Fast Arithmetic on Jacobians of Picard Curves

摘要

In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field IF_q of characteristic different from 3. This algorithm has a nice geometric interpretation, comparable to the classic "chord and tangent" law for the elliptic curves. Computational cost for addition is 144M+12SQ+2I and 158M+16SQ+2I for doubling.