On polynomial-factor approximations to the shortest lattice vector length

SIAM Journal on Discrete Mathematics

Volumn 16, Issue 3, 2003, Pages 422-425

  Kumar, Ravi ^a   Sivakumar, D ^a  

^a IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

Lattice algorithms; Shortest lattice vector; SVP

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING; VECTORS;

POLYNOMIAL-FACTOR APPROXIMATIONS; SHORTEST LATTICE VECTOR LENGTH;

APPROXIMATION THEORY;

EID: 0041384096     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480100379981     Document Type: Article

References (14)

1. M. Ajtai, Generating hard instances of lattice problems, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, Philadelphia, PA, 1996, pp. 99-108.
2. 2 is NP-hard for randomized reductions, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Dallas, TX, 1998, pp. 10-19.
3. M. Ajtai and C. Dwork, A public-key cryptosystem with worst-case/average-case equivalence, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, El Paso, TX, 1997, pp. 284-293.
4. M. Ajtai and R. Kumar, and D. Sivakumar, A sieve algorithm for the shortest lattice vector problem, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, Crete, Greece, 2001, pp. 601-610.
5. A. Blum, A. Kalai, and H. Wasserman, Noise-tolerant learning, the parity problem, and the statistical query model, in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, Portland, OR, 2000, pp. 435-440.
6. J.-Y. Cai, Applications of a new transference theorem to Ajtai's connection factor, in Proceedings of the 14th Annual IEEE Conference on Computational Complexity, Atlanta, GA, 1999, pp. 205-214.
7. J.-Y. Cai and A. Nerurkar, An improved worst-case to average-case connection for lattice problems, in Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, Miami Beach, FL, 1997, pp. 468-477.
8. O. Goldreich and S. Goldwasser, On the limits of non-approximability of lattice problems, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Dallas, TX, 1998, pp. 1-9.
9. R. Kannan, Minkowski's convex body theorem and integer programming, Math. Oper. Res., 12 (1987), pp. 415-440.
10. R. Kumar and D. Sivakumar, On polynomial approximation to the shortest lattice vector length, in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, Washington, D.C., 2001, pp. 126-127.
11. J. Lagarias, H. W. Lenstra, Jr., and C. P. Schnorr, Korkine-Zolotarev bases and successive minima of a lattice and its reciprocal lattice, Combinatorica, 10 (1990), pp. 334-348.
12. A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann., 261 (1982), pp. 515-534.
13. D. Micciancio, The shortest vector in a lattice is hard to approximate to within some constant, in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, Palo Alto, CA, 1998, pp. 92-98.
14. C. P. Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms, Theoret. Comput. Sci., 53 (1987), pp. 201-224.