Lecture 1 : Crypto Overview , Perfect Secrecy , One - time Pad

We overview the aims and the philosophy of modern cryptography. We exemplify this approach with the first shot at a definition of encryption scheme security, which we will develop later on in this class. We then give a classic definition given by Claude Shannon of perfect secrecy for an encryption. We show that various classic ciphers fail to satisfy this definition, but we also show a cipher called One-Time Pad which does satisfy it. However, this cipher has very limited applicability because the communicating parties must share a pre-agreed key which is as long as the message, i.e. as all the communication they will be able to secretly exchange between them. We show, moreover, that this is a fundamental limitation of every perfectly secure cipher. In other words, we show that no perfectly secure cipher can have keys shorter than the message. This motivates the need to relax Shannon’s information-theoretic perfect secrecy requirement on encryption schemes with a computational secrecy property instead. We’ll develop such computational secrecy property in the next lecture.