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 efficient, we choose to work with extension finite field of the form Fpk 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 Fp2 , Fp3 , Fp6 , Fp9 and Fp18 , thus we speed up the computation in optimal ate pairing.