solution homework 03

# Security in Computing (3rd Edition)

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CS 161 Computer Security Fall 2005 Joseph/Tygar/Vazirani/Wagner HW 3 Solution 1. (5 pts.) Any questions Any constructive response is given full credit. 2. (20 pts.) Zero knowledge (a) Simulator: i. Pick a random R ( mod N ) . ii. Let S = R e ( mod N ) . iii. Output the following transcript: step 1: Bob sends S to Alice step 2: Alice sends R to Bob step 3: Bob accepts The distribution on the output of Simulator is exactly the same as the distribution on the tran- script obtained by running honest-Alice + honest-Bob together. (b) You need to give an example of a dishonest-Bob that cannot be simulated. Here is one example. Suppose Bob always sends the same value 2 to Alice. Alice will respond with 2 d ( mod N ) . Note that this is a value the simulator cannot emulate: the simulator does not know d , and the security of RSA signatures means that the simulator cannot forge a signature on arbitrary messages (i.e., cannot compute 2 d ( mod N ) without knowledge of d ). Consequently, in this example Bob has

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