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

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 : y² + y = x⁵ + x³ + 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.