An Strong Substitution Box Generated by Point of Order Two on Elliptic Curve Over

https://doi.org/10.5281/zenodo.20340592

Abstract

Algebraic curves play a vital role in modern mathematical and cryptographic systems due to their extensive range of applications, particularly in cryptography. The efficiency and security of contemporary cryptographic algorithms largely stem from their formulation over finite fields. This study presents a novel method for constructing a secure substitution box (S-box) based on the rational points of order two on a supersingular elliptic curve defined over the finite field . Evaluation in accordance with established cryptographic benchmarks demonstrates that the proposed S-box satisfies the essential criteria of robustness and reliability required for secure cryptographic design.

Keywords: Elliptic Curve, Points of order two, Galois Field, Substitution Box and Non-linearity.