WANG Bei, OUYANG Yi, HU Honggang. Efficient Pairing Computation on Twisted Weierstrass Curves[J]. Chinese Journal of Electronics, 2018, 27(4): 739-745. doi: 10.1049/cje.2018.05.004
Citation: WANG Bei, OUYANG Yi, HU Honggang. Efficient Pairing Computation on Twisted Weierstrass Curves[J]. Chinese Journal of Electronics, 2018, 27(4): 739-745. doi: 10.1049/cje.2018.05.004

Efficient Pairing Computation on Twisted Weierstrass Curves

doi: 10.1049/cje.2018.05.004
Funds:  This work is supported by the National Key Basic Research Program of China (No.2013CB834202) and the National Natural Science Foundation of China (No.11571328, No.61522210).
  • Received Date: 2016-05-12
  • Rev Recd Date: 2017-09-21
  • Publish Date: 2018-07-10
  • In this paper, we construct the twists of twisted Edwards curves in Weierstrass form. Then we define a new twisted Ate pairing on twisted Weierstrass curves named the Tx-Ate pairing. Following Miller's algorithm, we give a computation of the Tx-Ate pairing on high degree twisted Weierstrass curves, where the point operations are over Edwards form, and the computation of Miller function is over Weierstrass form. Although, in one doubling loop, our method to compute the Tx-Ate pairing is a litter slower than the previously fastest method. By twists, the Tx-Ate pairing can be calculated on more twisted Weierstrass curves with short loop length. The TxAte pairing is even competitive with optimal Ate pairing when they have the same short loop length.
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