메뉴 건너뛰기




Volumn 207, Issue 1, 1998, Pages 105-116

A relation of primal-dual lattices and the complexity of shortest lattice vector problem

Author keywords

Interactive proofs; Lattice; NP hardness; Shortest vector problem

Indexed keywords


EID: 0004489099     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00058-9     Document Type: Article
Times cited : (21)

References (24)
  • 1
    • 0029719917 scopus 로고    scopus 로고
    • Generating hard instances of lattice problems
    • Full version available from ECCC, Electronic Colloquium on Computational Complexity TR96-007
    • M. Ajtai, Generating hard instances of lattice problems, in: Proc. 28th Annual ACM Symposium on the Theory of Computing, 1996. Full version available from ECCC, Electronic Colloquium on Computational Complexity TR96-007, at http://www.eccc.uni-trier.de/eccc/.
    • (1996) Proc. 28th Annual ACM Symposium on the Theory of Computing
    • Ajtai, M.1
  • 2
    • 85033918806 scopus 로고    scopus 로고
    • Electronic Colloquium on Computational Complexity, TR97-047
    • 2 is NP-hard for randomized reductions, Electronic Colloquium on Computational Complexity, TR97-047 at http://www.eccc.uni-trier.de/eccc/.
    • 2 is NP-hard for Randomized Reductions
    • Ajtai, M.1
  • 5
    • 51249173801 scopus 로고
    • On Lovász' lattice reduction and the nearest lattice point problem
    • L. Babai, On Lovász' lattice reduction and the nearest lattice point problem, Combinatorica 6 (1986) 1-13.
    • (1986) Combinatorica , vol.6 , pp. 1-13
    • Babai, L.1
  • 6
    • 0000303291 scopus 로고
    • New bounds in some transference theorems in the geometry of numbers
    • W. Banaszczyk, New bounds in some transference theorems in the geometry of numbers, Mathematische Annalen 296 (1993) 625-635.
    • (1993) Mathematische Annalen , vol.296 , pp. 625-635
    • Banaszczyk, W.1
  • 15
    • 0342349222 scopus 로고
    • Dual vectors and lower bounds for the nearest lattice point problem
    • J. Håstad, Dual vectors and lower bounds for the nearest lattice point problem, Combinatorica 8 (1988) pp. 75-81.
    • (1988) Combinatorica , vol.8 , pp. 75-81
    • Håstad, J.1
  • 16
    • 0022012583 scopus 로고
    • The computational complexity of simultaneous diophantine approximation problems
    • J. C. Lagarias, The computational complexity of simultaneous diophantine approximation problems, SIAM J. Comput. 14 (1985) pp. 196-209.
    • (1985) SIAM J. Comput. , vol.14 , pp. 196-209
    • Lagarias, J.C.1
  • 17
    • 34249953865 scopus 로고
    • Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice
    • J. C. Lagarias, H. W. Lenstra, C. P. Schnorr, Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice, Combinatorica 10 (4) (1990) 333-348.
    • (1990) Combinatorica , vol.10 , Issue.4 , pp. 333-348
    • Lagarias, J.C.1    Lenstra, H.W.2    Schnorr, C.P.3
  • 19
    • 0020845921 scopus 로고
    • Integer programming with a fixed number of variables
    • H. W. Lenstra, Jr., Integer programming with a fixed number of variables, Math. Oper. Res. 8 (1993) 538-548.
    • (1993) Math. Oper. Res. , vol.8 , pp. 538-548
    • Lenstra H.W., Jr.1
  • 22
    • 0009807286 scopus 로고
    • A hierarchy of polynomial time basis reduction algorithms
    • C. P. Schnorr, A hierarchy of polynomial time basis reduction algorithms, Theory of Algorithms (1985) 375-386.
    • (1985) Theory of Algorithms , pp. 375-386
    • Schnorr, C.P.1
  • 23
    • 0021420540 scopus 로고
    • The complexity of promise problems with applications to public-key cryptography
    • S. Even, A. L. Selman, Y. Yacobi, The complexity of promise problems with applications to public-key cryptography, information and control 61 (1984) 159-173.
    • (1984) Information and Control , vol.61 , pp. 159-173
    • Even, S.1    Selman, A.L.2    Yacobi, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.