A Reconfigurable Implementation of the Tate Pairing Computation over GF(2 m )

2010 ◽  
pp. 80-91 ◽  
Author(s):  
Weibo Pan ◽  
William Marnane
Keyword(s):  
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.

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

New formulae for Tate pairing computation on Weierstrass curves

2013 ◽  
Vol 20 (3) ◽  
pp. 85-89
Author(s):  
Hong WANG ◽  
Kun-peng WANG ◽  
Jun-de SONG
Keyword(s):  
Tate Pairing ◽  
Pairing Computation

Memory-saving computation of the pairing final exponentiation on BN curves

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Sylvain Duquesne ◽  
Loubna Ghammam
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Multiplicative Group ◽  
Field Extension ◽  
Second Step ◽  
Tate Pairing ◽  
Important Constraint ◽  
Memory Resources ◽  
Pairing Based Cryptography ◽  
Pairing Computation

AbstractTate pairing computation is made of two steps. The first one, the Miller loop, is an exponentiation in the group of points of an elliptic curve. The second one, the final exponentiation, is an exponentiation in the multiplicative group of a large finite field extension. In this paper, we describe and improve efficient methods for computing the hardest part of this second step for the most popular curves in pairing-based cryptography, namely Barreto–Naehrig curves. We present the methods given in the literature and their complexities. However, the necessary memory resources are not always given whereas it is an important constraint in restricted environments for practical implementations. Therefore, we determine the memory resources required by these known methods and we present new variants which require less memory resources (up to 37 %). Moreover, some of these new variants are providing algorithms which are also more efficient than the original ones.

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