Tate pairing computation on the divisors of hyperelliptic curves of genus 2

Abstract

We present an explicit Eta pairing approach for computing the Täte pairing on general divisors of hyperelliptic curves H d of genus 2, where H d : y 2 + y = x 5 + x 3 + d is defined over F 2n with d = 0 or 1. We use the resultant for computing the Eta pairing on general divisors. Our method is very general in the sense that it can be used for general divisors, not only for degenerate divisors. In the pairing-based cryptography, the efficient pairing implementation on general divisors is significantly important because the decryption process definitely requires computing a pairing of general divisors. ©2008 The Korean Mathematical Society.