sample_quiz1_solution

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

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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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## This note was uploaded on 09/22/2010 for the course MATH MATH187 taught by Professor Math187 during the Spring '10 term at UCSD.

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

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