A Construction of a Twisted Ate Pairing on a Family of Kawazoe-Takahashi Curves at 192-bit Security Level and Its Cost Estimate

摘要

Recently, there were major breakthroughs in computing DL in finite fields of small characteristics, as a result the symmetric pairings which is defined by using such finite fields became unsuitable for cryptography. This research aims to reveal a more efficient construction of pairings on hyperelliptic curves of genus 2, in the beginning, we focus on the ordinary genus 2 curves and the optimal pairing algorithms at high (192-bit) security level on such curves. In this paper, we show the method to construct optimal pairings over the family of pairing-friendly curves of genus 2 by Kawazoe and Takahashi and offered a twisted version of Ate pairing. We then provide the cost estimates to compare with the result of the pairings on elliptic curve at same security level.