sol1 - CS346 Cryptography, Fall 2009 Homework 1, SOLUTIONS...

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CS346 Cryptography, Fall 2009 Homework 1, SOLUTIONS 1. (5 points) Problem 1 (Chapter 2.13) Solution: Antony knows that Caesar used a shift cipher, but he does not know the key. He will not be able to figure out where to meet Caesar. When he tries to decrypt the ciphertext EVIRE with all possible shifts, he will find both the word ARENA (shifting by 4) and the word RIVER (shifting by 13). 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 of two congruences (using the table for the numeric values for the letters): 2 a · 7 + b mod 26 17 b mod 26 This gives away the value of the key: a=9, b=17. Thus, the encryption function is y = 9 x + 17 mod 26, and the corresponding decryption function is x = 3 y + 1 mod 26.
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sol1 - CS346 Cryptography, Fall 2009 Homework 1, SOLUTIONS...

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