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In this paper, we present an improvement of the Nguyen-Vidick heuristic sieve algorithm for shortest vector problem in general lattices, which time complexity is 2<sup>0.3836<i>n</i></sup> polynomial computations, and space complexity is 2<sup>0.2557<i>n</i></sup>. In the new algorithm, we introduce a new sieve technique with two-level instead of the… (More)

We prove three optimal transference theorems on lattices possessing n-unique shortest vectors which relate to the successive minima, the covering radius and the minimal length of generating vectors respectively. The theorems result in reductions between GapSVP γ and GapSIVPγ for this class of lattices. Furthermore, we prove a new transference theorem giving… (More)

Given an n-dimensional lattice L and some target vector, this paper studies the algorithms for approximate closest vector problem (CVPγ) by using an approximate shortest independent vectors problem oracle (SIVPγ). More precisely, if the distance between the target vector and the lattice is no larger than c c γ n λ 1 L $$ {\scriptscriptstyle \frac{c}{\gamma… (More)

This paper concerns the hardness of approximating the closest vector in a lattice with preprocessing in l 1 norm, and gives a polynomial time algorithm for GapCVPPγ in l 1 norm with gap γ = O(n/logn). The gap is smaller than that obtained by simply generalizing the approach given by Aharonov and Regev. The main technical ingredient used in this paper is the… (More)

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