Scalar multiplication in compressed coordinates in the trace-zero subgroup

Abstract

We consider trace-zero subgroups of elliptic curves over a degree three field extension. The elements of these groups can be represented in compressed coordinates, i.e. via the two coefficients of the line that passes through the point and its two Frobenius conjugates. In this paper we give the first algorithm to compute scalar multiplication in the degree three trace-zero subgroup using these coordinates.