Neue Schranken für SVP-Approximation und SVP-Aufzählungsalgorithmen
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چکیده
منابع مشابه
Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One
We show the first dimension-preserving search-to-decision reductions for approximate SVP and CVP. In particular, for any γ ≤ 1+O(logn/n), we obtain an efficient dimension-preserving reduction from γO(n/ log n)-SVP to γ-GapSVP and an efficient dimension-preserving reduction from γO(n)-CVP to γ-GapCVP. These results generalize the known equivalences of the search and decision versions of these pr...
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The most famous lattice problem is the Shortest Vector Problem (SVP), which has many applications in cryptology. The best approximation algorithms known for SVP in high dimension rely on a subroutine for exact SVP in low dimension. In this paper, we assess the practicality of the best (theoretical) algorithm known for exact SVP in low dimension: the sieve algorithm proposed by Ajtai, Kumar and ...
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We present a 2 O(n) time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+)-approximation to CVP. As a consequence, using the SVP algorithm from 1], we obtain a randomized 2 O(1+ ?1)n algorithm to obtain a...
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The shortest vector problem (SVP) in lattices is related to problems in combinatorial optimization, algorithmic number theory, communication theory, and cryptography. In 1996, Ajtai published his breakthrough idea how to create lattice-based oneway functions based on the worst-case hardness of an approximate version of SVP. Worst-case hardness is one of the outstanding properties of all modern ...
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تاریخ انتشار 2013