# sol4 - CS346 Cryptography, Fall 2009 Homework 4, SOLUTIONS...

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CS346 Cryptography, Fall 2009 Homework 4, SOLUTIONS 1. (5 points) Problem 4 (Chapter 8.8) Solution: In this case, the number of possible values of the “hash function” is 12. Using the formula we have seen in class, the probability that no two have birthdays in the same month is (1 - 1 12 )(1 - 2 12 )(1 - 3 12 ) = 165 288 which is about 0.573. 2. (10 points) Problem 10 (Chapter 8.8) Solution: It is easy to construct strings that map to any given value, you just have to maintain the parity of the corresponding bits in the blocks. For example, for part A, the hash value will always be equal to the string in the ﬁrst block if all other blocks contain only zeros. You can get any other speciﬁc image by changing the second block. For part B, the same idea works, taking into account the rotations. 3. (10 points) Using the Diﬃe-Lamport signature scheme (see class notes) with encryption e ( x,K ) = x K mod n , Alice chooses in advance the four keys a 1 = 2 ,a 2 = 5 ,b 1 = 7 ,b 2 = 3 . A. If

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## This note was uploaded on 10/07/2010 for the course C S 52475 taught by Professor Gal during the Fall '10 term at University of Texas at Austin.

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sol4 - CS346 Cryptography, Fall 2009 Homework 4, SOLUTIONS...

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