Dr. A. Betten
Fall 2006
M360 Mathematics of Information Security
homework sheet # 4
Problem # 1
Check whether the following arguments are logical or not. Explain!
a)
i) If Alice is wrong, then Bill is wrong. If Bill is wrong, then Connie is wrong. Connie
is wrong. Therefore, Alice is wrong.
ii) If turtles can sing, then artichokes can fly. If artichokes can fly, then turtles can
sing and dogs can’t play chess. Dogs can play chess if and only if turtles can sing.
Therefore, turtles can’t sing.
iii) If I oversleep, I will miss the bus. If I miss the bus, I’ll be late for work unless Sue
gives me a ride. If Sue’s car is not working, she won’t give me a ride. If I am late
for work, I’ll lose my job unless the boss is away. Sue’s car is not working. The boss
is not away. Therefore, if I oversleep, I’ll lose my job.
b) And a selection from Lewis Carroll:
i) No ducks waltz. No officers ever decline to waltz. All my poultry are ducks. Therefore, my poultry are not officers.
ii) Everyone who is sane can do Logic. No lunatics are fit to serve on a jury. None of
your sons can do Logic. Therefore, none of your sons are fit to serve on a jury.
iii) The only articles of food, that my doctor allows me, are such as are not very rich.
Nothing that agrees with me is unsuitable for supper. Wedding-cake is always very
rich. My doctor allows me all articles of food that are suitable for supper. Therefore,
wedding-cake always disagrees with me.
iv) Animals, that do not kick, are always unexcitable. Donkeys have no horns. A
buffalo can always toss one over a gate. No animals that kick are easy to swallow.
No hornless animal can toss one over a gate. All animals are excitable, except
buffaloes. Therefore, donkeys are not easy to swallow.
Problem # 2
Decrypt the simple-DES ciphertext
AQMn
using the key 011010011. Use the table below to code symbols to 6-bit integers. Use the simpleDES machines on the attached sheets (note that you have to change something for decryption).
The S-boxes are:
101 010 001 110 011 100 111 000
S1 :
001 100 110 010 000 111 101 011
100 000 110 101 111 001 011 010
S2 :
101 011 000 111 110 010 001 100
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
dec.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
binary
000000
000001
000010
000011
000100
000101
000110
000111
001000
001001
001010
001011
001100
001101
001110
001111
q
r
s
t
u
v
w
x
y
z
’’
0
1
2
3
4
dec.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
binary
010000
010001
010010
010011
010100
010101
010110
010111
011000
011001
011010
011011
011100
011101
011110
011111
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
dec.
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
binary
100000
100001
100010
100011
100100
100101
100110
100111
101000
101001
101010
101011
101100
101101
101110
101111
Q
R
S
T
U
V
W
X
Y
Z
’.’
5
6
7
8
9
dec.
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
binary
110000
110001
110010
110011
110100
110101
110110
110111
111000
111001
111010
111011
111100
111101
111110
111111