Групова структура точок на еліптичній кривій для криптографічних систем ЕСС

Abstract

The paper analyzes the group structure of points on an elliptic curve, which is a fundamental cornerstone for modern cryptographic algorithms known as ECC (Elliptic Curve Cryptography). The mathematical model of the elliptic curve is considered, including correctness conditions via non-zero discriminant, alongside operational guidelines for point addition forming an algebraic group. For practical demonstration, Python-based software has been developed to visualize the processes of curve interaction, execute necessary computation metrics and verify mathematical properties.