Tower Building Technique on Elliptic Curve with Embedding Degree 18

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_p² , 𝔽_p³, 𝔽_p⁶, 𝔽_p⁹ and 𝔽_p¹⁸, thus we speed up the computation in optimal ate pairing.