Elliptic Curve Cryptography: Basics and Applications

This lecture covers the fundamentals of elliptic curve cryptography, including the use of elliptic curves, elliptic curve cryptography, and pairing-based cryptography. It delves into the ECM factorization algorithm, standard curves, manipulating elliptic curves in practice, domain parameters, NIST standard curves, and other standards. The lecture also explores practical examples such as secp192r1 and sect163r2, as well as real-world applications like secp256r1 in Swiss biometric passports and Curve25519 in various technologies. Additionally, it discusses key concepts like ECDH, ECDSA, and ECIES, along with common protocols and activities related to elliptic curve cryptography.