Problem:

King A and King B need to exchange messages in secret, but they must rely on a messenger they do not trust. To ensure their communication remains private, they devise a clever method using locks and keys: Securing the Key: King A takes a secure box and places a duplicate key inside. He locks the box with a different key that only he possesses. The locked box is then handed to the messenger and sent to King B. Tamper Detection: If the messenger attempts to open the box, King B will immediately know of his treachery. Otherwise, King B adds his own lock to the already locked box and sends it back to King A. Removing the First Lock: Upon receiving the double-locked box, King A unlocks his own lock and sends the box—still secured by King B’s lock—back to King B. Retrieving the Key: Now that only his own lock remains, King B unlocks the box and retrieves the key placed inside by King A. Having securely exchanged the key without the messenger ever seeing it, both kings now share a secret means of encryption. With this key, they can communicate freely, knowing their messages are safe from prying eyes.

If King A sends the box locked with his own lock, the messenger could attempt to deceive both kings by adding his own lock and returning the box to King A instead of delivering it to King B. If King A, unaware of the trick, proceeds as before—removing his lock and sending the box back—the messenger could then claim to be King B and repeat the process. This would allow the messenger to obtain the key instead of King B.