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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.6 - Problem 17e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.6 - Problem 17e

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# Suppose you have intercepted a ciphertext message and when

ISBN: 9780073383095 37

## Solution for problem 17E Chapter 4.6

Discrete Mathematics and Its Applications | 7th Edition

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Problem 17E

Problem 17E

Suppose you have intercepted a ciphertext message and when you determine the frequencies of letters in this message. you find the frequencies are similar to the frequency of letters in English text. Which type of cipher do you suspect was used?

The Vigenère cipher is a block cipher, with a key that is a string of letters with numerical equivalents k1k2... km, where ki ∈ Z26 for i = 1, 2,…,m. Suppose that the numerical equivalents of the letters of a plaintext block are p1p2…pm. The corresponding numerical ciphertext block is (p1 + k1) mod 26 (p2 + k2) mod 26... (pm + km) mod 26. Finally, we translate back to letters. For example, suppose that the key string is RED, with numerical equivalents 17 4 3. Then, the plaintext ORANGE, with numerical equivalents 14 17 00 13 06 04, is encrypted by first splitting it into two blocks 14 17 00 and 13 06 04. Then, in each block we shift the first letter by 17, the second by 4, and the third by 3. We obtain 5 21 03 and 04 10 07. The ciphcrext is FVDEKH.

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