Point Decomposition Problem in Binary Elliptic Curves

TL;DR

This paper investigates the point decomposition problem in binary elliptic curves, proposing a modified system of equations that balances polynomial degree reduction with variable increase to improve solution strategies.

Contribution

It introduces a novel modification of the system of equations for PDP in binary elliptic curves, enhancing the approach by balancing polynomial degree and variable count.

Findings

Modified equations reduce polynomial degree

Trade-off improves solution efficiency

Potential impact on elliptic curve cryptography

Abstract

We analyze the point decomposition problem (PDP) in binary elliptic curves. It is known that PDP in an elliptic curve group can be reduced to solving a particular system of multivariate non-linear system of equations derived from the so called Semaev summation polynomials. We modify the underlying system of equations by introducing some auxiliary variables. We argue that the trade-off between lowering the degree of Semaev polynomials and increasing the number of variables is worth.