WSEAS Transactions on Computers
Print ISSN: 1109-2750, E-ISSN: 2224-2872
Volume 21, 2022
Tower Building Technique on Elliptic Curve with Embedding Degree 36
Authors: , ,
Abstract: Recent progress on pairing based cryptography was the use of extension of finite fields of the form $$\mathbb{F}_{p^k}$$, and it was a lot secure and efficient when $$ k\geq12$$. In this paper, we will use the tower building technique to study the case of k=36 to improve arithmetic operation. We will use a degree 2 or 3 twist to carry out most operations in $$\mathbb{F}_{p^2}, \mathbb{F}_{p^3}, \mathbb{F}_{p^4}, \mathbb{F}_{p^6}, \mathbb{F}_{p^9}, \mathbb{F}_{p^{12}}, \mathbb{F}_{p^{18}}$$ and $$ \mathbb{F}_{p^{32}} $$, many paths will be found. Finally we will take the optimal case to improve the computation in optimal ate pairing