### RSA Algorithm Example

- Choose p = 3 and q = 11
- Compute n = p * q = 3 * 11 = 33
- Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
- Choose e such that 1 < e < φ(n) and e and n are coprime.
Let e = 7
- Compute a value for d such that (d * e) % φ(n) = 1. One
solution is d = 3 [(3 * 7) % 20 = 1]
- Public key is (e, n) => (7, 33)
- Private key is (d, n) => (3, 33)
- The encryption of
*m = 2* is *c = 2*^{7} % 33 = 29
- The decryption of
*c = 29* is *m = 29*^{3} % 33 = 2