Titlebook: Complexity of Lattice Problems; A Cryptographic Pers Daniele Micciancio,Shafi Goldwasser Book 2002 Springer Science+Business Media New York

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Statistical Continuum Mechanicsto find the shortest nonzero vector in the lattice generated by . . In Chapter 3 we have already studied another important algorithmic problem on lattices: the closest vector problem (CVP). In CVP, in addition to the lattice basis ., one is given a target vector ., and the goal is to find the lattic

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Philip Kokic,Jens Breckling,Oliver Lübkeen that the minimum distance between lattice points (or, equivalently, the length of the shortest non-zero vector in the lattice) is at least λ? Clearly the answer depends on the ratio λ/. only, as both the lattice and the sphere can be scaled up or down preserving λ/.. If we drop the requirement th

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Philip Kokic,Jens Breckling,Oliver Lübkemplexity point of view. In fact, the algorithms presented in Chapter 2 to approximately solve SVP and CVP do somehow more than just finding an approximately shortest lattice vector, or a lattice vector approximately closest to a given target. For example, the LLL algorithm on input a lattice basis .

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Statistical Continuum Mechanicsiew, and, in particular we investigate the hardness of the closest vector problem. We first consider the problem of solving CVP exactly, and prove that this problem is hard for NP. Therefore no efficient algorithm to solve CVP exists, unless P equals NP.

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Low-Degree Hypergraphs,ces or matrices. A . is a pair (., .), where . is a finite set of . and . is a collection of subsets of ., called .. If all the elements of . have the same size, then we say that (., .) is ., and the common size of all hyperedges is called the . of the hypergraph.