Explicit endomorphism of the Jacobian of a hyperelliptic function field\n of genus 2 using base field operations

2014/05/22 by Eduardo Ruíz Duarte, Duarte, Eduardo Ruiz, Octavio Páez Osuna +1
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1405.5755

openalex publication_date 2014/05/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We present an efficient endomorphism for the Jacobian of a curve C of genus\n2 (hyperelliptic) for divisors having a Non disjoint support. This extends the\nwork of Costello and Lauter in [12] who calculated explicit formulae for\ndivisor doubling and addition of divisors with disjoint support in\n mathbbJ(C) using only base field operations. Explicit formulae is\npresented for this third case and a slightly different approach for divisor\ndoubling.\n

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