sample_quiz1_solution

sample_quiz1_solution - Math 187 Prof. Garsia (typed by...

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Math 187 Prof. Garsia (typed by Alex Brik) 04-06-2010 SAMPLE QUIZ 1 solution. 1. Decipher the following message YBQP USUN JIIY UUDS ELEV BYCB EQUP ULSI CJBC SUJY TQXC SBMB UHOI KFEI AYTU JCJC DNXY HCWB JQQS TCTH ENRY SICY INYF BGEL UWEG FFYW QNUX knowing that it is a Vigenere encrypted with a 2-letter key. Solution : Let 1,2,3,. ..,n be an indexing of ciphertext letters. A Vigenere cipher with a 2 letter key will encrypt every letter with index k 1 (mod 2) encrypt every letter with index k 0 (mod 2) using the second letter of the key as follows: for every letter of the alphabet let n ( ) be its index from 0 to 25 so that n ( 0 A 0 ) = 0 , n ( 0 B 0 ) = 1 , n ( 0 C 0 ) = 2 ;:::;n ( 0 Z 0 ) = 25 . For an integer k from 0 to 25 ket alpha ( k ) be the letter of the alphabet so that n ( ) = k . That is alpha (0) = 0 A 0 , alpha (1) = 0 B 0 ;:::;alpha (25) = 0 Z 0 . Let 1 , 2 be two letter key, where 1 , 2 are letters of the alphabet. Then for the letters with index k 1 (mod 2) the encryption will map: 0 A 0 ! 1 , 0 B 0 ! alpha ( n ( 1 ) + 1 (mod 26)) , ± C 0 ! alpha ( n ( 1 ) + 2 (mod 26)) , ... 0 Z 0 ! alpha ( n ( 1 ) + 25 (mod 26)) . For the letters with the index
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sample_quiz1_solution - Math 187 Prof. Garsia (typed by...

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