منابع مشابه
Sampling Methods for Shortest Vectors, Closest Vectors and Successive Minima
In this paper we introduce a new lattice problem, the subspace avoiding problem (Sap). We describe a probabilistic single exponential time algorithm for Sap for arbitrary `p norms. We also describe polynomial time reductions for four classical problems from the geometry of numbers, the shortest vector problem (Svp), the closest vector problem (Cvp), the successive minima problem (Smp), and the ...
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Lattice-based cryptography has recently emerged as a prime candidate for efficient and secure post-quantum cryptography. The two main hard problems underlying its security are the shortest vector problem (SVP) and the closest vector problem (CVP). Various algorithms have been studied for solving these problems, and for SVP, lattice sieving currently dominates in terms of the asymptotic time com...
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Given n vectors x0, x1, . . . , xn−1 in {0, 1}m, how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient ρ, then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme ...
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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 two classical hard problems underlying the security of lattice-based cryptography are the shortest vector problem (SVP) and the closest vector problem (CVP). For SVP, lattice sieving currently has the best (heuristic) asymptotic time complexity: in high dimensions d, sieving can solve SVP in time 2, using 2 memory [Becker– Ducas–Gama–Laarhoven, SODA’16]. The best heuristic time complexity t...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.03.019