# ss5 - Computer Science and Engineering UCSD CSE 207 Modern...

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Computer Science and Engineering, UCSD Spring 11 CSE 207: Modern Cryptography Instructor: Mihir Bellare Problem Set 5 Solutions May 11, 2011 Problem Set 5 Solutions Problem 1. [50 points] Let G = ( g ) be a cyclic group of order m , and let k = log 2 ( m ) . The group G as well as g,m,k are public and known quantities. Suppose you are given a (possibly randomized) algorithm B such that Adv dl G,g ( B ) 1 / 2. You are also given a positive integer s . We say that an algorithm A improves B if it uses the latter as a subroutine to achieve Adv dl G,g ( A ) 1 2 - s . The running time T A of A should be sT B + O ( skT G ) where T B is the running time of B and T G is the time to do a group operation. 1. [25 points] Consider the following algorithm A : algorithm A ( X ) 01 for i = 1 ,...,s do 02 y i \$ B ( X ) 03 if g y i = X then return y i 04 return Explain why A does not necessarily improve B . Give an example of B such that Adv dl G,g ( A ) 1 / 2. You may assume m is even.

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