A Secret Message: Answer

Here is the answer to yesterday’s question. If you haven’t read it, make sure to read it first.

As promised, I will give you two different answers. The first method has a slight drawback in that each lock can be used only once. The second method avoids this problem by not sending any keys through the mail.

Method 1:

Alice places the message into the box and locks it with a padlock. She then sends the locked box to Bob. Neither Bob nor Charlie can open the box, but Bob can take possession of the Box and put it in a safe place.

Bob then sends a plain letter back to Alice informing her that he received the box and it is securely stored away. Once Alice receives the letter she sends the key to Bob. Because the key is of no use without the box, Charlie can’t use the key to get to the original message. When Bob receives the key, he can take the box out from the safe place, open it, and read the secret message.

This method has a drawback. After the message is exchanged, Charlie had access to the key. Assuming that Charlie will make an effort when it comes to sniffing around, he might make a copy of that key. The next time Alice and Bob want to exchange a message, they will need to use a different padlock. So each lock and key can only be used once.

Method 2:

This method avoids the drawback of the first method.

Again, Alice starts by placing the message into the box and locking it with a padlock. Just like before, she sends the locked box to Bob. Neither Bob nor Charlie can open the box. Now instead of putting the box away, Bob adds another padlock to the box and sends the

Now instead of putting the box away, Bob adds another padlock to the box and sends the box with both locks secured back to Alice. When Alice receives the box back, she can now remove her lock and send the box to Bob again. This still leaves the box secured with Bob’s lock, and Charlie will not be able to open it. Bob now receives the box with only his lock, so he can open the box and read the message.

Charlie will never be able to open the box because it is locked with at least one lock whenever it is in transit. On top of that, the keys to the locks are never exchanged. This means that Charlie will never have access to the keys a thus will never be able to copy them. So the next time Alice and Bob want to exchange a secret message they can use the same locks.

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