Lecture 4 : Leftover Hash Lemma and One Way Functions
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چکیده
We recall some definitions and a claim proved in our previous lecture. These will be required to finish the proof for the Leftover Hash Lemma. Definition 1 H∞(X) = − log (maxx Pr [X = x]) ♦ Definition 2 A function Ext : U × S → V is a (k, ε) extractor if for all random variables X with H∞(X) ≥ k, we have: SD [(S,Ext(X,S)) , (S, V )] ≤ ε where S is uniformly distributed over S and V is uniformly distributed over V. ♦ Definition 3 A function H : U × S → V is a universal hash function if ∀x 6= x′ ∈ U :
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تاریخ انتشار 2015