WANG Hong, WANG Kunpeng, ZHANG Lijun, LI Bao. Pairing Computation on Elliptic Curves of Jacobi Quartic Form[J]. Chinese Journal of Electronics, 2011, 20(4): 655-661.
Citation: WANG Hong, WANG Kunpeng, ZHANG Lijun, LI Bao. Pairing Computation on Elliptic Curves of Jacobi Quartic Form[J]. Chinese Journal of Electronics, 2011, 20(4): 655-661.

Pairing Computation on Elliptic Curves of Jacobi Quartic Form

  • Received Date: 2010-10-01
  • Rev Recd Date: 2011-01-01
  • Publish Date: 2011-10-25
  • 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, 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.
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      沈阳化工大学材料科学与工程学院 沈阳 110142

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