1. Describe how to generate the pair of public key and private key in RSA algori
ID: 3874972 • Letter: 1
Question
1. Describe how to generate the pair of public key and private key in RSA algorithm?
2. Find the multiplicative inverse of 45 mod 238.
3. Let p = 7, q = 11, e = 13, and M = 5 (M: message). Show details of the following. a. What is the private key d ? b. Perform RSA encryption and decryption on the message M.
4. Suppose (e, n) is the receivers public key and M is the message needed to be encrypted by the sender. Why do we have this constraint M < n? (If we remove this constraint, what happens?)
Explanation / Answer
*) Public key generation:-
n=p*q.
Consider an ex:- Lets choose two primes:p=11 andq=13. Hence the modulus is
n=p*q =143, and (p-1)(q-1)=120 ,so choose e=7 greater than 1.
Public key(143,7).
*) Private key generation:-
n=p*q.
Consider an ex:- Lets choose two primes:p=11 andq=13. Hence the modulus is
n=p*q =143, and (p-1)(q-1)=120 ,so choose e=7 greater than 1.
d=inverse mod of 7 with 120=103.
private key(143,103)
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2) Find the multiplicative inverse of 45 mod 238
ans) Inverse of 45 mod 238=201
Val (val * n) mod m
1 45
2 90
3 135
4 180
5 225
6 32
7 77
8 122
9 167
10 212
11 19
12 64
13 109
14 154
15 199
16 6
17 51
18 96
19 141
20 186
21 231
22 38
23 83
24 128
25 173
26 218
27 25
28 70
29 115
30 160
31 205
32 12
33 57
34 102
35 147
36 192
37 237
38 44
39 89
40 134
41 179
42 224
43 31
44 76
45 121
46 166
47 211
48 18
49 63
50 108
51 153
52 198
53 5
54 50
55 95
56 140
57 185
58 230
59 37
60 82
61 127
62 172
63 217
64 24
65 69
66 114
67 159
68 204
69 11
70 56
71 101
72 146
73 191
74 236
75 43
76 88
77 133
78 178
79 223
80 30
81 75
82 120
83 165
84 210
85 17
86 62
87 107
88 152
89 197
90 4
91 49
92 94
93 139
94 184
95 229
96 36
97 81
98 126
99 171
100 216
101 23
102 68
103 113
104 158
105 203
106 10
107 55
108 100
109 145
110 190
111 235
112 42
113 87
114 132
115 177
116 222
117 29
118 74
119 119
120 164
121 209
122 16
123 61
124 106
125 151
126 196
127 3
128 48
129 93
130 138
131 183
132 228
133 35
134 80
135 125
136 170
137 215
138 22
139 67
140 112
141 157
142 202
143 9
144 54
145 99
146 144
147 189
148 234
149 41
150 86
151 131
152 176
153 221
154 28
155 73
156 118
157 163
158 208
159 15
160 60
161 105
162 150
163 195
164 2
165 47
166 92
167 137
168 182
169 227
170 34
171 79
172 124
173 169
174 214
175 21
176 66
177 111
178 156
179 201
180 8
181 53
182 98
183 143
184 188
185 233
186 40
187 85
188 130
189 175
190 220
191 27
192 72
193 117
194 162
195 207
196 14
197 59
198 104
199 149
Found it at 201
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3)Let p = 7, q = 11, e = 13, and M = 5 (M: message). Show details of the following. a. What is the private key d ? b. Perform RSA encryption and decryption on the message M.
a.) What is the private key d ?
Given p=7,q=11,e=13
n=p*q=11*7=77
ed=1 mod(p-1)(q-1)
d=Inverse 13 mod 60=37
Privatekey(77,37)
b. Perform RSA encryption and decryption on the message M.
Given p=7,q=11,e=13 and m=5
n=p*q=11*7=77
ed=1 mod(p-1)(q-1)
d=Inverse 13 mod 60=37
Encryption, c=me mod n= 513 mod 77=26
Decryption, c=ce mod n= 2613 mod 77=5
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4) Suppose (e, n) is the receivers public key and M is the message needed to be encrypted by the sender. Why do we have this constraint M < n? (If we remove this constraint, what happens?)
ana) Decrypt using public key = me mod n
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