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Lattice problems in NP ∩ coNP
Abstract
We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √n lie in NP intersect coNP. The result (almost) subsumes the three mutually-incomparable previous results regarding these lattice problems: Banaszczyk [1993], Goldreich and Goldwasser [2000], and Aharonov and Regev [2003]. Our technique is based on a simple fact regarding succinct approximation of functions using their Fourier series over the lattice. This technique might be useful elsewhere---we demonstrate this by giving a simple and efficient algorithm for one other lattice problem (CVPP) improving on a previous result of Regev[2003]. An interesting fact is that our result emerged from a “dequantization” of our previous quantum result in Aharonov and Regev [2003]. This route to proving purely classical results might be beneficial elsewhere.
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Cited by
On lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2009) · Journal of the ACM · doi:10.1145/1568318.1568324 · Cited by 2,315
Self-citationWorst‐Case to Average‐Case Reductions Based on Gaussian Measures
Micciancio, D., & Regev, O. (2007) · SIAM Journal on Computing · doi:10.1137/s0097539705447360 · Cited by 907
Self-citationMicciancio, D., & Regev, O. (2009) · Post-Quantum Cryptography · doi:10.1007/978-3-540-88702-7_5 · Cited by 615
Self-citationRegev, O. (2006) · Lecture Notes in Computer Science · doi:10.1007/11818175_8 · Cited by 485
Self-citationGeneralized Compact Knapsacks Are Collision Resistant
Lyubashevsky, V., & Micciancio, D. (2006) · Lecture Notes in Computer Science · doi:10.1007/11787006_13 · Cited by 268
Metadata
- Authors
- Aharonov, D., & Regev, O.
- Venue
- Journal of the ACM
- Published
- 2005-09
- Volume
- 52
- Issue
- 5
- Pages
- 749-765
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2037426925
- Cited by
- 179
- References
- 0
- FWCI
- 11.30
- Type
- journal article
- Language
- en
- Open access
- closed
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