Tower Building Technique on Elliptic Curve with Embedding Degree 54

Pairing based cryptography is one of the newest security solution that attract a lot of attention, because we can work with efficient and faster pairing to make the security a lot practical, also the working with extension finite field of the form Fpk is more useful and secure with k ≥ 12 the implementation become more important. In this paper, we will presents cases studies of improving pairing arithmetic calculation on curves with embedding degree 54. We use the tower building technique, and study the case when using a degree 3 twist to carry out most operations in Fp3 and Fp6 or Fp9 and Fp18 or Fp27, or when using a degree 2 twist to handle most of the operations in Fp2 and Fp6 and Fp18.