Fast computation of hyperelliptic curve isogenies in odd characteristic

2020/09/25 by Élie Eid, Eid, Élie · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2009.12180

arxiv created 2020/09/25 · arxiv updated 2020/09/28

Abstract

Let p be an odd prime number and g ≥ 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.

Cited by

• LCM decomposition of linear differential operators in positive characteristic
• Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields

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