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Fast computation of hyperelliptic curve isogenies in odd characteristic (2009.12180v1)

Published 25 Sep 2020 in math.AG and math.NT

Abstract: Let p be an odd prime number and g $\ge$ 2 be an integer. We present an algorithm for computing explicit rational representations of isogenies between Jacobians of hyperelliptic curves of genus g over an extension K of the field of p-adic numbers Qp. It relies on an efficient resolution, with a logarithmic loss of p-adic precision, of a first order system of differential equations.

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