Tower Building Technique on Elliptic Curve with Embedding Degree 36

Recent progress on pairing based cryptography was the use of extension of finite fields of the form F p k , and it was a lot secure and efficient when k 12. 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 F p 2 , F p 3 , F p 4 , F p 6 , F p 9 , F p 12 , F p 18 and F p 36 , many paths will be found. Finally we will take the optimal case to improve the computation in optimal ate pairing