Fast computation of Tate pairing on general divisors of genus 3 hyperelliptic curves.
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Bibliographic record
Abstract
For the Tate pairing computation over hyperelliptic curves, there are developments by DuursmaLee and Barreto et al., and those computations are focused on degenerate divisors. As divisors are not degenerate form in general, it is necessary to find algorithms on general divisors for the Tate pairing computation. In this paper, we present two e#cient methods for computing the Tate pairing over divisor class groups of the hyperelliptic curves y of genus 3. First, we provide the pointwise method, which is a generalization of the previous developments by Duursma-Lee and Barreto et al. In the second method, we use the resultant for the Tate pairing computation. According to our theoretical analysis of the complexity, the resultant method is 48.5% faster than the pointwise method in the best case and 15.3% faster in the worst case, and our implementation result shows that the resultant method is much faster than the pointwise method. These two methods are completely general in the sense that they work for general divisors with Mumford representation, and they provide very explicit algorithms.
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