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
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
ACM SIGACT News
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Approximating SVPinfty to within Almost-Polynomial Factors Is NP-Hard
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
An Overview of the Sieve Algorithm for the Shortest Lattice Vector Problem
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Shortest Vector Problem in Lattices with Many Cycles
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Non-standard approaches to integer programming
Discrete Applied Mathematics
The optimal LLL algorithm is still polynomial in fixed dimension
Theoretical Computer Science - Latin American theoretical informatics
Hardness of Approximating the Minimum Distance of a Linear Code
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Progress in computational complexity theory
Journal of Computer Science and Technology
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
A new transference theorem in the geometry of numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On routing in circulant graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Hypercubic lattice reduction and analysis of GGH and NTRU signatures
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
User selection criteria for multiuser systems with optimal and suboptimal LR based detectors
IEEE Transactions on Signal Processing
Multiuser diversity beamforming for downlink channels using modulation division multiplexing
Wireless Communications & Mobile Computing
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We show the shortest vector problem in the l_2 norm is NP-hard (for randomized reductions) to approximate within any constant factor less than sqrt(2). We also give a deterministic reduction under a reasonable number theoretic conjecture. Analogous results hold in any l_p norm (p=1). In proving our NP-hardness result, we give an alternative construction satisfying Ajtai's probabilistic variant of Sauer's lemma, that greatly simplifies Ajtai's original proof.