Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
Sampling methods for shortest vectors, closest vectors and successive minima
Theoretical Computer Science
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PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Proceedings of the forty-second ACM symposium on Theory of computing
Covering cubes and the closest vector problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Approximating the closest vector problem using an approximate shortest vector oracle
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
On bounded distance decoding for general lattices
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
A O(1/ε2)n-time sieving algorithm for approximate integer programming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Sampling methods for shortest vectors, closest vectors and successive minima
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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+epsilon)-approximation to CVP. As a consequence, using the SVP algorithm due to Ajtai et al (STOC 2001), we obtain a randomized 2^{O(1 + (1/epsilon))n} algorithm to obtain a (1 + epsilon)-approximation for the closest lattice vector problem in n dimensions. This improves the existing time bound of O(n!) for CVP (achieved by a deterministic algorithm of Blomer).