1. Asymmetric Encryption and Message Authentication:

a) The primitive root of a prime number is the basic principle of Diffie-Hellman.

i) Is 3 the primitive root of 11? Show the proof with your calculation.

ii) What are the important criteria for selecting a prime number in cryptography? Is 11 a good choice for such a purpose?

b) Find the parameters stated using the Diffie-Hellman methods, given the user A and B shared a prime number and its primitive root of 23 and 5, respectively.

i) If user A public key value is 8, find the A’s private key.

ii) If user B public key value is 19, what is the common secret key?

c) In the following scenario, we will compare the security services that are given by digital signatures (DS) and message authentication codes (MAC). We assume that James can read all messages send from Chan to Badrul and the other way around, too. James has no knowledge of any keys but the public one in the case of DS. State whether and how (i) DS and (ii) MAC protect against each attack. The value auth(x) is calculated with DS and MAC’s algorithm, correspondingly.

i) (Message integrity) Chan sends a message x = “Transfer RM200 to Darren” in the clear and also sends auth(x) to Badrul. James intercepts the message and replaces “Darren” with “James”. Will badrul detect this?.

ii) (Replay) Chan sends a message x = “Transfer RM200 to James” in the clear and also sends auth(x) to Badrul. James observes the message and signature and sends them 100 times to Badrul. Will Badrul detect this?

iii) (Sender Authentication with the cheating third party) James claims that he sent some message x with a valid auth(x) to Badrul, but Chan claims the same. Can Badrul clear the question in either case?

iv) (Authentication with Badrul cheating) Badrul claims that he received a message x with a valid signature auth(x) from Chan (e.g., “Transfer RM200 from Chan to Badrul”) but Chan claims she has never sent it. Can Chan clear this question in either case?
Transcribed Image Text:ASCII Table Char Oct Hex | Char Dec Oct Hex | Char Dec Dec Oct Нех Ox20 | @ Ox21 | A Ox22 | B Ох23 | С Ox24 | D Ох25 | E 0046 Ox26 | E Ox27 | G Ох28 | Н Ох29 | 1 Ox2a i J Ox2b | K Ох2с | L Ox2d | M Ox2e | N Ox2f | 0 Ох30 | P Ox31 | Q Ox32 | R Ox33 i s Ох34 | T Ox35 | U Ox36 | v Ox37 | W Ох38 | X Ox39 | Y ОхЗа | Z Ox3b Ох3с | Ox3d | ] Ox3e | Ox3f | Ox40 | Ox41 | a Ox42 | b Ox43 | C Ox44 | d Ox45 | e Ox46 | f Ox47 | g Ox48 | h Ох49 | i Ox4a | j Ox4b | k Ox4c || Ox4d | m Ox4e | n Ox4f | o Ox50 | p Ох51 | q Ox52 |r Ox53 | s Ox54 it Ox55 | u Ox56 | v Ox57 | w Ox58 | x Ox59 | y Ох5а | z Ox5b | { Ox5c || Ox5d | } Ox5e | Ox5f (sp) 32 0040 64 0100 96 0140 0141 0142 0143 0144 0145 0146 0147 Ox60 Ох61 Ox62 Ох63 Ох64 Ox65 Ох66 Ох67 Ох68 Ox69 Охба Ox6b 33 34 35 36 37 38 39 0041 0042 0043 0044 0045 65 66 67 68 69 70 71 0101 0102 0103 0104 0105 0106 0107 97 98 99 100 101 102 103 #3 & 0047 40 41 42 43 44 45 46 47 0050 0051 0052 0053 0054 0055 0056 0057 72 73 74 75 76 77 78 79 0110 0111 0112 0113 0114 0115 0116 104 105 106 107 108 109 110 111 0150 0151 0152 0153 0154 0155 0156 0157 Охбс Ox6d Охбе 0117 Ox6f 48 49 50 51 52 53 54 55 0060 0061 0062 0063 0064 0065 0066 0067 80 81 82 83 84 85 86 87 0160 0161 0162 0163 0164 0165 0166 0167 0120 0121 0122 0123 0124 0125 0126 0127 0130 0131 0132 0133 0134 0135 0136 0137 112 113 114 115 116 117 118 119 Ox70 071 Ox72 Ox73 Ox74 Ox75 Ox76 Ox77 1 4 6. 56 57 58 59 60 61 62 63 0070 0071 0072 0073 0074 0075 0076 88 89 90 91 92 93 94 95 0170 0171 0172 0173 0174 0175 0176 120 121 122 123 124 125 126 Ox78 Ox79 Ox7a Ox7b Ox7c Ox7d Ox7e > 0077

Question

1. Asymmetric Encryption and Message Authentication:

a) The primitive root of a prime number is the basic principle of Diffie-Hellman.

