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arXiv · 1801.09796

Communication-Efficient Search for an Approximate Closest Lattice Point

Maiara F. Bollauf·Vinay A. Vaishampayan·Sueli I. R. Costa
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Abstract

We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost and (ii) obtain the error probability. The approximate closest lattice point considered here is the one obtained using the nearest-plane (Babai) algorithm. Assuming a triangular special basis for the lattice, we develop communication-efficient protocols for computing the approximate lattice point and determine the communication cost for lattices of dimension n>1. Based on available parameterizations of reduced bases, we determine the error probability of the nearest plane algorithm for two dimensional lattices analytically, and present a computational error estimation algorithm in three dimensions. For dimensions 2 and 3, our results show that the error probability increases with the packing density of the lattice.

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Maiara F. Bollauf, Vinay A. Vaishampayan, Sueli I. R. Costa. 2018-01-29. Communication-Efficient Search for an Approximate Closest Lattice Point. https://arxiv.org/abs/1801.09796

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