Is there an encryption scheme that...

Works like a box?

By which I mean:

The box is lockable, can contain information, and only presents valid
information when opened with its corresponding key; that is, given a
box, full of information and locked, there is only one key which will
yield a 'valid' result? In other words, one can try opening the box
with other keys, but the information yielded by these keys is clearly
invalid; the correct key, on the other hand, clearly yields the true
information in the box. Perhaps validity is determined by the presence
of a pre-determined codeword...

In other words, Jim and Sue both think they know the answer to a
riddle. Each wants to give his or her answer to the other to prove to
him or her that he's figured it out. However, as soon as Jim tells Sue
his answer (assuming it is correct), Sue can no longer prove to Jim
that she had it right all along, too. Thus, Sue decides to seal her
answer in a lockable box to which she owns the key. Jim then reveals
his answer to Sue, Sue gives the key to Jim, and Jim opens the box to
reveal Sue's answer. However, if somehow using a different key made
the answer revealed by the box change (as happens with electronic
cryptography, as I understand it), Sue might be able to change her
answer after hearing Jim's by handing Jim a different key.

So... I'm thinking symmetric cipher with plaintext longer than the
key, and a portion of the plaintext agreed upon beforehand (to show
validity of the key and decrypted plaintext).

Will this work?
Did any of that make sense?

Thanks.
Nolan

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