Parallel Gcd and lattice basis reduction

Abstract

Gcd and lattice reduction are two major problems in the field of Parallel Algebraic Computations. To know if they are in NC is still an open question. We point out their correlations and difficulties. Concerning the lattice basis reduction which is of sequential cost O(n 7), we propose a parallelization leading to the time bound O(n 3 log2 n) for the reduction of good lattices. Experimentations show that high speed-ups can be obtained.Throughout the paper we refer to [34], many mathematical points are not detailed in this short presentation concerned with results which have relevance to parallelism.KeywordsParallel AlgorithmBasis ReductionLattice ReductionAlgebraic Number FieldGreatest Common DivisorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.