Galois Fields and Elliptic Curves

This lecture covers the fundamentals of Galois fields and elliptic curves in cryptography. It starts by explaining the construction of Galois fields, focusing on prime fields and binary fields. The lecture then delves into elliptic curves, discussing their group structure, addition operations, and their use in cryptography. The instructor also explains the concept of twists, j-invariants, and the importance of supersingular curves. Various algorithms for factorization, such as Pollard's p-1 and ECM, are presented with examples. The lecture concludes by discussing the hardness of the discrete logarithm problem in elliptic curve cryptography.