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Volumn 56, Issue 1, 2010, Pages 455-461

Optimal pairings

Author keywords

Ate pairing; Elliptic curves; Pairing based cryptography; Tate pairing

Indexed keywords

ELLIPTIC CURVE; PAIRING-BASED CRYPTOGRAPHY; TATE PAIRING;

EID: 73849138511     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034881     Document Type: Article
Times cited : (263)

References (29)
  • 3
    • 84937428623 scopus 로고    scopus 로고
    • Efficient algorithms for pairing-based cryptosystems
    • New York: Springer, Lecture Notes in Computer Science
    • P. S. L. M. Barreto, H. Y. Kim, B. Lynn, and M. Scott, "Efficient algorithms for pairing-based cryptosystems," in CRYPTO 2002. New York: Springer, 2002, vol. 2442, Lecture Notes in Computer Science, pp. 354-368.
    • (2002) CRYPTO 2002 , vol.2442 , pp. 354-368
    • Barreto, P.S.L.M.1    Kim, H.Y.2    Lynn, B.3    Scott, M.4
  • 4
    • 33745604534 scopus 로고    scopus 로고
    • Pairing-friendly elliptic curves of prime order
    • New York: Springer, Lecture Notes in Computer Science
    • P. S. L. M. Barreto and M. Naehrig, "Pairing-friendly elliptic curves of prime order," in SAC 2005 - Selected Areas in Cryptography. New York: Springer, 2006, vol. 3897, Lecture Notes in Computer Science, pp. 319-331.
    • (2006) SAC 2005- Selected Areas in Cryptography , vol.3897 , pp. 319-331
    • Barreto, P.S.L.M.1    Naehrig, M.2
  • 5
    • 0031232428 scopus 로고    scopus 로고
    • The Magma algebra system. I. The user language
    • W. Bosma, J. Cannon, and C. Playoust, "The Magma algebra system. I. The user language," J. Symbolic Comput., vol. 24, no. 3-4, pp. 235-265, 1997.
    • (1997) J. Symbolic Comput. , vol.24 , Issue.3-4 , pp. 235-265
    • Bosma, W.1    Cannon, J.2    Playoust, C.3
  • 6
    • 23944463638 scopus 로고    scopus 로고
    • Elliptic curves suitable for pairing based cryptography
    • F. Brezing and A. Weng, "Elliptic curves suitable for pairing based cryptography," Designs, Codes Cryptogr., vol. 37, no. 1, pp. 133-141, 2005.
    • (2005) Designs, Codes Cryptogr. , vol.37 , Issue.1 , pp. 133-141
    • Brezing, F.1    Weng, A.2
  • 7
    • 0345490614 scopus 로고    scopus 로고
    • P - x + d
    • New York: Springer, Lecture Notes in Computer Science
    • P - x + d," in ASIACRYPT 2003. New York: Springer, 2003, vol. 2894, Lecture Notes in Computer Science, pp. 111-123.
    • (2003) ASIACRYPT 2003 , vol.2894 , pp. 111-123
    • Duursma, I.M.1    Lee, H.-S.2
  • 8
    • 33746705572 scopus 로고    scopus 로고
    • Constructing pairing-friendly elliptic curves with embedding degree 10
    • Lecture Notes in Computer Science
    • D. Freeman, "Constructing pairing-friendly elliptic curves with embedding degree 10," in Algorithmic Number Theory Symposium - ANTS-VII, 2006, vol. 4076, Lecture Notes in Computer Science, pp. 452-465.
    • (2006) Algorithmic Number Theory Symposium - ANTS-VII , vol.4076 , pp. 452-465
    • Freeman, D.1
  • 9
    • 40249083661 scopus 로고    scopus 로고
    • A taxonomy of pairing-friendly elliptic curves
    • to be published
    • D. Freeman, M. Scott, and E. Teske, "A taxonomy of pairing-friendly elliptic curves," J. Cryptol., 2009, to be published.
    • (2009) J. Cryptol.
    • Freeman, D.1    Scott, M.2    Teske, E.3
  • 10
    • 84968502759 scopus 로고
    • A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
    • G. Frey and H.-G. Rück, "A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves," Math. Comp., vol. 62, no. 206, pp. 865-874, 1994.
    • (1994) Math. Comp. , vol.62 , Issue.206 , pp. 865-874
    • Frey, G.1    Rück, H.-G.2
  • 11
    • 84946832010 scopus 로고    scopus 로고
    • Supersingular curves in cryptography
    • New York: Springer-Verlag, Lecture Notes in Computer Science
    • S. D. Galbraith, "Supersingular curves in cryptography," in ASI-ACRYPT 2001. New York: Springer-Verlag, 2002, vol. 2248, Lecture Notes in Computer Science, pp. 495-513.
    • (2002) ASI-ACRYPT 2001 , vol.2248 , pp. 495-513
    • Galbraith, S.D.1
  • 12
    • 33746054375 scopus 로고    scopus 로고
