Abstract
Fully saturated zero-dimensional binomial ideals (lattice ideals) describe lattices on Z n that are of interest in cryptanalysis. Gröbner basis computation for these ideals are computationally very intensive. We sketch a modified version of Buchberger's algorithm for lattice ideals that are closed with respect to a group action on their indeterminates. The main idea is to exploit the symmetries of such ideals to avoid performing S-polynomial reductions that are "equivalent" with respect to the group action. Using our techniques the number of S-polynomials to be considered can be reduced by a factor up to the order of the group.
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