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Volumn , Issue , 2010, Pages 1468-1480

Faster exponential time algorithms for the shortest vector problem

Author keywords

Algorithm analysis; Cryptography; Shortest vector problem; Sieving algorithms; Software implementations

Indexed keywords

CRYPTOGRAPHY; VECTORS;

EID: 77951698499     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973075.119     Document Type: Conference Paper
Times cited : (178)

References (30)
  • 2
    • 38749147177 scopus 로고    scopus 로고
    • Generating hard instances of lattice problems
    • Preliminary version in STOC 1996
    • M. Ajtai. Generating hard instances of lattice problems. Complexity of Computations and Proofs, Quaderni di Matematica, 13:1-32, 2004. Preliminary version in STOC 1996.
    • (2004) Complexity of Computations and Proofs, Quaderni di Matematica , vol.13 , pp. 1-32
    • Ajtai, M.1
  • 3
    • 0030679849 scopus 로고    scopus 로고
    • A public-key cryptosystem with worst-case/average-case equivalence
    • ACM, May
    • M. Ajtai and C. Dwork. A public-key cryptosystem with worst-case/average-case equivalence. In Proceedings of STOC '97, pages 284-293. ACM, May 1997.
    • (1997) Proceedings of STOC '97 , pp. 284-293
    • Ajtai, M.1    Dwork, C.2
  • 4
    • 0001769755 scopus 로고    scopus 로고
    • A sieve algorithm for the shortest lattice vector problem
    • ACM, July
    • M. Ajtai, R. Kumar, and D. Sivakumar. A sieve algorithm for the shortest lattice vector problem. In Proceedings of STOC '01, pages 266-275. ACM, July 2001.
    • (2001) Proceedings of STOC '01 , pp. 266-275
    • Ajtai, M.1    Kumar, R.2    Sivakumar, D.3
  • 6
    • 38349062340 scopus 로고    scopus 로고
    • Positive applications of lattices to cryptography
    • I. Prívara and P. Ruzicka, editors, Mathematical Foundations of Computer Science 1997, Springer, Aug.
    • C. Dwork. Positive applications of lattices to cryptography. In I. Prívara and P. Ruzicka, editors, Mathematical Foundations of Computer Science 1997, volume 1295 of LNCS, pages 44-51. Springer, Aug. 1997.
    • (1997) LNCS , vol.1295 , pp. 44-51
    • Dwork, C.1
  • 7
    • 57049097675 scopus 로고    scopus 로고
    • Finding short lattice vectors within mordell's inequality
    • ACM, May
    • N. Gama and P. Q. Nguyen. Finding short lattice vectors within mordell's inequality. In Proceedings of STOC '08, pages 207-216. ACM, May 2008.
    • (2008) Proceedings of STOC '08 , pp. 207-216
    • Gama, N.1    Nguyen, P.Q.2
  • 8
    • 44449128937 scopus 로고    scopus 로고
    • Predicting lattice reduction
    • Proceedings of EUROCRYPT '08, Springer
    • N. Gama and P. Q. Nguyen. Predicting lattice reduction. In Proceedings of EUROCRYPT '08, volume 4965 of LNCS, pages 31-51. Springer, 2008.
    • (2008) LNCS , vol.4965 , pp. 31-51
    • Gama, N.1    Nguyen, P.Q.2
  • 9
    • 51849137205 scopus 로고    scopus 로고
    • Trapdoors for hard lattices and new cryptographic constructions
    • ACM, May
    • C. Gentry, C. Peikert, and V. Vaikuntanathan. Trapdoors for hard lattices and new cryptographic constructions. In Proceedings of STOC '08, pages 197-206. ACM, May 2008.
    • (2008) Proceedings of STOC '08 , pp. 197-206
    • Gentry, C.1    Peikert, C.2    Vaikuntanathan, V.3
  • 10
    • 77955338100 scopus 로고    scopus 로고
    • Improved Analysis of Kannan's Shortest Lattice Vector Algorithm
    • G. Hanrot and D. Stehlé. Improved Analysis of Kannan's Shortest Lattice Vector Algorithm. In Proceedings of Crypto '07.
    • Proceedings of Crypto '07
    • Hanrot, G.1    Stehlé, D.2
  • 11
    • 84947808606 scopus 로고    scopus 로고
    • NTRU: A ring based public key cryptosystem
    • Proceedings of ANTS-III, Springer, June
    • J. Hoffstein, J. Pipher, and J. H. Silverman. NTRU: a ring based public key cryptosystem. In Proceedings of ANTS-III, volume 1423 of LNCS, pages 267-288. Springer, June 1998.
    • (1998) LNCS , vol.1423 , pp. 267-288
    • Hoffstein, J.1    Pipher, J.2    Silverman, J.H.3
  • 14
    • 0000351029 scopus 로고
    • chapter Algorithmic Geometry of numbers, Annual Review Inc., Palo Alto, California
    • R. Kannan. Annual Review of Computer Science, volume 2, chapter Algorithmic Geometry of numbers, pages 231-267. Annual Review Inc., Palo Alto, California, 1987.
    • (1987) Annual Review of Computer Science , vol.2 , pp. 231-267
    • Kannan, R.1
  • 17
    • 38749089099 scopus 로고    scopus 로고
    • Generalized compact knapsacks, cyclic lattices, and efficient one-way functions