    • Pairings
    • Cambridge, U.K.: Cambridge Univ. Press, London Math. Soc. Lecture Note Ser.
    • S. D. Galbraith, "Pairings," in Advances in elliptic curve cryptography. Cambridge, U.K.: Cambridge Univ. Press, 2005, vol. 317, London Math. Soc. Lecture Note Ser., pp. 183-213.
    • (2005) Advances in Elliptic Curve Cryptography , vol.317 , pp. 183-213
    • Galbraith, S.D.1
  • 14
    • 73849141224 scopus 로고    scopus 로고
    • Hyperelliptic pairings
    • New York: Springer-Verlag, Lecture Notes in Computer Science
    • S. D. Galbraith, F. Hess, and F. Vercauteren, "Hyperelliptic pairings," in Pairing 2007. New York: Springer-Verlag, 2007, vol. 2575, Lecture Notes in Computer Science, pp. 108-131.
    • (2007) Pairing 2007 , vol.2575 , pp. 108-131
    • Galbraith, S.D.1    Hess, F.2    Vercauteren, F.3
  • 15
    • 38049150652 scopus 로고    scopus 로고
    • Ate pairing on hyperelliptic curves
    • New York: Springer-Verlag, Lecture Notes in Computer Science
    • R. Granger, F. Hess, R. Oyono, N. Thériault, and F. Vercauteren, "Ate pairing on hyperelliptic curves," in EUROCRYPT 2007. New York: Springer-Verlag, 2007, vol. 4515, Lecture Notes in Computer Science, pp. 430-447.
    • (2007) EUROCRYPT 2007 , vol.4515 , pp. 430-447
    • Granger, R.1    Hess, F.2    Oyono, R.3    Thériault, N.4    Vercauteren, F.5
  • 16
    • 52149117639 scopus 로고    scopus 로고
    • Pairing lattices
    • Springer-Verlag, Lecture Notes in Computer Science
    • F. Hess, "Pairing lattices," in Pairing 2009. : Springer-Verlag, 2009, vol. 5209, Lecture Notes in Computer Science, pp. 18-38.
    • (2009) Pairing 2009 , vol.5209 , pp. 18-38
    • Hess, F.1
  • 19
    • 0343736058 scopus 로고    scopus 로고
    • The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm
    • R. Balasubramanian and N. Koblitz, "The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm," J. Cryptology, vol. 11, no. 2, pp. 141-145, 1998.
    • (1998) J. Cryptology , vol.11 , Issue.2 , pp. 141-145
    • Balasubramanian, R.1    Koblitz, N.2
  • 21
    • 38349033352 scopus 로고    scopus 로고
    • Optimised versions of the Ate and twisted Ate pairings
    • Lecture Notes in Computer Science
    • S. Matsuda, N. Kanayama, F. Hess, and E. Okamoto, "Optimised versions of the Ate and twisted Ate pairings," in Proc. The 11th IMA Int. Conf. Cryptogr. Coding, 2007, vol. 4887, Lecture Notes in Computer Science, pp. 302-312.
    • (2007) Proc. the 11th IMA Int. Conf. Cryptogr. Coding , vol.4887 , pp. 302-312
    • Matsuda, S.1    Kanayama, N.2    Hess, F.3    Okamoto, E.4
  • 23
    • 22144445920 scopus 로고    scopus 로고
    • The Weil pairing, and its efficient calculation
    • V. S. Miller, "The Weil pairing, and its efficient calculation," J. Cryptol., vol. 17, no. 4, pp. 235-261, 2004.
    • (2004) J. Cryptol. , vol.17 , Issue.4 , pp. 235-261
    • Miller, V.S.1
  • 24
    • 0004093370 scopus 로고
    • Leipzig und Berlin: Druck und Verlag von B.G. Teubner
    • H. Minkowski, Geometrie der Zahlen. Leipzig und Berlin: Druck und Verlag von B.G. Teubner, 1910.
    • (1910) Geometrie der Zahlen
    • Minkowski, H.1
  • 25
    • 58349108198 scopus 로고    scopus 로고
    • Rigorous and efficient short lattice vectors enumeration
    • New York: Springer-Verlag, Lecture Notes in Computer Science
    • X. Pujol and D. Stehlé, "Rigorous and efficient short lattice vectors enumeration," in ASIACRYPT 2008. New York: Springer-Verlag, 2008, vol. 5350, Lecture Notes in Computer Science, pp. 390-405.
    • (2008) ASIACRYPT 2008 , vol.5350 , pp. 390-405
    • Pujol, X.1    Stehlé, D.2
  • 26
    • 33646843808 scopus 로고    scopus 로고
    • Faster pairings using an elliptic curve with an efficient endomorphism
    • New York: Springer-Verlag, Lecture Notes in Computer Science
    • M. Scott, "Faster pairings using an elliptic curve with an efficient endomorphism," in INDOCRYPT 2005. New York: Springer-Verlag, 2005, vol. 3797, Lecture Notes in Computer Science, pp. 258-269.
    • (2005) INDOCRYPT 2005 , vol.3797 , pp. 258-269
    • Scott, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.