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 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.

Faster Ate pairing computation on Selmer's model of elliptic curves

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Emmanuel Fouotsa ◽  
Abdoul Aziz Ciss
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Ate Pairing ◽  
Pairing Computation

AbstractThis paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye

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