    • Dec. Preliminary version in FOCS 2002
    • D. Micciancio. Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Computational Complexity, 16(4):365-411, Dec. 2007. Preliminary version in FOCS 2002.
    • (2007) Computational Complexity , vol.16 , Issue.4 , pp. 365-411
    • Micciancio, D.1
  • 18
    • 0012524599 scopus 로고    scopus 로고
    • Complexity of Lattice Problems: A Cryptographic Perspective, Kluwer Academic Publishers, Boston, Massachusetts, Mar.
    • D. Micciancio and S. Goldwasser. Complexity of Lattice Problems: a cryptographic perspective, volume 671 of The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, Boston, Massachusetts, Mar. 2002.
    • (2002) The Kluwer International Series in Engineering and Computer Science , vol.671
    • Micciancio, D.1    Goldwasser, S.2
  • 19
    • 38749097694 scopus 로고    scopus 로고
    • Worst-case to average-case reductions based on Gaussian measure
    • Preliminary version in FOCS 2004
    • D. Micciancio and O. Regev. Worst-case to average-case reductions based on Gaussian measure. SIAM Journal on Computing, 37(1):267-302, 2007. Preliminary version in FOCS 2004.
    • (2007) SIAM Journal on Computing , vol.37 , Issue.1 , pp. 267-302
    • Micciancio, D.1    Regev, O.2
  • 20
    • 33846867921 scopus 로고    scopus 로고
    • The two faces of lattices in cryptology
    • Proceedings of CaLC '01, Springer, Mar.
    • P. Nguyen and J. Stern. The two faces of lattices in cryptology. In Proceedings of CaLC '01, volume 2146 of LNCS, pages 146-180. Springer, Mar. 2001.
    • (2001) LNCS , vol.2146 , pp. 146-180
    • Nguyen, P.1    Stern, J.2
  • 21
    • 57049145514 scopus 로고    scopus 로고
    • Sieve algorithms for the shortest vector problem are practical
    • Jul
    • P. Nguyen and T. Vidick. Sieve algorithms for the shortest vector problem are practical. J. of Mathematical Cryptology, 2(2):181-207, Jul 2008.
    • (2008) J. of Mathematical Cryptology , vol.2 , Issue.2 , pp. 181-207
    • Nguyen, P.1    Vidick, T.2
  • 22
    • 51849152661 scopus 로고    scopus 로고
    • Lossy trapdoor functions and their applications
    • ACM, May
    • C. Peikert and B. Waters. Lossy trapdoor functions and their applications. In Proceedings of STOC '08, pages 187-196. ACM, May 2008.
    • (2008) Proceedings of STOC '08 , pp. 187-196
    • Peikert, C.1    Waters, B.2
  • 23
    • 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(1):37-44, 1981.
    • (1981) ACM SIGSAM Bulletin , vol.15 , Issue.1 , pp. 37-44
    • Pohst, M.1
  • 24
    • 58349108198 scopus 로고    scopus 로고
    • Rigorous and efficient short lattice vectors enumeration, 2008
    • Springer
    • X. Pujol and D. Stehlé. Rigorous and efficient short lattice vectors enumeration, 2008. In Proceedings of Asiacrypt '08, pages 390-405. Springer, 2008.
    • (2008) Proceedings of Asiacrypt '08 , pp. 390-405
    • Pujol, X.1    Stehlé, D.2
  • 25
    • 20444451186 scopus 로고    scopus 로고
    • New lattice based cryptographic constructions
    • Preliminary version in STOC 2003
    • O. Regev. New lattice based cryptographic constructions. Journal of the ACM, 51(6):899-942, 2004. Preliminary version in STOC 2003.
    • (2004) Journal of the ACM , vol.51 , Issue.6 , pp. 899-942
    • Regev, O.1
  • 26
    • 33745571012 scopus 로고    scopus 로고
    • On lattices, learning with errors, random linear codes, and cryptography
    • ACM, June
    • O. Regev. On lattices, learning with errors, random linear codes, and cryptography. In Proceedings of STOC '05, pages 84-93. ACM, June 2005.
    • (2005) Proceedings of STOC '05 , pp. 84-93
    • Regev, O.1
  • 28
    • 0023532388 scopus 로고
    • A hierarchy of polynomial time lattice basis reduction algorithms
    • C.-P. Schnorr. A hierarchy of polynomial time lattice basis reduction algorithms. Theoretical Computer Science, 53(2-3):201-224, 1987.
    • (1987) Theoretical Computer Science , vol.53 , Issue.2-3 , pp. 201-224
    • Schnorr, C.-P.1
  • 29
    • 33846200465 scopus 로고
    • Lattice basis reduction: Improved practical algorithms and solving subset sum problems
    • Aug. Preliminary version in FCT 1991
    • C.-P. Schnorr and M. Euchner. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Mathematical programming, 66(1-3):181-199, Aug. 1994. Preliminary version in FCT 1991.
    • (1994) Mathematical Programming , vol.66 , Issue.1-3 , pp. 181-199
    • Schnorr, C.-P.1    Euchner, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.