Public Key Encryption

In this lecture, we will introduce the notion of Public-Key Encryption. We will define the basic notion of security for this primitive, i.e. Semantic Security. We will discuss an alternative formulation of the semantic security definition that is sometimes more intuitive to work with. Finally, we will give two examples of semantically-secure public-key encryption schemes, namely the El-Gamal Encryption and the Paillier Encryption schemes. Throughout the sequel, we denote the security parameter by λ.