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Published bySamir Paddock Modified over 2 years ago

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f(x 1 )h h( x 1 ) 1 … n+|h|+ 1 bits of next-block pseudoentropy f(x 2 )h h( x 2 )f(x t )h h( x t ) g(x t,h t )= g(x 2,h 2 )= g(x 1,h 1 )= G(x 1,h 1 …,x t,h t ) extractors … Next-Block Pseudoentropy ! PRG

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2 Distinguisher for G ) next-bit predictor for G ) (hybrid) next-bit predictor for g ) g does not have high next-bit pseudoentropy Seed length O(n 3 ), but construction is (highly) non-uniform “Entropy equalization” ) uniform construction with seed length O(n 4 )

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Entropy Equalization Task: Given X=(X 1 …X n ) with next-block-entropy k, construct X’ =(X’ 1 …X’ n’ ) for which Y’=(Y’ 1 …Y’ n’ ) with 1. 8 i (X’ 1 …X’ i-1,X’ i ) ≈ C (X’ 1 …X’ i-1,Y’ i ) 2. 8 i H(Y’ i |X’ 1 …X’ i-1 ) = k/n - ± X’ = ( X (1) I, X (1) I+1 … X (1) n, X (2) 1, … X (t) I-n ) and Y’ = ( Y (1) I, Y (1) j+1 … Y (1) n, Y (2) 1, … Y (t) I-n ) 8 i H(Y’ i |X’ 1 …X’ i-1 ) = k/n - k/(t-1)n X (1) 1 X (1) 2 …X (1) n X (1) 1 X (2) 2 …X (2) n … X (t) 1 X (t) n … jn-j

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