Paper 2010/475

Pairing Computation on Elliptic Curves of Jacobi Quartic Form

Hong Wang, Kunpeng Wang, Lijun Zhang, and Bao Li


This paper proposes explicit formulae for the addition step and doubling step in Miller's algorithm to compute Tate pairing on Jacobi quartic curves. We present a geometric interpretation of the group law on Jacobi quartic curves, %and our formulae for Miller's %algorithm come from this interpretation. which leads to formulae for Miller's algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully choosing the coefficients, there exist quartic twists of Jacobi quartic curves from which pairing computation can benefit a lot. Finally, we provide some examples of supersingular and ordinary pairing friendly Jacobi quartic curves.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. unpublished
elliptic curvepairinggeometric interpretation
Contact author(s)
hwang @ is ac cn
2010-10-25: revised
2010-09-08: received
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      author = {Hong Wang and Kunpeng Wang and Lijun Zhang and Bao Li},
      title = {Pairing Computation on Elliptic Curves of Jacobi Quartic Form},
      howpublished = {Cryptology ePrint Archive, Paper 2010/475},
      year = {2010},
      note = {\url{}},
      url = {}
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