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- Oded Regev
- J. ACM
- 2005

Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the 'learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these… (More)

- 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 a small amount of noise, from truly uniform ones. The problem has been shown to be as hard as worst-case lattice problems, and in recent years it has served as the foundation for a plethora of cryptographic applications.… (More)

- Daniele Micciancio, Oded Regev
- 45th Annual IEEE Symposium on Foundations of…
- 2004

We show 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. The lattice problems we consider are the shortest vector problem, the shortest independent vectors problem and the covering radius problem. The approximation… (More)

- Subhash Khot, Oded Regev
- J. Comput. Syst. Sci.
- 2003

Based on a conjecture regarding the power of unique 2-prover-1-round games presented in [Khot02], we show that vertex cover is hard to approximate within any constant factor better than 2. We actually show a stronger result, namely, based on the same conjecture, vertex cover on k-uniform hypergraphs is hard to approximate within any constant factor better… (More)

- Julia Kempe, Alexei Y. Kitaev, Oded Regev
- FSTTCS
- 2004

The k-LOCAL HAMILTONIAN problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NPcomplete for k ≥ 2. It was known that the problem is QMA-complete for any k ≥ 3. On the other hand 1-LOCAL HAMILTONIAN is in P, and hence not believed to be QMA-complete. The complexity of the… (More)

- Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, Oded Regev
- 45th Annual IEEE Symposium on Foundations of…
- 2004

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm. This implies that the adiabatic computation model and the standard quantum… (More)

- Oded Regev
- STOC
- 2003

We introduce the use of Fourier analysis on lattices as an integral part of a lattice-based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two cryptographic constructions that are based on the worst-case hardness of the unique shortest vector problem. The main… (More)

- Phong Q. Nguyen, Oded Regev
- Journal of Cryptology
- 2006

Lattice-based signature schemes following the Goldreich–Goldwasser–Halevi (GGH) design have the unusual property that each signature leaks information on the signer’s secret key, but this does not necessarily imply that such schemes are insecure. At Eurocrypt ’03, Szydlo proposed a potential attack by showing that the leakage reduces the key-recovery… (More)

- Nicolas Gama, Phong Q. Nguyen, Oded Regev
- EUROCRYPT
- 2010

Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanalysis either as standalone algorithms, or as subroutines in lattice reduction algorithms. Here we revisit these fundamental algorithms and show that… (More)

- Noam Nisan, Shmulik London, Oded Regev, Noam Camiel
- ICDCS
- 1998