The architecture of Bitcoin is based on digital signatures that provide users with access to their BTC with the ability to send and receive coins. Unlike real signatures, digital signatures are supported by strong cryptography, so they cannot be forged without access to the "private key". However, they take up a lot of space, which leads to long delays in transactions on the first cryptocurrency network. Note that signatures were not merged in the original Bitcoin protocol. In this article, we will discuss the advantages and disadvantages of the signature aggregation method.

Aggregating cryptographic signatures
Aggregating cryptographic signatures is an old, well-studied technique. Initially in Bitcoin, this method was used to aggregate signatures in a single transaction.

But standard signature aggregation protocols have one drawback: all parties that want to aggregate signatures must participate in a multi-stage off-chain protocol to create a common transaction from separate inputs and outputs. It is easy to aggregate signatures of transaction inputs that you can control yourself, but it does not lead to significant space savings since standard transactions have few inputs. Creating transactions that combine inputs and outputs for hundreds of parties opens up the possibility of aggregating signatures as well. Saving space at this stage is more relevant than ever, however, multilateral aggregation raises several problems:

Users usually want their transactions to be confirmed as soon as possible. In this case, a confirmation delay may occur because the input data must be co-signed, mixed, or aggregated. For example, some cryptocurrency exchanges use aggregation to combine user transactions into one in order to pay lower fees. This practice can lead to misunderstandings on the part of the user, because the transaction identifier becomes available only after a while.
Running a multiparty Aggregated Signature Protocol usually requires exposing the IP address, and this violates user privacy. To avoid disclosing data, users need to use Tor or other IP deanonymization networks.
The aggregation protocol must be protected from DoS attacks: an unscrupulous participant can tamper with the protocol or leave it at any stage, thus preventing others from completing it.
As you can see, solving the problem of aggregating signatures is associated with additional risks. However, signature aggregation can be applied in other forms as well. MimbleWimble's solution can aggregate signatures from different transactions and remove transitions. This is a huge advantage for scalability and privacy, but the disadvantage is that many other features will have to be dropped. Therefore, Bitcoin developers proposed to partially aggregate signatures according to the Schnorr scheme.