Elliptic Curve Cryptography (ECC)
Aiden A. Bruen, Mario Professor Forcinito, James Professor McQuillan · 2021
This chapter presents an overview of elliptic curves as well as some cryptographic and geometric applications. In particular, it presents a detailed derivation of the algebraic formula for addition on the curve based on the geometrical definition. From the point of view of cryptography, the crucial fact is that the points on any elliptic curve actually form an abelian group. The chapter provides a detailed overview of the idea of a nonsingular cubic curve, i.e. an elliptic curve. It briefly describes the brilliant insight due to Frey, which was a major catalyst for the solution to Fermat’s last theorem. The chapter provides a brief discussion of homogeneous coordinates. The unknown identity of the identity point makes the task of an eavesdropper that much more difficult. Also, the computerized attacks are programmed in accordance with the usual version of elliptic curve cryptography.