ewcommand{\NP}{\mathsf{NP}}ewcommand{\GapSVP}{extrm{GapSVP}} ewcommand{\NP}{\mathsf{NP}}ewcommand{\GapSVP}{extrm{GapSVP}} We give a simple proof that the (approximate, decisional) Shortest Vector Problem is \NP \NP -hard under a randomized reduction. Specifically, we show that for...
Lattice reduction with random sampling is a kind of randomized heuristic algorithm for solving approximate Shortest Vector Problem (SVP). In this paper, we propose a lattice vector sampling method for solving approximate SVP. Firstly, we apply enumeration techniques into vector sampling using natural ...
The problem of finding a shortest vector v∈L is known as the Shortest Vector Problem (SVP), while the problem of finding v∈L such that ‖vv‖≤γλ1(L) for some γ≥1 is known as γ-SVP. A solution vv to γ-SVP satisfies ‖vv‖∈O(γndet(L)1/n). Given the matrix of a...
Improving the factor 2 log 0.5 ε n to dimension for either of the lattice problems would imply the hardness of the Shortest Vector Problem in l 2 norm; an old open problem. Our proofs use reductions from few-prover, one-round interactive proof systems [FL], BG+], either directly, or ...
We also construct an NISZK proof for a special kind of disjunction (i.e., OR gate) related to the shortest vector problem. This may serve as a useful tool in potential constructions of noninteractive (computational) zero knowledge proofs... Chris Jason Peikert,V Vaikuntanathan - Springer Berl...
The ℓ(G)1+ℓ(G)-core of (V,c) is always non-empty, where ℓ(G) is the length of the shortest odd cycle in G. Moreover, a vector in the ℓ(G)1+ℓ(G)-core of (V,c) can be computed efficiently. Since the length of odd cycle is no less than 3, the factor ...
As in [AKS02],[BN09], we also extend this algorithm to obtain significantly faster algorithms for approximate versions of the shortest vector problem and the closest vector problem (CVP) in the $\\\ell_\\\infty$ norm. We also... D Aggarwal,P Mukhopadhyay 被引量: 2发表: 2018年 ...
5.1. The self-convolution vector Definition 14 Let S be a string of length n over alphabet Σ, and let S¯ be the string S concatenated with n $'s (where $∉Σ). The self-convolution vector of S, v, is defined for every i, 0≤i≤n/2−1,v[i]=∑j=0n−1f(S¯[i+...
For each mixed-effects regression test, the dependent variable was a vector of the mean contrast statistic within each relevant fROI in each participant. In analyses of only one fROI, the independent variables were dummy variables indicating the contrast map from which the corresponding mean ...
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