Lecture 1 : Perfect Secrecy and Statistical Authentication

• Definition of perfect secrecy • One-time pad and optimality (Shannon's theorem) • Definition of statistical one-time MAC and construction. Historically, cryptography was treated as a practical problem with practical applications. Many of these schemes were insecure due to a lack of a mathematical foundation combined with no understanding of desirable properties in cryptography systems. However, at the time they were good enough due to the limitations of computational power. Modern cryptography has its foundations in mathematical rigor, with definitions of what it means for schemes to be secure. It is more concerned with elegant constructions and simple to describe systems over contrived protocols. In particular, there is an emphasis on the proofs of security. In this class, our focus will be on modern cryptography and provable security. Consider two persons Alice and Bob, who wish to communicate messages of a sensitive nature. However, an eavesdropper by the name of Eve has the ability to read all the messages that pass between Alice and Bob. Despite this, Alice and Bob would still like to be able to communicate in a way that Eve cannot determine what they are saying to each other. This is done via an encryption scheme, which is a set of functions Enc and Dec for encryption and decryption of messages: plaintext m Alice computes c = Enc(m) ciphertext c Bob computes m = Dec(c) m Eve reads c, should not learn m Lecture 1, Page 1