Randomness in Cryptography February 14 , 2013 Lecture 6 : Encryption / Extraction

Let K ∈ {0, 1}n be a key distribution and let K ∈ S, where S is a family of distributions. From now on we call S a source. We want to use K as a secret key for some encryption scheme (Enc,Dec) to encrypt message m ∈ {0, 1}b. We take two approaches. Approach 1: Extract a traditional key R and use R to encrypt. R = Ext(K) where Ext is an extractor for distribution K. For example, if |R| = b set C = m ⊕ R, (One-Time pad). This approach is modular but can possibly be restrictive. Approach 2: Encrypt directly using K and bypass extraction. In particular, can we encrypt better without extraction?