A note on pairing computation on Edwards curves

作者：Wu Hongfeng^*; Feng Rongquan

来源：Journal of Information and Computational Science, 2012, 9(15): 4381-4388.

• Edwards curves
• Elliptic curve
• Explicit formula
• Geometric interpretation
• Miller function
• Miller's algorithm
• Tate pairing

Various elliptic curve models reveal different efficiency of pairing computation. This paper proposes new explicit formulas for the doubling and addition steps in Millers algorithm to compute the Tate pairing on Edwards curves. We present the first a simpler geometry approach to explain the group law on Edwards curves. Then we present explicit formulae for the addition step and doubling step in Miller's algorithm to compute Tate pairing on twisted Edwards curves. The approach proposed in this paper is different from the previously proposed ones. This new geometric interpretation on Edwards curves is clear and not complicated comparing to that on cubic curves defined by the chord and tangent rule. This is helpful in further understanding the Tate pairing computation on Edwards curves.

• 出版日期2012