All of the aforementioned mechanisms require that there is a M-of-N multisignature wallet guarding each Deposit on Bitcoin.

Bitcoin’s consensus rules restrict script size to 520 bytes (10,000 bytes for Segwit outputs), limiting the maximum size of multisignature scripts to about 80 participants (OP_CHECKMULTISIG is limited to 20 public keys, but this can be bypassed by using OP_CHECKSIG ADD and OP_GREATERTHAN as shown by Nomic Labs). Future proposals such as MAST would allow implementing larger multisigs, however the activation of new features on Bitcoin has historically been a procedure with unclear timelines.

Finally, large multisignature wallets in Ethereum and Bitcoin both have increasing verification costs as the number of participants increases. Building multisigs on Ethereum is particularly hard. By utilizing aggregate signatures with public key aggregation, we can remove all of the above complexities and replace them by a simple single signature verification.

Intuitively, an aggregate public key is generated from all multisignature participants who communicate via an out of band protocol, a process also known as Distributed Key Generation (DKG). Each participant signs the intended message with their private key and contributes a "share" of the final aggregate signature. Assuming ECDSA, the aggregate signature can then be verified against the aggregate public key with an OP_CHECKSIGVERIFY on Bitcoin, or an ECRECOVER operation on Ethereum. This process is simple and inexpensive, and avoids the path of implementing complex multisignature verification logic which can be upgraded for different M-ofN configurations. If another configuration is required, the script or the smart contract only needs to be configured to use a new aggregate public key after re-executing the DKG.

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