Elliptic Curve Cryptography: Galois Fields

This lecture covers the concepts of Galois fields and elliptic curve cryptography. It starts by explaining the properties of finite fields and their cardinality. Then, it delves into the construction of Galois fields and their isomorphism. The lecture also explores the arithmetic operations in elliptic curves, including addition and multiplication. Additionally, it discusses the group structure in elliptic curves and the points of order 2. The lecture concludes with practical examples and tips related to characteristic 2 fields and twist curves. Various cryptographic problems related to RSA security are also addressed, such as RSA decryption, key recovery, and factorization problems.