Scalar multiplication in compressed coordinates in the trace-zero subgroup

TL;DR

This paper introduces the first algorithm for scalar multiplication in the trace-zero subgroup of elliptic curves over degree three field extensions, utilizing compressed coordinates based on line coefficients.

Contribution

It presents a novel algorithm for scalar multiplication in trace-zero subgroups using compressed coordinates, improving efficiency in elliptic curve cryptography.

Findings

First algorithm for scalar multiplication in this setting

Uses line coefficients for compressed coordinates

Enhances cryptographic computation efficiency

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.