Details:
Title  MXL3: An Efficient Algorithm for Computing Gröbner Bases of ZeroDimensional Ideals  Author(s)  Johannes Buchmann, Stanislav Bulygin, Daniel Cabarcas, Jintai Ding, Mohamed Saied Emam Mohamed  Type  Book, Chapter in Book, Conference Proceeding  Abstract  This paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zerodimensional ideals. The MXL3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Gröbner basis. We present experimental results comparing the behavior of MXL3 to F4 on HFE and random generated instances of the MQ problem. In both cases the first implementation of the MXL3 algorithm succeeds faster and uses less memory than Magma’s implementation of F4.  Keywords  Multivariate polynomial systems  Gröbner basis  XL algorithm  Mutant  MutantXL algorithm 
Language  English  Series  Lecture Notes in Computer Science  Volume  5984  Pages  87100  Publisher  Springer  Year  2010  Translation 
No  Refereed 
Yes  Book  Information, Security and Cryptology – ICISC 2009 
