What is cross-input signature aggregation and how would it work? I'm seeing lots of mentions of cross-input signature aggregation (CISA) lately. It appears to be something that one can do with Schnorr signatures. What is the main idea of CISA? What would a transaction look like that makes use of CISA?
Schnorr Signatures and public keys can be aggregated (added together) such that
S1 + S2 = S3 and P1 + P2 = P3 where (S3, P3) is a valid signature-pubkey pair IFF (S1, P1) and (S2,P2) were valid signature-pubkey pairs.
Because of this, if a transaction has n inputs, the signatures of those inputs can be aggregated, so the transaction only needs one signature and public key even with any number of inputs, whereas a regular transaction would need n signatures and public keys.
The main benefit being block space (fee) savings.