# ps4 - Computer Science and Engineering, UCSD Spring 11 CSE...

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Unformatted text preview: Computer Science and Engineering, UCSD Spring 11 CSE 207: Modern Cryptography Instructor: Mihir Bellare Problem Set 4 April 25, 2011 Problem Set 4 Due: Wednesday May 4, 2011, in class. Problem 1. [30 points] Let E : { , 1 } k { , 1 } l { , 1 } l be a block cipher. Let D be the set of all strings whose length is a positive multiple of l . 1. [10 points] Define the hash function H 1 : { , 1 } k D { , 1 } l via the CBC construction, as follows: algorithm H 1 ( K,M ) M [1] M [2] ... M [ n ] M C [0] l For i = 1 ,...,n do C [ i ] E ( K,C [ i 1] M [ i ]) Return C [ n ] Show that H 1 is not collision-resistant. 2. [20 points] Define the hash function H 2 : { , 1 } k D { , 1 } l as follows: algorithm H 2 ( K,M ) M [1] M [2] ... M [ n ] M C [0] l For i = 1 ,...,n do B [ i ] E ( K,C [ i 1] M [ i ]) ; C [ i ] E ( K,B [ i ] M [ i ]) Return C [ n ] Is H 2 collision-resistant? If you say NO, present an attack. If YES, explain your answer, or,collision-resistant?...
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## ps4 - Computer Science and Engineering, UCSD Spring 11 CSE...

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