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TitleMXL3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals
Author(s) Johannes Buchmann, Stanislav Bulygin, Daniel Cabarcas, Jintai Ding, Mohamed Saied Emam Mohamed
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zero-dimensional 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.
KeywordsMultivariate polynomial systems - Gröbner basis - XL algorithm - Mutant - MutantXL algorithm
SeriesLecture Notes in Computer Science
Translation No
Refereed Yes
BookInformation, Security and Cryptology – ICISC 2009