RSA Cryptosystem

Public and secret keys are created as follows:

1.

Select at random two large prime numbers p and q (say >100 decimal digits each).

2.

Compute n = pq.

3.

Select a small odd integer e that is relatively prime to = (p-1)(q-1).

4.

Compute d = e^-1mod $\phi$(n) (multiplicative inverse).

5.

Publish pair P = (e, n) as RSA Public Key.

6.

Keep pair S = (d, n) as RSA Secret Key.

7.

P(M) = M^e (mod n)

8.

S(C) = C^d (mod n)