Public Key Cryptography: Diffie-Hellman Key Exchange
The idea here is that (3^24 mod 17) ^ 54 mod 17 = 3^(24*54) mod 17 = 3^(54*24) mod 17 = (3^54 mod 17) ^ 24 mod 17. Alice has result of (3^24 mod 17) from Bob and her private number 54, while Bob has result of (3^54 mod 17) from Alice and his private number 24 so they calculate the same result