The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
New lattice-based cryptographic constructions
Abstract
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 result is a new public key cryptosystem whose security guarantee is considerably stronger than previous results ( O ( n 1.5 ) instead of O ( n 7 )). This provides the first alternative to Ajtai and Dwork's original 1996 cryptosystem. Our second result is a family of collision resistant hash functions with an improved security guarantee in terms of the unique shortest vector problem. Surprisingly, both results are derived from one theorem that presents two indistinguishable distributions on the segment [0, 1). It seems that this theorem can have further applications; as an example, we use it to solve an open problem in quantum computation related to the dihedral hidden subgroup problem.
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Cites
Lecture Notes in Computer Science 1205
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
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NTRU: A ring-based public key cryptosystem
Hoffstein, J., Pipher, J., & Silverman, J. H. (1998) · Lecture Notes in Computer Science · doi:10.1007/bfb0054868 · Cited by 1,947
Generating hard instances of lattice problems (extended abstract)
Ajtai, M. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237838 · Cited by 1,405
A public-key cryptosystem with worst-case/average-case equivalence
Ajtai, M., & Dwork, C. (1997) · Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97 · doi:10.1145/258533.258604 · Cited by 642
Generating Hard Instances of Lattice ProblemsPreprint
Ajtai, M. (1996) · Electronic colloquium on computational complexity · Cited by 606
Complexity of Lattice Problems
Micciancio, D., & Goldwasser, S. (2002) · Springer eBooks · doi:10.1007/978-1-4615-0897-7 · Cited by 484
Public-key cryptosystems from lattice reduction problems
Goldreich, O., Goldwasser, S., & Halevi, S. (1997) · Lecture Notes in Computer Science · doi:10.1007/bfb0052231 · Cited by 482
New bounds in some transference theorems in the geometry of numbers
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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-citationOn lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2005) · Proceedings of the thirty-seventh annual ACM symposium on Theory of computing · doi:10.1145/1060590.1060603 · Cited by 2,313
Self-citationFully Homomorphic Encryption without Modulus Switching from Classical GapSVP
Brakerski, Z. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-32009-5_50 · Cited by 1,252
Worst‐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-citationBetter Key Sizes (and Attacks) for LWE-Based Encryption
Lindner, R., & Peikert, C. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-19074-2_21 · Cited by 688
Metadata
- Authors
- Regev, O.
- Venue
- Journal of the ACM
- Published
- 2004-11
- Volume
- 51
- Issue
- 6
- Pages
- 899-942
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W1972050218
- Cited by
- 292
- References
- 27
- FWCI
- 9.49
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
