Citation: | CHEN Shan, ZHANG Xusheng, WANG Kunpeng, et al., “Six Subfamilies of Implementation-Friendly Barreto-Naehrig Curves,” Chinese Journal of Electronics, vol. 23, no. 1, pp. 169-174, 2014, |
D. Boneh, B. Lynn, H. Shacham,"Short signatures from the Weil pairing", ASIACRYPT 2001, Gold Coast, Australia, pp.514-532, 2001.
|
T. Nakanishi, N. Funabiki,"Verifier-Local revocation group signature schemes with backward unlinkability from bilinear maps", ASIACRYPT 2005, Chennai, India, pp.533-548, 2005.
|
A. Joux,"A One Round Protocol for Tripartite Diffie-Hellman", Journal of Cryptology, Vol.17, No.4, pp.263-276, 2004.
|
J. Boxall, N.E. Mrabet, F. Laguillaumie, D.P. Le,"A variant of Miller's formula and algorithm", Pairing 2010, Yamanaka Hot Spring, Japan, pp.417-434, 2010.
|
E. Lee, H. Lee, C. Park,"Efficient and generalized pairing computation on Abelien varieties", IEEE Transactions on Information Theory, Vol.55, No.4, pp.1793-1803, 2009.
|
Y. Nogami, M. Akane, Y. Sakemi, H. Kato, Y. Morikawa,"Integer variable χ-based Ate pairing", Pairing 2008, Egham, UK, pp.178-191, 2008.
|
F. Vercauteren,"Optimal pairings", IEEE Transactions on Information Theory, Vol.56, No.1, pp.455-461, 2010.
|
H. Wang, K.P. Wang, L.J. Zhang, B. Li,"Pairing computation on elliptic curves of Jacobi quartic form", Chinese Journal of Electronics, Vol.20, No.4, pp.655-661, 2011.
|
P.S.L.M. Barreto, M. Naehrig,"Pairing-friendly elliptic curves of prime order", SAC 2005, Waterloo, Ontario, Canada, pp.319-331, 2006.
|
C. Costello, K. Lauter, M. Naehrig,"Attractive subfamilies of BLS curves for implementing high-security pairings", INDOCRYPT 2011, Chennai, India, pp.320-342, 2011.
|
C. Costello, H. Hisil, C. Boyd, J. Nieto, K. Wong,"Faster pairings on special Weierstrass curves", Pairing 2009, Palo Alto, CA, USA, pp.89-101, 2009.
|
D. Freeman, M. Scott, E. Teske,"A Taxonomy of pairingfriendly elliptic curves", Journal of Cryptology, Vol.23, No.2, pp.224-280, 2010.
|
G.C.C.F. Pereira, M.A. Simplício Jr., M. Naehrig, P.S.L.M. Barreto,"A family of implementation-friendly BN elliptic curves", The Journal of Systems and Software, Vol.84, No.8, pp.13191326, 2011.
|
K. Rubin, A. Silverberg,"Choosing the correct elliptic curve in the CMmethod", Mathematics of Computation, Vol.79, No.269, pp.545-561, 2010.
|
P.S.L.M. Barreto, B. Lynn, M. Scott,"Constructing elliptic curves with prescribed embedding degrees", SCN 2002, Amalfi, Italy, pp.257-267, 2003.
|
V. Miller,"The Weil pairing and its efficient calculation", Journal of Cryptology, Vol.17, No.4, pp.235-261, 2004.
|
F. Hess, N. Smart, F. Vercauteren,"The eta pairing revisited", IEEE Transactions on Information Theory, Vol.52, No.10, pp.4595-4602, 2006.
|
N. Benger, M. Scott,"Constructing tower extensions for the implementation of pairing-based cryptography", Arithmetic of Finite Fields-WAIFI 2010, Istanbul, Turkey, pp.180-195, 2010.
|
M. Shirase,"Barreto-Naehrig curve with fixed coefficient", http://eprint.iacr.org/2010/134.pdf, 2011.
|
K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, USA, 1990.
|
J.H. Silverman, The Arithmetic of Elliptic Curves, SpringerVerlag, New York, USA, 1986.
|
D.F. Aranha, K. Karabina, P. Longa, C.H. Gebotys, J. López,"Faster explicit formulas for computing pairings over ordinary curves", EUROCRYPT 2011, Tallinn, Estonia, pp.48-68, 2011.
|