In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central toâ€¦Â (More)

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Highly Cited

2010

Highly Cited

2010

- Vadim Lyubashevsky, Chris Peikert, Oded Regev
- EUROCRYPT
- 2010

The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by aâ€¦Â (More)

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Highly Cited

2007

Highly Cited

2007

- Craig Gentry, Chris Peikert, Vinod Vaikuntanathan
- STOC
- 2007

We show how to construct a variety of "trapdoor" cryptographic tools assuming the worst-case hardness of standard latticeâ€¦Â (More)

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Highly Cited

2005

Highly Cited

2005

- Oded Regev
- STOC
- 2005

Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learningâ€¦Â (More)

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Highly Cited

2004

Highly Cited

2004

- Dorit Aharonov, Oded Regev
- 2004

We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of âˆš n lie in NPâ€¦Â (More)

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Highly Cited

2002

Highly Cited

2002

- Oded Regev
- FOCS
- 2002

We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solutionâ€¦Â (More)

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Highly Cited

2001

Highly Cited

2001

- MiklÃ³s Ajtai, Ravi Kumar, D. Sivakumar
- STOC
- 2001

We present a randomized 2^{<italic>O(n)</italic>} time algorithm to compute a shortest non-zero vector in an <italic>n</italicâ€¦Â (More)

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Highly Cited

1997

Highly Cited

1997

- Oded Goldreich, Shafi Goldwasser
- STOC
- 1997

We show simple constant-round interactive proof systems for problems capturing the approximability, to within a factor of n, ofâ€¦Â (More)

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Highly Cited

1996

Highly Cited

1996

- MiklÃ³s Ajtai
- Electronic Colloquium on Computational Complexity
- 1996

We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which nds a short vectorâ€¦Â (More)

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Highly Cited

1996

Highly Cited

1996

- Oded Goldreich, Shafi Goldwasser, Shai Halevi
- Studies in Complexity and Cryptography
- 1996

In 1995, Ajtai described a construction of one-way functions whose security is equivalent to the difficulty of some well knownâ€¦Â (More)

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Highly Cited

1996

Highly Cited

1996

- MiklÃ³s Ajtai
- STOC
- 1996

We give a random class of lattices in Zn whose elements can be generated together with a short vector in them so that, if thereâ€¦Â (More)

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