Journal of the
Korean Mathematical Society JKMS

We present an explicit Eta pairing approach for computing the Tate 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 $\mathbb F_{2^n}$ 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.

Keywords: Tate pairing, Ate pairing, Eta pairing, hyperelliptic curve, pairing-based cryptosystems

MSC numbers: 11T71, 14G50, 94A60