On the Final Exponentiation in Tate Pairing Computations

2013 ◽  
Vol 59 (6) ◽  
pp. 4033-4041 ◽  
Author(s):  
Taechan Kim ◽  
Sungwook Kim ◽  
Jung Hee Cheon
Keyword(s):  
Tate Pairing

scholarly journals Faster computation of the Tate pairing

2011 ◽  
Vol 131 (5) ◽  
pp. 842-857 ◽  
Author(s):  
Christophe Arène ◽  
Tanja Lange ◽  
Michael Naehrig ◽  
Christophe Ritzenthaler
Keyword(s):  
Tate Pairing

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.

Improved Implementations of Cryptosystems Based on Tate Pairing

2009 ◽  
pp. 145-151
Author(s):  
Chang-An Zhao ◽  
Dongqing Xie ◽  
Fangguo Zhang ◽  
Chong-Zhi Gao ◽  
Jingwei Zhang
Keyword(s):  
Tate Pairing
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