Solving low-density subset sum problems
Journal of the ACM (JACM)
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 hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
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
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Approximating the domatic number
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
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
New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An Improved Worst-Case to Average-Case Connection for Lattice Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Hardness of Approximating the Shortest Vector Problem in Lattices
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The geometry of lattice cryptography
Foundations of security analysis and design VI
Algorithms and hardness for subspace approximation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We present a new hardness of approximation result for the Shortest Vector Problem in @?"p norm (denoted by SVP"p). Assuming NP @? ZPP, we show that for every @e0, there is a constant p(@e) such that for all integers p=p(@e), the problem SVP"p has no polynomial time approximation algorithm with approximation ratio p^1^-^@e. For large values of p, this improves the factor 2^1^/^p-@d hardness shown by Micciancio [The shortest vector problems in NP-hard to approximate to within some constant, SIAM J. Comput. 30(6) (2001) 2008-2035].