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CIS 3362 Exam #1 – Classical Encryption Schemes
Solution
Date: 9/22/08
1)
(10 pts) Encrypt "KNIGHTS" using the affine cipher with the encryption function f(x)
= (11x + 6)%26.
f(10) = 11(10) + 6 = 116 % 26 = 12 (M)
f(13) = 11(13) + 6 = 149 % 26 = 19 (T)
f(8)
= 11(8)
+ 6 = 94 % 26 = 16 (Q)
f(6)
= 11(6)
+ 6 = 72 % 26 = 20 (U)
f(7)
= 11(7)
+ 6 = 83 % 26 = 5 (F)
f(19) = 11(19) + 6 = 215 % 26 = 7 (H)
f(18) = 11(18) + 6 = 204 % 26 == 22 (W)
Answer = MTQUFHW (1 pt for each letter, 3 pts bonus for getting 5 or more)
2)
(10 pts) Determine the corresponding decryption function for the encryption function
given in question #1.
x = 11y + 6 mod 26 (2 pts)
x – 6 = 11y mod 26 (2 pts)
19(x – 6) = 19(11y) mod 26 (2 pts)
y = 19x – 114 (mod 26) (2 pts)
y = 19x + 16 (mod 26) (2 pts)
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View Full Document3)
(15 pts) Determine the value of 46
1
mod 87.
87 = 1 x 46 + 41
46 = 1 x 41 +
5
41 = 8 x 5
+
1 (3 pts)
41 – 8 x 5 = 1
41 – 8(46 – 41) = 1
41 – 8 x 46 + 8 x 41 = 1
9 x 41 – 8 x 46 = 1 (5 pts)
9(87 – 46) – 8 x 46 = 1
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 Fall '08
 Staff
 Information Security

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