Partial Enlargement to Accelerate Grobner Basis Computation over F2," AFRICACRYPT 2010, May 03-06, 2010, Stellenbosch, South Africa, to be published in LNCS by Springer
5. N. COURTOIS, A. KLIMOV, J. PATARIN, AND A. SHAMIR, "Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations," in Proceedings of International Conference on the Theory and Application of Cryptographic Techniques (EUROCRYPT), volume 1807 of Lecture Notes in Computer Science, pages 392-407, Bruges, Belgium, May 2000. Springer.
6. D. Cox, J. LITTLE AND D. O'SHEA, Using algebraic geometry, Graduate Texts in Mathematics, 185. Springer-Verlag, New York, 1998.
7. J. DING, J. BUCHMANN, M. S. E. MOHAMED, W. S. A. M. MOHAMED, R. WEINMANN, "Mutant XL," First International Conference on Symbolic Computation and Cryptography, SCC 2008
8. C. EDER AND J. PERRY, "F5C: a variant of Faugère's F5 algorithm with reduced Gröbner bases," arXiv: 0906.2967v5, July 2009.
9. J.-C. FAUGÈRE, "A new efficient algorithm for computing Gröbner bases (F4)," Effective methods in algebraic geometry (Saint-Malo, 1998), J. Pure Appl. Algebra 139 (1999), no. 1-3, 61-88.
10. J.-C. FAUGÈRE, "A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)," Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, 75-83 (electronic), ACM, New York, 2002.
11. A. Joux AND V. VITSE, "A variant of the F4 algorithm," preprint 2010. http://eprint.iacr.org/2010/158.
12. A. KEHREIN AND M. KREUZER, "Computation of Border Bases," J. Pure Appl. Algebra 205 (2006), 279-295.
13. D. LAZARD, "Gaussian Elimination and Resolution of Systems of Algebraic Equations," in Proc. EUROCAL 83 (1983), vol. 162 of Lect. Notes in Comp. Sci, 146-157.
14. F. MACAULAY, "Some formulae in elimination," Proceedings of London Mathematical Society (1902), 3-38.
15. M. S. E. MOHAMED, D. D. CABARCAS, J. DING, J. BUCHMANN AND S. BULYGIN, "MXL3: An efficient algorithm for computing Groebner bases of zero-dimensional ideals," the 12th International Conference on Information Security and Cryptology (ICISC 2009), Dec. 2009, Seoul, Korea. (To be published in LNCS by Springer).
16. M. S. E. MOHAMED, W. S. A. E. MOHAMED, J. DING, J. BUCHMANN, "MXL2: Solving Polynomial Equations over GF (2) Using an Improved Mutant Strategy," PQCrypto 2008: 203-215, LNCS 5299, Springer 2008
17. Y. SUN AND D.K. WANG, "A New Proof of the F5 Algorithm," preprint 2009. http://www.mmrc.iss.ac.cn/pub/mm28.pdf/06F5Proof.pdf