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The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
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Approximating the SVP to within a factor (1+1/dimE) is NP-Hard under randomized reductions
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On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
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The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
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ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
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COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
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EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
NTRUSign: digital signatures using the NTRU lattice
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
A Digital Signature Scheme Based on NP-Complete Lattice Problems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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In this paper, we introduce a new decision problem associated with lattices, named the Exact Length Vector Problem (ELVP), and prove the NP-completeness of ELVP in the ℓ∞ norm. Moreover, we define two variants of ELVP. The one is a binary variant of ELVP, named the Binary Exact Length Vector Problem (BELVP), and is shown to be NP-complete in any ℓp norm (1 ≤ p ≤ ∞). The other is a nonnegative variant of ELVP, named the Nonnegative Exact Length Vector Problem (NELVP). NELVP is defined in the ℓ1 norm, and is also shown to be NP-complete.