The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth 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
A relation of primal-dual lattices and the complexity of shortest lattice vector problem
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Approximating the SVP to within a Factor is NP-Hard under Randomized Reductions
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
Applications of a New Transference Theorem to Ajtai's Connection Factor
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
An Improved Worst-Case to Average-Case Connection for Lattice Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating-CVP to within Almost-Polynomial Factors is NP-Hard
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The hardness of approximate optima in lattices, codes, and systems of linear equations
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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We prove a new transference theorem in the geometry of numbers, giving optimal bounds relating the successive minima of a lattice with the minimal length of generating vectors of its dual. It generalizes the transference theorem due to Banaszczyk. The theorem is motivated by our efforts to improve Ajtai's connection factors in the connection of average-case to worst-case complexity of the shortest lattice vector problem. Our proofs are non-constructive, based on methods from harmonic analysis.