Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating shortest lattice vectors is not harder than approximating closet lattice vectors
Information Processing Letters
Complexity of Lattice Problems
Complexity of Lattice Problems
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Sampling Short Lattice Vectors and the Closest Lattice Vector Problem
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Proceedings of the forty-second ACM symposium on Theory of computing
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We give a polynomial time Turing reduction from the γ2 √n- approximate closest vector problem on a lattice of dimension n to a γ-approximate oracle for the shortest vector problem. This is an improvement over a reduction by Kannan, which achieved γ2n3/2.