Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields

2022/03/02 by Elie Eid, Eid, Elie
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2203.00983

arXiv admin note: substantial text overlap with arXiv:2009.12180

arxiv created 2022/03/02 · arxiv updated 2022/03/03

Abstract

Let p be an odd prime number. We propose an algorithm for computing rational representations of isogenies between Jacobians of hyperelliptic curves via-adic differential equations with a sharp analysis of the loss of precision. Consequently, after having possibly lifted the problem in the p-adics, we derive fast algorithms for computing explicitly Cantor's division polynomials of hyperelliptic curves defined over finite fields.

Citations

• Fast computation of hyperelliptic curve isogenies in odd characteristic

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