1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
|
//Man-in-the-middle attack in Diffie-Hellman key exchange
n = 11 //Large prime numbers
g = 7 //which are public
printf("n: %d\ng: %d\n",n,g)
x_a = 3 //Alice's x
x_t = 8 //Tom's x
y_t = 6 //Tom's y
y_b = 9 //Bob's y
A_a = modulo(g^x_a,n) //Alice's A
A_t = modulo(g^x_t,n) //Tom's A
B_t = modulo(g^y_t,n) //Tom's B
B_b = modulo(g^y_b,n) //Bob's B
disp("Before intrusion by Tom: ")
disp("For Alice:")
printf("x: %d\nA: %d\n",x_a,A_a)
disp("For Tom:")
printf("x: %d\ty: %d\nA: %d\tB: %d\n",x_t,y_t,A_t,B_t)
disp("For Bob:")
printf("y: %d\nB: %d\n",y_b,B_b)
A_b = A_t //Substituting Tom's A as A for Bob
B_a = B_t //Substituting Tom's B as B for Alice
A_t = A_a //Changing Tom's A to Alice's A
B_t = B_b //Changing Tom's B to Bob's B
disp("After intrusion by Tom during exhange of keys: ")
disp("For Alice:")
printf("x: %d\nA: %d\tB: %d\n",x_a,A_a,B_a)
disp("For Tom:")
printf("x: %d\ty: %d\nA: %d\tB: %d\n",x_t,y_t,A_t,B_t)
disp("For Bob:")
printf("y: %d\nA: %d\tB: %d\n",y_b,A_b,B_b)
//Now, Tom can calculate separate keys for Alice and Bob
K1_a = modulo(B_a^x_a,n) //Alice's key
K1_t = modulo(B_t^x_t,n) //Tom's key for Bob
K2_t = modulo(A_t^y_t,n) //Tom's key for Alice
K2_b = modulo(A_b^y_b,n) //Bob's key
printf("\n\nKeys:\n")
disp("Alice''s key:")
printf("\tK1: %d\n\n",K1_a)
disp("Tom''s keys:")
printf("\nTo communicate with Alice\n\tK2: %d",K2_t)
printf("\nTo communicate with Bob\n\tK1: %d\n\n",K1_t)
disp("Bob''s key:")
printf("\tK2: %d",K2_b)
//We can see that K1_a == K2+t and K1_t == K2_b
//Thus, Tom can communicate with Alice using K2_t and with Bob using K1_t
//and easily carry out
|
