• Publications
  • Influence
On lattices, learning with errors, random linear codes, and cryptography
  • O. Regev
  • Mathematics, Computer Science
  • STOC '05
  • 22 May 2005
TLDR
A public-key cryptosystem whose hardness is based on the worst-case quantum hardness of SVP and SIVP, and an efficient solution to the learning problem implies a <i>quantum</i>, which can be made classical. Expand
On Ideal Lattices and Learning with Errors over Rings
TLDR
The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones, by introducing an algebraic variant of LWE called ring-LWE, and proving that it too enjoys very strong hardness guarantees. Expand
On lattices, learning with errors, random linear codes, and cryptography
  • O. Regev
  • Mathematics, Computer Science
  • JACM
  • 1 September 2009
TLDR
A (classical) public-key cryptosystem whose security is based on the hardness of the learning problem, which is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem that is quantum. Expand
Vertex cover might be hard to approximate to within 2-epsilon
TLDR
A stronger result is shown, namely, based on the same conjecture, vertex cover on k-uniform hypergraphs is hard to approximate within any constant factor better than k. Expand
Worst-Case to Average-Case Reductions Based on Gaussian Measures
TLDR
It is shown that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice, and it is proved that the distribution that one obtains after adding Gaussian noise to a lattice has the following interesting property. Expand
The Complexity of the Local Hamiltonian Problem
TLDR
This paper settles the question and shows that the 2-LOCAL HAMILTONIAN problem is QMA-complete, and demonstrates that adiabatic computation with two-local interactions on qubits is equivalent to standard quantum computation. Expand
A Toolkit for Ring-LWE Cryptography
TLDR
This work designs cryptographic schemes whose efficiency is competitive with that of more traditional number-theoretic ones, along with entirely new applications like fully homomorphic encryption. Expand
Lattice-Based Cryptography
  • O. Regev
  • Computer Science
  • CRYPTO
  • 20 August 2006
We describe some of the recent progress on lattice-based cryptography, starting from the seminal work of Ajtai, and ending with some recent constructions of very efficient cryptographic schemes.
Worst-case to average-case reductions based on Gaussian measures
TLDR
It is shown that solving modular linear equation on the average is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the rank of the lattice, and it is proved that the distribution that one obtains after adding Gaussian noise to the lattices has the following interesting property. Expand
Lattice Enumeration Using Extreme Pruning
TLDR
This work revisits lattice enumeration algorithms and shows that surprising exponential speedups can be achieved both in theory and in practice by using a new technique, which is called extreme pruning. Expand
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