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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 Fall '10
 GAL
 Cryptography, 11 m, 10 l, 5 g, 9 K, 8 J

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