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In this paper, the authors propose a practical lattice based reduction by sampling to avoid any dependence on Schnorr's Geometric Series Assumption. It is a generalization of Schnorr's RSR algorithm. It is also well defined for bases where this algorithm is not applicable. It demonstrates that the sampling reduction can significantly reduce the length of the base vectors. They also propose a practical sampling reduction algorithm for lattice bases based on work by Schnorr. They report the empirical behaviour of these algorithms.
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