Title  Arithmetic on superelliptic curves 
Author(s)  S. D. Galbraith, S. M. Paulus, N. P. Smart 
Type  Article in Journal 
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. 
Length  13 
File 

Language  English 
Journal  Mathematics of Computation 
Volume  71 
Number  237 
Pages  393405 
Year  2002 
Edition  0 
Translation 
No 
Refereed 
No 