Efficient peer to peer untrusted signature aggregation Suppose I had a peer to peer system, there are a few writers with the same signing key, and all readers have the verification key.
A naive system is that each document $d_1..d_n$ gets signed $s_i=sign(d_i)$. This would allow anybody to verify that every documents is written by authorized writers.
However it would be inefficient for a new user to join this group, as they need to verify every document, taking $O(n)$ time.
Now a writer can create a group signature $sign([d_1..d_n])$ in addition to the individual signatures. This means a new user can verify all documents in $O(1)$ time. This works because the writer has every document.
It will not work in a peer-to-peer system where no writer may observe the complete set of documents, for example due to being offline.
That suggests that readers need the power to merge the signature independent of the writers. Is there some system where a untrusted user can generate an aggregate signature like $sign([d_1..d_n])$ above by combining the $s_i$ values?
BLS Multi Signatures - the aggregated signature is the product of signatures
Homomorphic Signature Schemes - the aggregated hash is the product of (prime) hashes.
(not a signature) it might be worth investigating signing Homomorphic Hashes, you cannot combine them