Arithmetic on superelliptic curves

SD Galbraith, S Paulus, NP Smart

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

This paper is concerned with algorithms for computing in the divisor class group of a nonsingular plane curve of the form $y^n = c(x)$ which has only one point at infinity. Divisors are represented as ideals and an ideal reduction algorithm based on lattice reduction is given. We obtain a unique representative for each divisor class and the algorithms for addition and reduction of divisors run in polynomial time. An algorithm is also given for solving the discrete logarithm problem when the curve is defined over a finite field.
Translated title of the contributionArithmetic on superelliptic curves
Original languageEnglish
Pages (from-to)393 - 405
Number of pages12
JournalMathematics of Computation
Volume71 (?)
Publication statusPublished - Jan 2001

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