Cryptographic Pairings Based on Elliptic Nets

2011 ◽  
pp. 65-78 ◽  
Author(s):  
Naoki Ogura ◽  
Naoki Kanayama ◽  
Shigenori Uchiyama ◽  
Eiji Okamoto
Keyword(s):  
Elliptic Nets

scholarly journals The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

JSIAM Letters ◽  
2016 ◽  
Vol 8 (0) ◽  
pp. 9-12 ◽  
Author(s):  
Hiroshi Onuki ◽  
Tadanori Teruya ◽  
Naoki Kanayama ◽  
Shigenori Uchiyama
Keyword(s):  
Ate Pairing ◽  
Elliptic Nets

Implementing optimized pairings with elliptic nets

2013 ◽  
Vol 57 (5) ◽  
pp. 1-10 ◽  
Author(s):  
ChunMing Tang ◽  
DongMei Ni ◽  
MaoZhi Xu ◽  
BaoAn Guo ◽  
YanFeng Qi
Keyword(s):  
Elliptic Nets

scholarly journals Constructing Scalar Multiplication via Elliptic Net of Rank Two

2018 ◽  
Vol 7 (4.34) ◽  
pp. 403
Author(s):  
Norliana Muslim ◽  
Mohamad Rushdan Md. Said
Keyword(s):  
Scalar Multiplication ◽  
Powerful Method ◽  
Arithmetic Properties ◽  
Initial Values ◽  
Koblitz Curves ◽  
Starting Point ◽  
Division Polynomials ◽  
Rank One ◽  
Elliptic Nets

Elliptic nets are a powerful method for computing cryptographic pairings. The theory of rank one nets relies on the sequences of elliptic divisibility, sets of division polynomials, arithmetic upon Weierstrass curves, as well as double and double-add properties. However, the usage of rank two elliptic nets for computing scalar multiplications in Koblitz curves have yet to be reported. Hence, this study entailed investigations into the generation of point additions and duplication of elliptic net scalar multiplications from two given points on the Koblitz curve. Evidently, the new net had restricted initial values and different arithmetic properties. As such, these findings were a starting point for the generation of higher-ranked elliptic net scalar multiplications with curve transformations. Furthermore, using three distinct points on the Koblitz curves, similar methods can be applied on these curves.  

scholarly journals Elliptic nets and elliptic curves

2011 ◽  
Vol 5 (2) ◽  
pp. 197-229 ◽  
Author(s):  
Katherine Stange
Keyword(s):  
Elliptic Curves ◽  
Elliptic Nets

scholarly journals On symmetries of elliptic nets and valuations of net polynomials

2016 ◽  
Vol 158 ◽  
pp. 185-216 ◽  
Author(s):  
Amir Akbary ◽  
Jeff Bleaney ◽  
Soroosh Yazdani
Keyword(s):  
Elliptic Nets
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