1. RSA Algorithm:
1. Select two very large prime numbers.
2. n = p.q
3. ɸ = (p - 1).(q - 1)
4. Select e; such that, e is relatively prime to ɸ and
e < ɸ, gcd (e, ɸ) = 1
5. Select d; such that, d.e mod ɸ = 1 or
e = 1 mod ɸ
6. Public key : {e, n}
Private key : {d, n}
7. e = pe mod n
p = cd mod n
Example:
1. p = 3, q = 11
2. n = 3 x 11 = 33
3. ɸ = (3 – 1).(11 – 1) = 2 x 10 = 20
4. e = 3, 7, 9, 11, 13, 17, 19
d = 1, 3 mod 20 ≠ 1
5. d = 7, d.e mod 20 = 1
d = 2, 6 mod 20 ≠ 1
d.3 mod 20 = 1 d = 3, 9 mod 20 ≠ 1
d = 4, 12 mod 20 ≠ 1
8. Public key : {33, 33} d = 5, 15 mod 20 ≠ 1
d = 6, 18 mod 20 ≠ 1
Private key : {7, 33}
d = 7, 21 mod 20 = 1

2. Diffe-Hellman Protocol:
k = gxy mod p
Alice Bob
R1 gx mod p R2 gy mod p
R R
k = R2x mod p k = R1y mod p
= (gy mod p)x mod p = (gx mod p)y mod p
= gxy mod p = gxy mod p
k is the shared key
p and g : two large number with some properties.