Elliptic Curves and Lattices

This lecture covers the best known algorithm to solve Elliptic Curve Discrete Logarithm Problem (EC DLP) in prime cases, comparing key sizes with RSA. It also discusses applications like EC Diffie-Hellman key exchange and El Gamal. Furthermore, it delves into lattice-based cryptography, short signature schemes, identity-based encryption, and knowledge protocols. The lecture explores the security aspects based on Elliptic Curve Discrete Logarithm Problem (ECDLP) and touches on various cryptographic schemes like ECDSA. It concludes with a study of computational aspects, including the geometry of numbers and factoring polynomials.