Representations of divisors on hyperelliptic curves, Gröbner bases and plane curves with quasi-toric relations

2021/02/11 by Ai Takahashi, Takahashi, Ai, Hiro‐o Tokunaga +1 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2102.05794

Abstract

In the study of hyperelliptic curve cryptography, presentations of semi-reduced divisors on a hyperelliptic curve play important roles. In this note, we give an interpretation for such presentations from view points of Gröbner bases. As applications, (i) we give a method to construct weak n-contact curves and (ii) we study plane curves satisfying quasi-toric relations of type (2, n, 2)

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