The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
A hierarchy of polynomial time lattice basis reduction algorithms
Open accessAbstract
We present a hierarchy of polynomial time lattice basis reduction algorithms that stretch from Lenstra, Lenstra, Lovász reduction to Korkine–Zolotareff reduction. Let λ(L) be the length of a shortest nonzero element of a lattice L. We present an algorithm which for k∈N finds a nonzero lattice vector b so that |b|2⩽(6k2)nkλ(L)2. This algorithm uses O(n2(kk+o(k))+n2)log B) arithmetic operations on O(n log B)-bit integers. This holds provided that the given basis vectors b1,…,bn∈Zn are integral and have the length bound B. This algorithm successively applies Korkine–Zolotareff reduction to blocks of length k of the lattice basis. We also improve Kannan's algorithm for Korkine-Zolotareff reduction.
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Cites
Factoring polynomials with rational coefficients
Lenstra, A. K., Lenstra, H. W., & Lovász, L. (1982) · Mathematische Annalen · doi:10.1007/bf01457454 · Cited by 4,018
Integer Programming with a Fixed Number of Variables
Lenstra, H. W. (1983) · Mathematics of Operations Research · doi:10.1287/moor.8.4.538 · Cited by 1,440
Improved algorithms for integer programming and related lattice problems
Kannan, R. (1983) · Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83 · doi:10.1145/800061.808749 · Cited by 441
An Algorithmic Theory of Numbers, Graphs and Convexity
Lovász, L. (1986) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970203 · Cited by 358
Korkine, A., & Zolotareff, G. (1873) · Mathematische Annalen · doi:10.1007/bf01442795 · Cited by 287
Another NP-complete problem and the complexity of computing short vectors in a lattice
Boas, P. V. E. (1981) · Medical Entomology and Zoology · Cited by 161
Worst-case complexity bounds for algorithms in the theory of integral quadratic forms
Lagarias, J. C. (1980) · Journal of Algorithms · doi:10.1016/0196-6774(80)90021-8 · Cited by 71
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
On 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
Efficient Fully Homomorphic Encryption from (Standard) LWE
Brakerski, Z., & Vaikuntanathan, V. (2011) · 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2011.12 · Cited by 1,449
(Leveled) Fully Homomorphic Encryption without Bootstrapping
Brakerski, Z., Gentry, C., & Vaikuntanathan, V. (2014) · ACM Transactions on Computation Theory · doi:10.1145/2633600 · Cited by 1,430
Metadata
- Authors
- Schnorr, C. P.
- Venue
- Theoretical Computer Science
- Publisher
- Elsevier BV
- Published
- 1987
- Volume
- 53
- Issue
- 2-3
- Pages
- 201-224
- ISSN
- 0304-3975 (ISSN-L)
- OpenAlex
- W1989510734
- Cited by
- 648
- References
- 7
- FWCI
- 4.24
- Type
- journal article
- Language
- en
- Open access
- hybrid
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