I solved it a little differently than the suggested method.
The suggested solution requires a box that is capable of being locked in both the lid and box by two padlocks. It also requires (Spoiler!) the ring to make two pointless transits, which could be expensive if it was large.
What if, instead, the box was capable of admitting only one padlock? Then Jan would padlock it closed. On receiving the locked box, Maria locks her padlock to Jan's, and returns the box (still locked with Jan's padlock, and not necessarily containing anything.) Then, on receiving the box back from Maria, Jan can form a chain that can be broken by either his padlocks (which he can remove) or by Maria's padlock (which she can remove). Then he can attach the chain to any box. Perhaps he should clip one more of his padlocks only to hers, so she can also select a new box.
Of course, this relies on some properties of padlocks that are not necessarily transferrable to cryptography.
Jan can open his padlock, releasing hers, and transform this to:
Box - J - M - J - Lid
Which Maria can open. An optimization could be:
Box - M - J - Lid
This is available if Maria could fit her padlock through the port in the box simultaneously with Jan's there, and send that back so Jan could remove his initial box padlock.
And the arrangement
Box - M - J - Lid
| |
J M
Would let either start a new box, using the J - M - J or M - J - M chaining as needed.
Nicely done. Understood the chaining solution now. One small assumption in that would be that the chain remains taut enough to not leave any gaps to slide the hands into the box (since the lid's hook is no longer in touch with the box).
The suggested solution requires a box that is capable of being locked in both the lid and box by two padlocks. It also requires (Spoiler!) the ring to make two pointless transits, which could be expensive if it was large.
What if, instead, the box was capable of admitting only one padlock? Then Jan would padlock it closed. On receiving the locked box, Maria locks her padlock to Jan's, and returns the box (still locked with Jan's padlock, and not necessarily containing anything.) Then, on receiving the box back from Maria, Jan can form a chain that can be broken by either his padlocks (which he can remove) or by Maria's padlock (which she can remove). Then he can attach the chain to any box. Perhaps he should clip one more of his padlocks only to hers, so she can also select a new box.
Of course, this relies on some properties of padlocks that are not necessarily transferrable to cryptography.