Abstract
The reduced sum of two divisors is one of the fundamental operations in many problems and applications related to hyperelliptic curves. This paper investigated the operation of the reduced sum of two divisors implemented by M.J. Jacobson et al. That algorithm relied on two pivotal algorithms in terms of continued fraction expansions on the three different possible models of a hyperelliptic curve: imaginary, real, and unusual, and required quadratic cost. By applying Half-GCD algorithm, the pivotal algorithms decreases the time cost. Consequently, the algorithm for computing the reduced sum of two divisors of an arbitrary hyperelliptic curve is accelerated from quadratic to nearly linear time.
Supported by the Foundation of Zhejiang Ocean University (No. 21065013009).
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Ding, X. (2010). Acceleration of Algorithm for the Reduced Sum of Two Divisors of a Hyperelliptic Curve. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16336-4_24
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DOI: https://doi.org/10.1007/978-3-642-16336-4_24
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