Compression for trace zero points on twisted Edwards curves

TL;DR

This paper introduces two optimal methods for compressing trace zero points on twisted Edwards curves, providing efficient algorithms and comparing their performance with existing methods on Weierstrass form elliptic curves.

Contribution

It presents novel optimal representations and algorithms for trace zero points on twisted Edwards curves, enhancing compression efficiency.

Findings

Algorithms achieve efficient compression and decompression.

Performance comparisons show advantages over Weierstrass form methods.

New representations optimize storage and transmission of elliptic curve points.

Abstract

We propose two optimal representations for the elements of trace zero subgroups of twisted Edwards curves. For both representations, we provide efficient compression and decompression algorithms. The efficiency of the algorithm is compared with the efficiency of similar algorithms on elliptic curves in Weierstrass form.