Imagine the following senario. We have $n$ participants. Participant $i$ has a set of elements $S_i$ with the elements being in a random order, possibly different for each participant.
The participants want some way to get something like a "hash" of the sets. Particularly they want for the hash to be collision resistant, so that it is hard to find two different sets with the same hash.
The hash function should also be pre-image attack resistant, so that given a hash (or a set) it is hard to find a (another) set that hashes to this values.
The catch is that the participants cannot reorder their sets. This means that the hash function must be order independant of the order of the elements but not of their contents.
Is there a secure and solid way to fulfil the requirements?
( I had a simple idea, to compute something like $SetHash(S) = Hash(e_1) \oplus Hash(e_2) \oplus \dots \oplus Hash(e_n)$ which i think satisfies the preimage attack resistance property but i cant formally prove that it is also collision resistant)