sol110 - CS346 Cryptography Fall 2010 Homework 1 SOLUTIONS...

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Homework 1 SOLUTIONS 1. (5 points) You are told that the plaintext “ proof ” yields the ciphertext “ QUPRG ”, and you know the cipher used is one of Substitution, Vigen` ere, or Permutation. Which type of cipher was used, and what is the key? Solution: It can’t be a substitution cipher, since the two o’s are enciphered as two diﬀerent letters PR. It can’t be a permutation cipher, because the letters in the ciphertext and plaintext are diﬀerent. The type of cipher used is Vigen` ere. The shift used is (1, 3, 1, 3, 1). So the key is (1, 3) or BD. 2. (5 points) Problem 5 (Chapter 2.13) You should use the following table for the standard numeric values associated with letters of the English alphabet. A 0 N 13 B 1 O 14 C 2 P 15 D 3 Q 16 E 4 R 17 F 5 S 18 G 6 T 19 H 7 U 20 I 8 V 21 J 9 W 22 K 10 X 23 L 11 Y 24 M 12 Z 25 Solution: The encryption function is of the form y = ax + b mod 26. We need to ﬁnd the value of a and b. Knowing that the plaintext starts with “ha”, we get the following system

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sol110 - CS346 Cryptography Fall 2010 Homework 1 SOLUTIONS...

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