Abstract
We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a criterion for PGP to obtain an optimal pairing.
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Acknowledgments
The authors would like to thank the anonymous referees for the helpful comments. Eunjeong Lee was supported by Basic Science Research Program (Grant No. 2011-0022600). Hyang-Sook Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. 2012R1A2A1A03006706).
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Lee, E., Lee, HS. & Park, CM. Polynomial generating pairing and its criterion for optimal pairing. AAECC 25, 227–247 (2014). https://doi.org/10.1007/s00200-014-0225-4
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DOI: https://doi.org/10.1007/s00200-014-0225-4