1. Generating the public key,
2. Using the public key to generate the private key,
3. Encrypting the text into ciphertext, and
4. Decrypting the ciphertext into the original text.

First, pick two random giant prime numbers. This example picks two small primes to keep it simple: 17 and 11. Multiply them to get 17×11 = 187. Pick another prime: 7. That is our public key including two numbers, 187 and 7.

      Pick  p = 17 and q = 11 
   ⇒ p×q = 17×11 = 187 = N
   ⇒ Public key is (N=187, e=7)

Pick an algorithm, modular arithmetic in this example, to generate the private key from the public key. One of the modular arithmetic examples is 38 = 2 (mod 12) because 38–2 = 36, which is a multiple of 12.

     e × d = 1 ( mod (p–1)×(q–1) ), the algorithm used
   = 7 × d = 1 ( mod (17–1)×(11–1) )   ∵ e=7, p=17, q=11
   = 7 × d = 1 ( mod 16×10 )
   = 7 × d = 1 ( mod 160 )
   ⇒ Private key d = 23