Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors [chapter]

Steven D. Galbraith, Michael Harrison, David J. Mireles Morales
2008 Lecture Notes in Computer Science  
We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P∞ ∈ C and represent divisor classes in the form E − d(P∞) where E is effective and 0 ≤ d ≤ g. We propose a different representation which is balanced at infinity. The resulting arithmetic is more efficient than previous approaches when there are 2 points at infinity. This is the full version of the paper.
doi:10.1007/978-3-540-79456-1_23 fatcat:sa6jkdyfonh3pl5w3a3ntvfita