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Unformatted text preview: ICS 180: Introduction to Cryptography 5/13/2004 Homework 4 Due Tuesday , 5/20/2004 1 “Onebitstreching” PRG implies “polynomiallystreching” PRG Assume that G is a PRG which stretches input by only one bit, i.e. for all inputs x , the length  G ( x )  , of the output of G on x is equal to  x  + 1. 1.1 For any polynomial p ( · ), use the 1bit stretching PRG G to construct a PRG G ′ which stretches the (random) kbit input into a (pseudorandom) output of length p ( k ). Prove that your construction G ′ is indeed a PRG if G is a PRG. Hint(s) : First try to construct a twobit stretching G ′ , i.e. do it for p ( k ) = k + 2. (Note that in the subsection below you have some wrong ways of making the 2bit stretching PRG. I think that all ways where you try to use G just once will fail, and to get (2+ k )bit output you need to use G twice.) If you do get it for 2bit stretching PRG, chances are that your construction generalizes to any polynomial number of extra bits, and that you can prove this generalized construction using the proof you did for the 2bit case and induction....
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This homework help was uploaded on 01/30/2008 for the course ICS 180 taught by Professor Jarecki during the Spring '04 term at UC Irvine.
 Spring '04
 Jarecki

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