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,
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,

Six Subfamilies of Implementation-Friendly Barreto-Naehrig Curves

Funds:  This work is supported by the National 973 Program of China (No.2011CB302400), the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDA06010701, No.XDA06010702) and Institute of Information Engineering's Research Project on Cryptography (No.Y3Z0023103, No.Y3Z0011102).
  • Received Date: 2013-01-01
  • Rev Recd Date: 2013-02-01
  • Publish Date: 2014-01-05
  • In this paper, we depict in detail six subfamilies of implementation-friendly Barreto-Naehrig (BN) elliptic curves by choosing six special congruency classes of the curve-finding search parameter. These curves have small curve constants, support efficient tower extension options of finite field required in fast pairing implementation and have obvious generators for the bilinear cycle group G1. The detailed description will supply the implementor with more choices of suitable BN curves.
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  • 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",, 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.
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