A consideration of towering scheme for efficient arithmetic operation over extension field of degree 18

Abstract

Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in Fpi2. Therefore the arithmetic of Fp12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. Fp18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use Fp element to construct irreducible binomial for building tower of extension field up to Fp6, where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using Fp elements in irreducible binomial construction, reduces the number of multiplications in Fp to calculate inversion and multiplication over Fp18, which effects acceleration in total arithmetic operation over Fp18.