Computing the trace of an algebraic point on an elliptic curve

TL;DR

This paper introduces an efficient algorithm for calculating the sum of algebraic conjugates of a point on an elliptic curve, simplifying a key step in elliptic curve computations.

Contribution

The paper proposes a novel, straightforward algorithm for computing the trace of an algebraic point on an elliptic curve, improving computational efficiency.

Findings

Algorithm is simple and efficient

Reduces computational complexity in elliptic curve operations

Applicable to algebraic points in cryptographic contexts

Abstract

We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.