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Generating hard instances of lattice problems (extended abstract)
Open accessAbstract
. We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice with a probability of at least 1 2 then there is also a probabilistic polynomial time algorithm which solves the following three lattice problems in every lattice in Z n with a probability exponentially close to one. (1) Find the length of a shortest nonzero vector in an n-dimensional lattice, approximately, up to a polynomial factor. (2) Find the shortest nonzero vector in an n-dimensional lattice L where the shortest vector v is unique in the sense that any other vector whose length is at most n c kvk is parallel to v, where c is a sufficiently large absolute constant. (3) Find a basis b 1 ; :::; b n in the n-dimensional lattice L whose length, defined as max n i=1 kb i k, is the smallest possible up to a polynomial factor. A large number of the existing techniques of cryptography include the generation of a specific ins...
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Cited by
Fully homomorphic encryption using ideal lattices
Gentry, C. (2009) · Proceedings of the forty-first annual ACM symposium on Theory of computing · doi:10.1145/1536414.1536440 · Cited by 6,806
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
Advances in quantum cryptography
Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., et al. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.361502 · Cited by 2,033
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Acar, A., Aksu, H., Uluagac, A. S., & Conti, M. (2019) · ACM Computing Surveys · doi:10.1145/3214303 · Cited by 1,397
A Framework for Efficient and Composable Oblivious Transfer
Peikert, C., Vaikuntanathan, V., & Waters, B. (2008) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-85174-5_31 · Cited by 678
Metadata
- Authors
- Ajtai, M.
- Venue
- Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
- Publisher
- ACM Press
- Published
- 1996
- Pages
- 99-108
- OpenAlex
- W2142048307
- Cited by
- 1,405
- References
- 0
- FWCI
- 8.58
- Type
- conference paper
- Language
- en
- Open access
- bronze
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- Ajtai, M. (1996). Generating hard instances of lattice problems (extended abstract). Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96. https://doi.org/10.1145/237814.237838
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