Randomness in Cryptography May 2 , 2013 Lecture 16 : Special Purpose Extractors
نویسنده
چکیده
In previous lectures we defined a randomness extractor as follow, Definition 1 Function Ext : {0, 1}n × {0, 1}d → {0, 1}m is (k, ε)extractor if for any distribution W ∈ {0, 1}n, with H∞(W ) ≥ k SD(Ext(W ; I), Um) ≤ ε. ♦ If (I,Ext(W ; I) ≈ε (I, Um) we say Ext is a strong extractor. We saw that if H = {hi : {0, 1}n → {0, 1}m|∀i ∈ {0, 1}d} is a universal hash family and m ≤ k − 2 log(1/ε) then Ext(X; I) = hI(X) is (k, ε)-strong extractor (LHL). We also saw the LHL is pretty robust. If I has entropy deficiency c then we can extract m = k − c− 2 log(1/ε) bits.
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