Diffie-Hellman key exchange.
Alice and Bob use Diffie-Hellman key exchange to share secrets. They start with prime numbers, pick private keys, generate and share public keys, and then generate a shared secret key.
The test program supplies prime numbers p and g.
Alice picks a private key, a, greater than 1 and less than p. Bob does the same to pick a private key b.
Alice calculates a public key A.
A = gᵃ mod p
Using the same p and g, Bob similarly calculates a public key B from his private key b.
Alice and Bob exchange public keys. Alice calculates secret key s.
s = Bᵃ mod p
Bob calculates
s = Aᵇ mod p
The calculations produce the same result! Alice and Bob now share secret s.