Example: Alice and Bob agree on y = 327 and p = 919.

Alice chooses a = 400; this is her private key. She then computes α = 327⁴⁰⁰ mod 919 = 231 which is her public key and can be known by anyone. She can send this number to Bob in cleartext.

Bob chooses b = 729 for his private key and computes β = 327⁷²⁹ mod 919 = 162 and sends this number (his public key) to Alice.