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I can help you write a paper about M and N constraints in m-of-n multi-subscripted addresses. Here is the draft:
Ethereum: understanding multi-signature address limits
In Ethereum, creating a multi-signature address is an important step towards achieving decentralization and security for your smart contracts. A multi-signature address is a combination of two or more addresses that requires at least one of them to be signed by a member of the (m-of-n) group. The number of parts in a multi-signature address can limit the flexibility of users, developers, and the Ethereum ecosystem as a whole.
Limit 3 of 3
One of the most significant limitations of multi-signature addresses is the inherent 3 out of 3 limitation. According to the Ethereum specification, any new method of creating a multi-signature address must comply with this rule. This means that only three parts can be used in an address with several signatures: two signatories and one holder.
M and N restrictions
Although there is no explicit limit on the number of parts (M) in a multisig address, the standard method described above does not allow more than 3 parts. However, it is important to note that the specification guarantees this rule only for creating new multisig addresses. Existing multisig contracts and wallets will likely use these restrictions.
Why not more than 3 parts?
The reason we have a limit on M is due to historical reasons and Ethereum’s design philosophy. Before version 1.0, there were concerns about the possibility of m-of-n multisig attacks (more on this later). To reduce these risks, the core team decided to introduce a hard limit of 3 parts in the new multisig address creation methods.
M-of-N Attacks
Prior to the 1.0 release, some developers asked to use the m-of-n multisig contract constraints, creating more than three parts. However, due to the security inherent in these contracts, such demands were largely unsuccessful. The 3 out of 3 limitation is a direct result of these efforts.
Conclusion
In conclusion, although there is no explicit limit on the number of parts in a multi-signature address, the standard method described above does not allow more than three parts. This 3 out of 3 limitation has been part of Ethereum’s design philosophy since its inception and has been in place since version 1.0. As developers and users continue to explore the possibilities of Ethereum, we can expect that this limitation will be removed with the help of updates or extensions.
Future Developments
Although there is no apparent plan to increase the number of parts in m-of-n multi-signature addresses, ongoing research and development may lead to new improvements or extensions. The Ethereum community remains open to suggestions from developers and users that may eventually lead to new functionality and flexibility for creating multi-signature addresses.
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