Elliptic Curve Cryptography(ECC): Foundations, Applications, and Quantum Future

This video provide a comprehensive overview of **Elliptic Curve Cryptography (ECC)**, a modern public-key encryption method. It explain that ECC leverages the **Elliptic Curve Discrete Logarithm Problem (ECDLP)** for its security, allowing for **smaller key sizes** and **greater efficiency** compared to traditional algorithms like RSA. The video detail **ECC's mathematical foundations**, including curve definitions and point operations, and illustrate its **widespread applications** in areas like secure web communication (TLS), cryptocurrencies, and mobile devices. Crucially, the sources also discuss **implementation vulnerabilities** and highlight the **existential threat posed by quantum computing** via Shor's algorithm, leading to the necessary development and adoption of **Post-Quantum Cryptography (PQC)** solutions for future security.