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quiz4_solution - Quiz 4 solution Math 187 Prof Garsia Alex...

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Quiz 4 solution Math 187, Prof. Garsia Alex Brik UC San Diego May 7, 2010 1. a) Suppose that the plaintext is composed of the columns P 1 , P 2 , ... P n in that order. A permutation a = ( a 1 ; a 2 ; :::; a n ) means that the ciphertext is composed of collumns P a 1 , P a 2 , ... P a n in that order. Given the matrix of statistics M such as that in this problem M ( i; j ) = B indicates that in the plaintext, columns j of ciphertext follows column i of the ciphertext. That is a j = a i + 1 . For the matrix M in this problem we note that M (1 ; 3) = M (2 ; 1) = M (4 ; 2) = M (5 ; 6) = M (6 ; 4) = B with all the other entries equal to s . (Here B means "big" number and s means small number). Hence a 3 = a 1 + 1 , a 1 = a 2 + 1 , a 2 = a 4 + 1 , a 6 = a 5 + 1 , and a 4 = a 6 + 1 . Note that a 3 is the largest number and a 5 is the smallest number. Hence a 5 = 1 and a 3 = 6 . Thus we have a 5 a 6 a 4 a 2 a 1 a 3 1 2 3 4 5 6 Thus it must be that ( a 1 ; a 2 ; a 3 ; a 4 ; a 5 ; a 6 ) = (5 ; 4 ; 6 ; 3 ; 1 ; 2) : Thus the permutation is (5 ; 4 ; 6 ; 3 ; 1 ; 2) b) WEBSTER IS USED TO LOOKUP WORDS IN THE ONLINE COPY OF THE MER- RIAM WEBSTER NINTH COLLEGIATE DICTI 2.
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