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1

You need to be clearer on exactly what you are seeking to keep private before you attempt to design something. There are various things you may want to keep private in an onchain or Lightning setting e.g. your total Bitcoin wealth, when you make a transaction, which address you are sending from (source), which Bitcoin address you are sending to (destination),...


2

There is no limitation that requires multisig addresses to be created using special multisig keys. A key from an old wallet can be used in conjunction with new keys from a different wallet to create a multisig address and its redeem script. You could even create a multisig address using a few different brain wallets if you wanted to (definitely not ...


0

The Script define in bip-0199 may suffer from OP_IF malleability if not used in a witness Script (which enforces that the argument to OP_IF is minimal, that is either the empty vector or 0x01). There may be other malleability sources in this Script that i didn't spot, and more generally malleability being very difficult to reason about it's worth using tools ...


2

Is there a multi-signature scheme that only need the private keys, thus simplifying backup (and restore) considerably? Yes, the 2-of-2 scheme. The 2-of-2 is highly underrated in context of cold storage. Obviously, no single key can be lost, but that can be managed with a multi-location backups.


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A disadvantage of a multi-signature scheme compared to a Shamir's Shared Secret Scheme is the need to back up the xpub keys. If you don't want to backup the xpub (or xpriv) you can backup the individual private keys used in the multisig and ignore the fact that they were generated as part of a HD tree (if indeed they were). To spend from a 2-of-3 multisig ...


4

Your analysis is correct. The weakness in this scheme is that if one location is compromised, only 80 bits of security are left. But 80 bits is sufficient for practical purposes and would likely take at least a decade to break assuming a highly-resourced attacker was willing to devote significant resources to breaking it. This assumes the original seed was ...


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