Homomorphic Encryption: BGV Cryptosystem

This lecture covers the BGV cryptosystem, focusing on security, correctness, encrypted addition, noise growth, and encrypted multiplication. It explains the key generation, encryption, and decryption processes, emphasizing noise management and the challenges of homomorphic operations. The lecture also discusses practical considerations, such as generalized operations, relinearization, and post-quantum resistance. It explores the transition from somewhat to fully homomorphic encryption using bootstrapping and the Lattigo library. Practical implementations of lattice-based cryptosystems and noise management techniques are highlighted, along with references to seminal works in the field.