Key Generation
Generate two random primes, p and q, e.g p=3, q=11.
Compute n = pq, n = 3 * 11 = 33.
Compute phi = (p-1)(q-1) = (3-1)(11-1) = 20
Choose an integer e, 1 < e < phi, such that gcd(e, phi) = 1, e.g e = 7, gcd(7, 20) = 1
Compute the secret exponent d, 1 < d < phi, such that (e * d) mod phi = 1, (7 * d) mod 20 = 1, d = 3
11^37 = ?
37 = 100101 in binary
1 -> first “One” lists number = 11
0 -> square = (11)^2
0 -> square = ((11)^2)^2
1 -> square + multiply = (((11)^2)^2)^2*11
0 -> square = ((((11)^2)^2)^2*11)^2
1 -> square + multiply = (((((11)^2)^2)^2*11)^2)^2*11
gcd(11, 17) == 1
17 = 11(1) + 6 // 1 is floor(17/11), 6 is 17 mod 11
11 = 6(1) + 5
6 = 5(1) + 1 // done
p = prime number (public)
g = modulus (public)
a = Alice private key (private)
b = Bob private key (private)
A = Alice public key (public)
B = Bob public ket = (public)
Sx = Shared key (public)
eA = Eve private key for Alice (private)
eB = Eve private key for Bob (private)
Ea = Spoofed Alice public key will be sent to Bob (public)
Eb = Spoofed Bob public key will be sent to Alice (public)