Parallel gcd and Lattice Basis Reduction

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(n7), we propose a parallelization leading to the time bound O(n3 log2n) for the reduction of good lattices. Experimentations show that high speed-ups can be obtained.

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