Approximate CVP in time 20.802 n - now in any norm!

We show that a constant factor approximation of the shortest and closest lattice vector problem in any norm can be computed in time 20.802n . This contrasts the corresponding 2n time, (gap)SETH based lower bounds for these problems that even apply for small constant approximation. For both problems, SVP and CVP, we reduce to the case of the Euclidean norm. A key technical ingredient in that reduction is a twist of Milman’s construction of an M-ellipsoid which approximates any symmetric convex body K with an ellipsoid E so that 2εn translates of a constant scaling of E can cover K and vice versa.

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