Generation and Tate Pairing Computation of Ordinary Elliptic Curves with Embedding Degree One

2013 ◽  
pp. 393-403 ◽  
Author(s):  
Zhi Hu ◽  
Lin Wang ◽  
Maozhi Xu ◽  
Guoliang Zhang
Keyword(s):  
Elliptic Curves ◽  
Tate Pairing ◽  
Embedding Degree ◽  
Pairing Computation

An optimal Tate pairing computation using Jacobi quartic elliptic curves

2018 ◽  
Vol 35 (4) ◽  
pp. 1086-1103
Author(s):  
Srinath Doss ◽  
Roselyn Kaondera-Shava
Keyword(s):  
Elliptic Curves ◽  
Tate Pairing ◽  
Pairing Computation

scholarly journals Elliptic Curves with Low Embedding Degree

2006 ◽  
Vol 19 (4) ◽  
pp. 553-562 ◽  
Author(s):  
Florian Luca ◽  
Igor E. Shparlinski
Keyword(s):  
Elliptic Curves ◽  
Embedding Degree

scholarly journals The Pairing Computation on Edwards Curves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfeng Wu ◽  
Liangze Li ◽  
Fan Zhang
Keyword(s):  
Geometric Interpretation ◽  
Tate Pairing ◽  
Quadric Surfaces ◽  
Edwards Curves ◽  
Explicit Formulae ◽  
Pairing Computation ◽  
Twisted Edwards Curves ◽  
Group Law

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.

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