A Smaller Final Exponentiation for Tate and Ate Pairings with Barreto-Naehrig Curve

Abstract

This paper shows an approach for reducing the size of the exponent of final exponentiation with multiplying some extra terms. In the case of Tate and Ate pairings with Barreto-Naehrig curve whose embedding degree is 12, the exponent is reduced to (p4 - p2+ 1)/r, where p is the characteristic of the base field and r is the order of pairing.