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# hw1 - (b Write the formula used by the Beaufort cipher to...

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CS 555, Spring, 2010, Homework 1 Due: February 3, 2010, 9:30 AM. 1. Let the 26 letters have the numerical values A = 0, B = 1, . . . , Z = 25. Write plaintext as M = m 0 m 1 . . . and ciphertext as C = c 0 c 1 . . . , where the m i and c i are letters of the alphabet. Recall that the Vigen` ere cipher (after Blaise de Vigen` ere, but invented earlier by Giovan Battista Bellaso) with key word K = k 0 k 1 . . . k t - 1 enciphers m i as c i = ( m i + k ( i mod t ) ) mod 26 and deciphers c i as m i = ( c i - k ( i mod t ) ) mod 26. The Beaufort cipher (after English Admiral Sir Francis Beaufort, but invented earlier by Giovanni Sestri) is similar to the Vigen` ere cipher in that it has a key word of length t letters. The Beaufort cipher enciphers the i -th plaintext letter m i as c i = ( k ( i mod t ) - m i ) mod 26. (a) Encipher the plaintext ATTACKATDAWN using the Beaufort cipher with key word KEY.
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Unformatted text preview: (b) Write the formula used by the Beaufort cipher to decipher the i-th ci-phertext letter c i . (c) Explain why Kasiski’s method works to ±nd the length t of the key word for Beaufort just as it does for Vigen` ere. (d) Explain why the Index of Coincidence method works to ±nd the length t of the key word for Beaufort just as it does for Vigen` ere. 2. Suppose a Kasiski analysis identi±es these six pairs of repeated sequences in the ciphertext of a Vigen` ere cipher: Location of start of ±rst occurrence 10 21 37 49 58 72 second occurrence 34 65 109 105 162 132 What can you conclude about the length t of the key word used to encrypt the message? Explain your answer. 1...
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