Hardness of approximating the closest vector problem with pre-processing

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 2005, Issue , 2005, Pages 216-225

  Alekhnovich, Mikhail ^a   Khot, Subhash A ^b   Kindler, Guy ^a   Vishnoi, Nisheeth K ^c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b Georgia Institute of Technology   (United States)

^c INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSEST VECTOR PROBLEM;

APPROXIMATION THEORY; CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; DATA PROCESSING; PROBLEM SOLVING;

VECTORS;

EID: 33748617126     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.2005.40     Document Type: Conference Paper

References (20)

1. D. Aharonov and O. Regev. Lattice problems in NP intersect coNP. In Annual Symposium on Foundations of Computer Science, number 45, pages 362-371, 2004.
2. M. Ajtai. The shortest vector problem in £2 is NP-hard for randomized reductions. In Proceedings of the ACM Symposium on the Theory of Computing, number 30, pages 10-19, 1998.
3. M. Ajtai, R. Kumar, and D. Sivakumar. A sieve algorithm for the shortest lattice vector problem. In Proceedings of the ACM Symposium on the Theory of Computing, number 33, pages 601-610, 2001.
4. S. Arora, L. Babai, J. Stern, and Z. Sweedyk. Hardness of approximate optima in lattices, codes, and linear systems. Journal of Computer and System Sciences, 54(2):317-331, 1997.
5. J. Bruck and M. Naor. The hardness of decoding linear codes with preprocessing. IEEE Transactions on Information Theory, 36(2):381-385, 1990.
6. I. Dinur, V. Guruswami, S. Khot, and O. Regev. A new multilayered pep and the hardness of hypergraph vertex cover. SIAM J. Comput., 34(5):1129-1146, 2005.
7. I. Dinur, G. Kindler, R. Raz, and S. Safra. Approximating cvp to within almost-polynomial factors is np-hard. Combinatorica, 23(2):205-243, 2003.
8. U. Feige and D. Micciancio. The inapproximability of lattice and coding problems with preprocessing. Journal of Computer and System Sciences, 69(1):45-67, 2004.
9. C. Gauss. Disquisitiones arithmeticae. Yale Univ. Pres, 1966. English translation by A. A. Clarke.
10. R. Kannan. Improved algorithms for integer programming and related lattice problems. In Proceedings of the ACM Symposium on the Theory of Computing, number 15, pages 193-206, 1983.
11. S. Khot. Hardness results for coloring 3-colorable 3-uniform hypergraphs. In Annual Symposium on Foundations of Computer Science, number 43, pages 23-32, 2002.
12. J. Lagarias, H. Lenstra, and C. Schnorr. Korkine-Zolotarev bases and successive minima of a lattice and its reciprocal lattice. Combinatorica, 10:333-348, 1990.
13. J. Lagarias and A. Odlyzko. Solving low-density subset sum problems. Journal of the ACM, 32(1):229-246, 1985.
14. A. Lenstra, H. Lenstra, and L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., 261:513-534, 1982.
15. H. Lenstra. Integer programming with a fixed number of variables. Technical Report 81-03, Univ. of Amsterdam, Amsterdam, 1981.
16. D. Micciancio. The hardness of the closest vector problem with preprocessing. IEEE Transactions on Information Theory, 47:1212-1215, 2001.
17. D. Micciancio and S. Goldwasser. Complexity of lattice problems: A cryptographic perspective, volume 671. Kluwer Academic Publishers, 2002.
18. R. Raz. A parallel repetition theorem. SIAM Journal of Computing, 27(3):763-803, 1998.
19. O. Regev. Improved inapproximability of lattice and coding problems with preprocessing. IEEE Transactions on Information Theory, 50(9):2031-2037, 2004.
20. C. Schnorr. A hierarchy of polynomial-time basis reduction algorithms. In Proceedings of Conference on Algorithms, pages 375-386, Péecs, Hungary, 1985.