Introduction to Elliptic Curves

This lecture introduces the concept of elliptic curves, focusing on their properties and applications in cryptography. The instructor explains how elliptic curves are used in index calculus and other special attacks on the discrete logarithm problem. The lecture covers the motivation behind studying elliptic curves, their shorter computation times compared to other methods, and their significance in public key cryptography. Various topics such as Weierstrass equations, Abel-Jacobi theorem, Mordell's theorem, and Frey curves are discussed in detail.