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Volumn 2, Issue 2, 2008, Pages 181-207

Sieve algorithms for the shortest vector problem are practical

Author keywords

AKS Algorithm; Enumeration; Lattices; LLL; Sieve

Indexed keywords


EID: 57049145514     PISSN: 18622976     EISSN: 18622984     Source Type: Journal    
DOI: 10.1515/JMC.2008.009     Document Type: Article
Times cited : (180)

References (34)
  • 3
    • 0031644084 scopus 로고    scopus 로고
    • 2 is NP-hard for randomized reductions
    • as TR97-047
    • 2 is NP-hard for Randomized Reductions. Proc. of 30th STOC. ACM, 1998, Available at as TR97-047.
    • (1998) Proc. of 30th STOC. ACM
    • Ajtai, M.1
  • 5
    • 38749118638 scopus 로고    scopus 로고
    • Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
    • DOI 10.1109/FOCS.2006.49, 4031381, 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006
    • A. Andoni and P. Indyk, Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions. FOCS '06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), pp. 459-468. IEEE Computer Society, Washington, DC, USA, 2006. (Pubitemid 351175534)
    • (2006) Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS , pp. 459-468
    • Andoni, A.1    Indyk, P.2
  • 6
    • 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), pp. 1-13.
    • (1986) Combinatorica , vol.6 , pp. 1-13
    • Babai, L.1
  • 7
    • 11944269154 scopus 로고    scopus 로고
    • Covering the sphere by equal spherical balls. Discrete and Computational Geometry
    • K. Böröczky and G. Wintsche, Covering the sphere by equal spherical balls. Discrete and Computational Geometry, The Goodman-Pollack Festschrift, pp. 237-253, 2003.
    • (2003) The Goodman-Pollack Festschrift , pp. 237-253
    • Böröczky, K.1    Wintsche, G.2
  • 11
    • 84966239268 scopus 로고
    • Improved methods for calculating vectors of short length in a lattice, including a complexity analysis
    • U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44 (1985), pp. 463-471.
    • (1985) Math. Comp. , vol.44 , pp. 463-471
    • Fincke, U.1    Pohst, M.2
  • 16
    • 0042671501 scopus 로고    scopus 로고
    • On the equidistribution of Hecke points
    • D. Goldstein and A. Mayer, On the equidistribution of Hecke points, Forum Math. 15 (2003), pp. 165-189. (Pubitemid 36932024)
    • (2003) Forum Mathematicum , vol.15 , Issue.2 , pp. 165-189
    • Goldstein, D.1    Mayer, A.2
  • 20
    • 0022285409 scopus 로고
    • Algorithms to construct minkowski reduced and hermite reduced lattice bases
    • DOI 10.1016/0304-3975(85)90067-2
    • B. Helfrich, Algorithms to construct Minkowski reduced and Hermite reduced bases, Theoretical Computer Science 41 (1985), pp. 125-139. (Pubitemid 16593835)
    • (1985) Theoretical Computer Science , vol.41 , Issue.2-3 , pp. 125-139
    • Helfrich Bettina1
  • 22
    • 0033896372 scopus 로고    scopus 로고
    • Finding the closest lattice vector when it's unusually close
    • P. Klein, Finding the Closest Lattice Vector when It's Unusually Close. Proc. of SODA '00, ACM-SIAM, 2000.
    • (2000) Proc. of SODA '00, ACM-SIAM
    • Klein, P.1
  • 23
    • 34250244723 scopus 로고
    • Factoring polynomials with rational coefficients
    • A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Ann. 261 (1982), pp. 513-534.
    • (1982) Mathematische Ann. , vol.261 , pp. 513-534
    • Lenstra, A.K.1    Lenstra, Jr.H.W.2    Lovász, L.3
  • 24
    • 0012524599 scopus 로고    scopus 로고
    • Complexity of lattice problems
    • Kluwer Academic Publishers, Boston, MA A cryptographic perspective. MR MR2042139 (2004m:94067)
    • D. Micciancio and S. Goldwasser, Complexity of lattice problems, The Kluwer International Series in Engineering and Computer Science, 671. Kluwer Academic Publishers, Boston, MA, 2002, A cryptographic perspective. MR MR2042139 (2004m:94067)
    • (2002) The Kluwer International Series in Engineering and Computer Science , vol.671
    • Micciancio, D.1    Goldwasser, S.2
  • 25
    • 33746766947 scopus 로고    scopus 로고
    • LLL on the average. Proc. of the 7th International algorithmic number theory symposium, ANTS-VII)
    • Springer-Verlag
    • P. Q. Nguyen and D. Stehlé, LLL on the Average. Proc. of the 7th International Algorithmic Number Theory Symposium, (ANTS-VII), LNCS 4076, pp. 238-256. Springer-Verlag, 2006.
    • (2006) LNCS , vol.4076 , pp. 238-256
    • Nguyen, P.Q.1    Stehlé, D.2
  • 26
    • 33846867921 scopus 로고    scopus 로고
    • The two faces of lattices in cryptology
    • Springer-Verlag
    • P. Q. Nguyen and J. Stern, The Two Faces of Lattices in Cryptology. Proc. of CALC '01, LNCS 2146. Springer-Verlag, 2001.
    • (2001) Proc. of CALC '01, LNCS , vol.2146
    • Nguyen, P.Q.1    Stern, J.2
  • 27
    • 57049107634 scopus 로고    scopus 로고
    • Lossy trapdoor functions and their applications
    • Report 2007/279. To appear in STOC '08
    • C. Peikert and B. Waters, Lossy Trapdoor Functions and Their Applications, Cryptology ePrint Archive, Report, 2007. Report 2007/279. To appear in STOC '08.
    • (2007) Cryptology EPrint Archive Report
    • Peikert, C.1    Waters, B.2
  • 28
    • 0002586419 scopus 로고
    • On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications
    • M. Pohst, On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications, ACM SIGSAM Bulletin 15 (1981), pp. 37-44.
    • (1981) ACM SIGSAM Bulletin , vol.15 , pp. 37-44
    • Pohst, M.1
  • 30
    • 84976024989 scopus 로고
    • Lattice coverings of space
    • C. A. Rogers, Lattice coverings of space, Mathematika 6 (1959), pp. 33-39.
    • (1959) Mathematika , vol.6 , pp. 33-39
    • Rogers, C.A.1
  • 31
    • 0023532388 scopus 로고
    • A hierarchy of polynomial lattice basis reduction algorithms
    • C.-P. Schnorr, A hierarchy of polynomial lattice basis reduction algorithms, Theoretical Computer Science 53 (1987), pp. 201-224.
    • (1987) Theoretical Computer Science , vol.53 , pp. 201-224
    • Schnorr, C.-P.1
  • 32
    • 35248874386 scopus 로고    scopus 로고
    • Lattice reduction by random sampling and birthday methods, Proc. STACS 2003
    • Springer, Berlin
    • -, Lattice reduction by random sampling and birthday methods, Proc. STACS 2003, Lecture Notes in Comput. Sci. 2607, Springer, Berlin, 2003, pp. 145-156.
    • (2003) Lecture Notes in Comput. Sci. , vol.2607 , pp. 145-156
    • Schnorr, C.-P.1
  • 33
    • 33846200465 scopus 로고
    • Lattice basis reduction: Improved practical algorithms and solving subset sum problems
    • C.-P. Schnorr and M. Euchner, Lattice basis reduction: improved practical algorithms and solving subset sum problems, Math. Programming 66 (1994), pp. 181-199.
    • (1994) Math. Programming , vol.66 , pp. 181-199
    • Schnorr, C.-P.1    Euchner, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.