A Public-Key Encryption Example (Cont.)

The following steps show how to perform public-key encryption (cont.):
  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.
Encrypting the Text
Assume sending a single character; ‘X’. ASCII for X is 88. As we are the sender, we only know the public key’s 2 values: 187 and 7, or N and e. Running 88 through the simple algorithm gives us the value 11. We send the ciphertext value 11 to the ecommerce web server. 
   Ciphertext = 88e ( mod N ), where public key = (N, e)
   Ciphertext = 887 ( mod 187 )   ∵ N=187 and e=7
   Ciphertext = 11

Decrypting the Ciphertext
The web server passes the plaintext through the algorithm shown above and gets us the original ‘X’ that was sent. 
   Plaintext = Cd ( mod N ), where public key = N and private key = d     
   Plaintext = 1123 ( mod 187 )   ∵ d=23 and N=187
   Plaintext = 88 or ‘X’