Homomorphic Encryption

This lecture introduces homomorphic encryption, focusing on the Paillier cryptosystem and fully homomorphic encryption. It covers the historical development of homomorphic encryption, from the early challenges in the late 1970s to the recent practical implementations. The lecture explains the concepts of lattice-based cryptography, the Ring Learning with Errors problem, and the security aspects related to error distributions and parameter choices. It also discusses the construction of cryptosystems from R-LWE, with a detailed look at the simplified version of the BGV cryptosystem. The lecture concludes with insights into the correctness and security aspects of the BGV cryptosystem.