Tower Building Technique on Elliptic Curve with Embedding Degree 18

Abstract

Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽 p k with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽 p 2 , 𝔽 p 3, 𝔽 p 6, 𝔽 p 9 and 𝔽 p 18, thus we speed up the computation in optimal ate pairing.