Imperfect Logic Puzzle

That's essentially the same solution that Freeduck proposed. The weakness here is if Eve knows what the first box contains.

That's why I said if.

Also, you have not specified how Alice knows that Bob has received the box.

chai2 wrote:

I think the box part can be solved by Alice calling Bob, and asking him to call her back in X number of minutes, and tell him to use a password when he calls back, one that will change each time.

Eve can eavesdrop. She'll know the password as well.

Where does it say she can eavesdrop?

What the hell does "spoofed" mean?

No, Eve can't open the box. I said that Alice should send a box with a key
inside the box. The box itself is locked and Eve cannot open the box. She
can keep it, but Alice resends the box until Bob has gotten it. Again, Eve
cannot open the box and doesn't know what it contains - she only can
intercept the box, that's all. So Alice keeps resending until Bob's got it.

So, once he got the box, Alice sends a key for the outer box, and Eve can
copy the key, it won't do her any good. Once Bob receives the key, he
opens the box and finds inside a key. The key will work with the next box
he receives.

Since Eve cannot open the next box either, she only can intercept, and
Alice keeps resending until Bob received the box and can open it with
the key he's got previously.

I mean, Alice calls Bob like you say. Eve listens to the conversation.

Then Eve calls Alice back instead of Bob, and impersonates Bob.

Now Alice thinks she's talking to Bob, but she's really talking to Eve.

How does she know Bob has the real box? If she sends a box with key inside, and Eve keeps it, but sends Bob a box with key inside, then Bob will say he got Alice's box. He has no way of knowing it is really Eve's box, which is where the whole password in a box thing came from.

Eve and Bob must not discuss this plan ahead of time, though.

Eve could intercept the first package, and replace it with her own if the contents can be spoofed.

Intercept the key, replace it with her own.

Intercept the second box, and horrible things happen.

No. Now she has two keys, but she still doesn't have The Package.

FreeDuck wrote:

No. Now she has two keys, but she still doesn't have The Package.

Alice sends box with key to Bob.

Eve intercepts box, replaces it with her own box-with-key.

Alice sends key to Bob.

Eve intercepts key, sends her own key to Bob.

Eve can send her own packages but she can't spoof the contents. She can't see inside the box so she has no idea that the first box contains a key and not The Package.

But what if Eve intercepts the box and then sends a dummy box to Bob and then intercepts the key when Alice sends it?

There is no solution to this problem. Not even a half one, because Eve will just keep everything, and you'll never be able to get the real packages to Bob.

The only way that Eve will not be able to open the box is if Alice never sends it, or never sends the key for it, or if she sends the key for it in a box which she hasn't sent the key for.