i) Is 3 the primitive root of 11? Show the proof with your calculation.

ii) What are the important criteria for selecting a prime number in cryptography? Is 11 a good choice for such a purpose?

b) Find the parameters stated using the Diffie-Hellman methods, given the user A and B shared a prime number and its primitive root of 23 and 5, respectively.

i) If user A public key value is 8, find the A’s private key.

ii) If user B public key value is 19, what is the common secret key?

c) In the following scenario, we will compare the security services that are given by digital signatures (DS) and message authentication codes (MAC). We assume that James can read all messages send from Chan to Badrul and the other way around, too. James has no knowledge of any keys but the public one in the case of DS. State whether and how (i) DS and (ii) MAC protect against each attack. The value auth(x) is calculated with DS and MAC’s algorithm, correspondingly.

i) (Message integrity) Chan sends a message x = “Transfer RM200 to Darren” in the clear and also sends auth(x) to Badrul. James intercepts the message and replaces “Darren” with “James”. Will badrul detect this?.

ii) (Replay) Chan sends a message x = “Transfer RM200 to James” in the clear and also sends auth(x) to Badrul. James observes the message and signature and sends them 100 times to Badrul. Will Badrul detect this?

iii) (Sender Authentication with the cheating third party) James claims that he sent some message x with a valid auth(x) to Badrul, but Chan claims the same. Can Badrul clear the question in either case?

iv) (Authentication with Badrul cheating) Badrul claims that he received a message x with a valid signature auth(x) from Chan (e.g., “Transfer RM200 from Chan to Badrul”) but Chan claims she has never sent it. Can Chan clear this question in either case?

ASCII Table
Char
Oct
Hex | Char
Dec
Oct
Hex | Char
Dec
Dec
Oct
Нех
Ox20 | @
Ox21 | A
Ox22 | B
Ох23 | С
Ox24 | D
Ох25 | E
0046 Ox26 | E
Ox27 | G
Ох28 | Н
Ох29 | 1
Ox2a i J
Ox2b | K
Ох2с | L
Ox2d | M
Ox2e | N
Ox2f | 0
Ох30 | P
Ox31 | Q
Ox32 | R
Ox33 i s
Ох34 | T
Ox35 | U
Ox36 | v
Ox37 | W
Ох38 | X
Ox39 | Y
ОхЗа | Z
Ox3b
Ох3с |
Ox3d | ]
Ox3e |
Ox3f |
Ox40 |
Ox41 | a
Ox42 | b
Ox43 | C
Ox44 | d
Ox45 | e
Ox46 | f
Ox47 | g
Ox48 | h
Ох49 | i
Ox4a | j
Ox4b | k
Ox4c ||
Ox4d | m
Ox4e | n
Ox4f | o
Ox50 | p
Ох51 | q
Ox52 |r
Ox53 | s
Ox54 it
Ox55 | u
Ox56 | v
Ox57 | w
Ox58 | x
Ox59 | y
Ох5а | z
Ox5b | {
Ox5c ||
Ox5d | }
Ox5e |
Ox5f
(sp)
32
0040
64
0100
96
0140
0141
0142
0143
0144
0145
0146
0147
Ox60
Ох61
Ox62
Ох63
Ох64
Ox65
Ох66
Ох67
Ох68
Ox69
Охба
Ox6b
33
34
35
36
37
38
39
0041
0042
0043
0044
0045
65
66
67
68
69
70
71
0101
0102
0103
0104
0105
0106
0107
97
98
99
100
101
102
103
#3
&
0047
40
41
42
43
44
45
46
47
0050
0051
0052
0053
0054
0055
0056
0057
72
73
74
75
76
77
78
79
0110
0111
0112
0113
0114
0115
0116
104
105
106
107
108
109
110
111
0150
0151
0152
0153
0154
0155
0156
0157
Охбс
Ox6d
Охбе
0117
Ox6f
48
49
50
51
52
53
54
55
0060
0061
0062
0063
0064
0065
0066
0067
80
81
82
83
84
85
86
87
0160
0161
0162
0163
0164
0165
0166
0167
0120
0121
0122
0123
0124
0125
0126
0127
0130
0131
0132
0133
0134
0135
0136
0137
112
113
114
115
116
117
118
119
Ox70
071
Ox72
Ox73
Ox74
Ox75
Ox76
Ox77
1
4
6.
56
57
58
59
60
61
62
63
0070
0071
0072
0073
0074
0075
0076
88
89
90
91
92
93
94
95
0170
0171
0172
0173
0174
0175
0176
120
121
122
123
124
125
126
Ox78
Ox79
Ox7a
Ox7b
Ox7c
Ox7d
Ox7e
>
0077

Accepted Answer

To check 3 the primitive root of 11 , we  simply compute the first φ(11) = 10 powersof each unit…