Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems

In recent papers [4], [9] they worked on hyperelliptic curves Hb defined by y +y = x+x+b over a finite field F2n with b = 0 or 1 for a secure and efficient pairing-based cryptosystems. We find a completely general method for computing the Tate-pairings over divisor class groups of the curves Hb in a very explicit way. In fact, Tate-pairing is defined over the entire divisor class group of a curve, not only over the points on a curve. So far only pointwise approach has been made in [4], [9] for the Tate-pairing computation on the hyperelliptic curves Hb over F2n . Furthermore, we obtain a very efficient algorithm for the Tate pairing computation over divisors by reducing the cost of computing. We also find a necessary condition for hyperelliptic curve to have a significant reduction of the loop cost in the Tate pairing computation. KeywordsTate pairing computation, hyperelliptic curve, cryptosystem, divisors