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Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Abstract
We construct public-key cryptosystems that are secure assuming theworst-case hardness of approximating the minimum distance on n-dimensional lattices to within small Poly(n) factors. Prior cryptosystems with worst-case connections were based either on the shortest vector problem for a special class of lattices (Ajtai and Dwork, STOC 1997; Regev, J. ACM 2004), or on the conjectured hardness of lattice problems for quantum algorithms (Regev, STOC 2005). Our main technical innovation is a reduction from variants of the shortest vector problem to corresponding versions of the "learning with errors" (LWE) problem; previously, only a quantum reduction of this kind was known. As an additional contribution, we construct a natural chosen ciphertext-secure cryptosystem having a much simpler description and tighter underlying worst-case approximation factor than prior schemes.
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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
CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM
Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J. M., Schwabe, P., Seiler, G., & Stehle, D. (2018) · 2018 IEEE European Symposium on Security and Privacy (EuroS&P) · doi:10.1109/eurosp.2018.00032 · Cited by 1,192
On Ideal Lattices and Learning with Errors over Rings
Lyubashevsky, V., Peikert, C., & Regev, O. (2013) · Journal of the ACM · doi:10.1145/2535925 · Cited by 836
Self-citationMaking NTRU as Secure as Worst-Case Problems over Ideal Lattices
Stehlé, D., & Steinfeld, R. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-20465-4_4 · Cited by 444
Survey on Fully Homomorphic Encryption, Theory, and Applications
Marcolla, C., Sucasas, V., Manzano, M., Bassoli, R., Fitzek, F. H. P., & Aaraj, N. (2022) · Proceedings of the IEEE · doi:10.1109/jproc.2022.3205665 · Cited by 323
Metadata
- Authors
- Peikert, C.
- Venue
- Proceedings of the forty-first annual ACM symposium on Theory of computing
- Publisher
- ACM
- Published
- 2009-05-31
- Pages
- 333-342
- OpenAlex
- W2058785578
- Cited by
- 813
- References
- 0
- FWCI
- 33.85
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Peikert, C. (2009). Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. Proceedings of the forty-first annual ACM symposium on Theory of computing. https://doi.org/10.1145/1536414.1536461
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