hw6 - CSci 5403, Spring 2010 Homework 6 due: April 15, 2010...

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Unformatted text preview: CSci 5403, Spring 2010 Homework 6 due: April 15, 2010 1. Isomorphic to Nothing? Prove that the interactive proof system for Graph Noniso- morphism given in section 8.3 is honest-verifier perfect zero-knowledge. 2. Predicting versus distinguishing Finish the proof from Lecture 21 that next-bit unpredictability and indistinguishability are equivalent. In particular, let G : { , 1 } * → { , 1 }* be polynomial-time computable, and satisfy | G ( x ) | = ‘ ( | x | ) where ‘ ( n ) > n . (a) Complete the proof that the ability to distinguish G ( U n ) from U ‘ ( n ) with advantage implies the ability to predict some bit of the output of G with advantage at least /‘ : Let B be the distinguisher with advantage , and let i be the index of the hybrid distribution such that Pr[ B ( H i ) = 1]- Pr[ B ( H i +1 ) = 1] ≥ /‘ . Prove that the next-bit predictor given by: predict(x, B): r = [ random.bit() for i in {1, ..., l-(i+1)}] c = B(x+[0]+r) d = B(x+[1]+r) if (c==d): return random.bit()if (c==d): return random....
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This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.

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hw6 - CSci 5403, Spring 2010 Homework 6 due: April 15, 2010...

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