Pairings on Hyperelliptic Curves with Considering Recent Progress on the NFS Algorithms

Abstract

In this paper, we analyze and reexamine the key lengths of the pairings on the hyperelliptic curves of genus 2 and considering the estimated run time of the (special) extended tower number field sieve. Pairing-based cryptosystems have become a major research topic in cryptography and have attracted more attention because of the increasing interest in the efficient and functional cryptographic protocols, e.g., functional encryption. Recently, the algorithm of number field sieve and its variants have made progress, and it is urgently necessary to estimate key lengths of pairings taking into account of impact of the algorithms. We report the detailed computational cost of the pairings on the Kawazoe–Takahashi curves of genus 2, and give the comparison of our pairing and the pairing on the BLS24 elliptic curves at the 192-bit security level. The estimated cost of our pairing is approximately 2.5 times more than the cost of the BLS24 pairing.