I'm trying to solve a problem that goes as follow. There is a set of item and that set is very large. Several actors needs to exchange information about this set, such as adding and removing element from the set and querying if an element is in the set. These actors do not trust each others so they need solid proof. Because the set is very large, actors need to be able to operate with partial knowledge of the set.
So I've been able to find scheme that solve some of the constraints, but not all of them. Here are the direction I explored:
This allows to commit to a set of items and recompute the commitment easily when items are added/removed, even when the content of the set is unknown.
Sorted Merkle tree: This satisfy the ability to prove membership, however, adding and removing elements from the set require knowledge of the whole set.