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ps3 - 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 3 October 13, 2011 Problem Set 3 Due: Wednesday April 20, 2011, in class. Problem 1. [80 points] Let E : { 0 , 1 } k × { 0 , 1 } n → { 0 , 1 } n be a block cipher and let algorithm K return K $ ← { 0 , 1 } k . Assume messages to be encrypted have length ‘ < n . Let E be the following encryption algorithm: algorithm E K ( M ) if | M | 6 = then return // Only encrypts -bit messages R $ ← { 0 , 1 } n - C E K ( R k M ) return C Above, “ x k y ” denotes the concatenation of strings x and y . 1. [10 points] Specify a decryption algorithm D such that SE = ( K , E , D ) is a symmetric encryption scheme providing correct decryption. 2. [30 points] Give the best attack you can on this scheme. Given an even number q , your attack should take the form of an ind-cpa adversary A that makes q oracle queries and has running time around that for O ( q ) applications of E . Specify Adv ind - cpa SE ( A ) as a function of q, n, ‘ . Letting n = 128, make a table showing, for values = 1 , 16 , 32 , 64 ,
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