A strong framework for creating safe and effective cryptographic systems, elliptic curve cryptography (ECC) is especially useful for digital signature and key exchange protocols. Based on the principles of algebraic geometry and discrete mathematics, ECC requires significantly shorter key lengths while achieving the same level of security as traditional algorithms like RSA, making it ideal for contemporary settings where resource optimization and computational speed are crucial. With a focus on combinatorial logic and discrete structures, this paper explores the mathematical foundations of ECC and highlights how they contribute to its reliability and robustness. In-depth examinations of signature systems like the Elliptic Curve Digital Signature Algorithm (ECDSA) and key exchange strategies like Elliptic Curve Diffie–Hellman (ECDH) are given. In-depth analyses are also conducted of implementation issues, potential attack routes, and the importance of ECC in both present-day and next-generation cryptographic frameworks.