Elliptic Curve Cryptography: Secure Digital Communication

The goal of this article is to explain the basic operations of elliptic curves in modular arithmetic. Knowing the principles behind elliptic curves is important for understanding the cryptographic security they provide. The widespread use of elliptic curves in cryptocurrencies and devices of the Fourth Industrial Revolution, both defining movements of our day, demonstrates its real-world significance. The target audience is early-year undergraduate students. We include appropriate formulas and figures to present elliptic curves both mathematically and geometrically. We conclude by illustrating elliptic curve applications in cryptography.