Welcome to the resource topic for 2009/623
Title:
Universally Constructing 12-th Degree Extension Field for Ate Pairing
Authors: Masaaki Shirase
Abstract:We need to perform arithmetic in \Fpt to use Ate pairing on a Barreto-Naehrig (BN) curve, where p(z) is a prime given by p(z)=36z^4+36z^3+24z^2+6z+1 with an integer z. In many implementations of Ate pairing, \Fpt has been regarded as the 6-th extension of \Fpp, and it has been constructed as \Fpt=\Fpp[v]/(v^6-\xi) for an element \xi\in \Fpp such that v^6-\xi is irreducible in \Fpp[v]. Such \xi depends on the value of p(z), and we may use mathematic software to find \xi. This paper shows that when z \equiv 7,11 \pmod{12} we can universally construct \Fpp as \Fpt=\Fpp[v]/(v^6-u-1), where \Fpp=\Fp[u]/(u^2+1).
ePrint: https://eprint.iacr.org/2009/623
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .