참고문헌
- A. Menezes, T. Okamoto, and S. Vanstone, "Reducing elliptic curve logarithms to logarithms in a finite field," IEEE Trans. Inform. Theory, vol. 39, no. 5, pp. 1639-1646, Sep. 1993. https://doi.org/10.1109/18.259647
- G. Frey and H.G. Rück, "A remark concening m-divisibility and the discrete logarithm in the divisor class group of curves," Math. Comput., vol. 62, no. 206, pp. 865-874, Apr. 1994.
- D. Boneh and M. Franklin, "Identity based encryption from the weil pairing," SIAM J. on Computing, vol. 32, no. 3, pp. 586-615, Mar. 2003. https://doi.org/10.1137/S0097539701398521
- R. Sakai and M. Kasahara, "ID based cryptosystems with pairing on elliptic curve," IACR ePrint 2003-054, Mar. 2003.
- J.C. Cha and J.H. Cheon, "An Indentity-Based Signature from Gap Diffie-Hellman Groups," PKC 2003, LNCS 2567, pp. 18-30, 2003.
- F. Hess, "Exponent group signature schemes and efficient identity based signature schems based on pairing," SAC 2002, LNCS 2595, pp. 310-324, 2002.
- K.G. Paterson, "ID-based signature from pairings on elliptic curves," Electronics Letters, vol. 38, no. 18, pp. 1025-1026, Aug. 2002. https://doi.org/10.1049/el:20020682
- A. Joux, "A One Round Protocol for Tripartite Diffie-Hellman," Journal of Cryptology, vol. 17, no. 4, pp. 263-276, Sep. 2004.
- D. Boneh, B. Lynn, and H. Shacham, "Short Signatures from the Weil Pairing," Journal of Cryptology, vol. 17, no. 4, pp. 297-319, Sep. 2004.
- N.P. Smart, "An identity based authentication key agreement protocol based on pairing," Electronics Letters, vol. 38, no. 13, pp. 630-632, June 2002. https://doi.org/10.1049/el:20020387
- P.S.L.M. Barreto, H.Y. Kim, B. Lynn, and M. Scott, "Efficient algorithms for pairing-based cryptosystems," CRYPTO 2002, LNCS 2442, pp.354-368, 2002.
- S.D. Galbraith, K. Harrison, and D. Soldera, "Implementing the Tate pairing," ANTS V, LNCS 2369, pp. 324-337, 2002.
- V. Miller, "Short Programs for Functions on Curves," unpublished manuscript, 1986.
-
I. Duursma and H.S. Lee, "Tate pairing implementation for hyperelliptic curves
$y^2=x^p-x+d$ ," Asiacrypt 2003, LNCS 2894, pp. 111-123, 2003. - S. Kwon, "Efficient Tate Pairing Computation for Elliptic Curves over Binary Fields," ACISP 2005, LNCS 3574, pp. 134-145, 2005.
- P.S.L.M. Barreto, S. Galbraith, C. O hEigeartaigh, and M. Scott, "Efficient Pairing Computation on Supersingular Abelian Varieties," IACR ePrint 2004-375, Sep. 2005.
- F. Hess, N. Smart, and F. Vercauteren, "The eta pairing revisited," IEEE Transactions on Information Theory, vol. 52, no. 10, pp. 4595-4602, Oct. 2006. https://doi.org/10.1109/TIT.2006.881709
- C. Shu, S. Kwon, and K. Gaj, "FPGA accelerated Tate pairing based cryptosystem over binary fields," Proceedings of the 2006 IEEE International Conference on Field Programmable Technology, pp. 173-180, Dec. 2006.
-
M. Keller, T. Kerins, F. Crowe, and W.P. Marnane, "FPGA implementation of a
$GH(2^m)$ Tate pairing architecture," In K. Bertels, J.M.P. Cardoso, and S. Vassiliadis, editors, International Workshop on Applied Reconfigurable Computing (ARC 2006), number 3985 in Lecture Notes in Computer Science, pp. 358–369, Mar. 2006. -
R. Ronan, C. Murphy, T. Kerins, C. O hEigeartaigh, and P.S.L.M. Barreto, "A flexible processor for the characteristic
$3\;{\eta}_T$ pairing," International Journal of High Performance Systems Architecture, vol. 1, no. 2, pp. 79–88, Oct. 2007. https://doi.org/10.1504/IJHPSA.2007.015393 - R. Ronan, C. O hEigeartaigh, C. Murphy, M. Scott, and T. Kerins, "FPGA acceleration of the Tate pairing in characteristic 2," Proceedings of the 2006 IEEE International Conference on Field Programmable Technology, pp. 213–220, Dec. 2006.
- J. Jiang, "Bilinear pairing (Eta T Pairing) IP core," City University of Hong Kong – Department of Computer Science, May 2007.
- D.H. Choi, D.G. Han, and H.W. Kim, "Construction of Efficient and Secure Pairing Algorithm and Its Application," Journal of Communications and Networks, vol. 10, no. 5, pp. 437-443, Dec. 2008. https://doi.org/10.1109/JCN.2008.6389860
- K. Fong, D. Hankerson, J. Lopez, and A. Menezes, "Field inversion and point halving revisited," CORR 2003-18, University of Waterloo, 2002.
- D. Hankerson, J.L. Hernandez, and A. Menezes, "Software Implementation of Elliptic Curve Cryptography Over Binary Fields," CHES 2000, LNCS 1965, pp. 1-24, 2000.