Is possible especify the keys rather how many in multisignature wallets? I search about multisignature wallets, but it seems very limited. Far I understand, we can create a wallet with N keys, and specify how many keys is needed to create a transactions.

So, I can create one wallet with 5 keys (K1, K2, K3, K4, K5) and I can specify how many keys (but not which keys!) are needed, so is possible to say: “you need 3 of 5 keys”. However, it makes a K1 + K2 + K3 and K5 + K4 + K2 a valid signature. 

It’s possible to specify that which keys are needed rather than how many?

Imagine that have three people (K2, K3, K4) and have a server (K1). Only with K1 + (K2 or K3 or K4) will be valid. It means that K2 + K3 or K4 + K3 can’t be able to create a valid transaction. To be a valid signature we need two signatures, but one of that two need to be the K1.

It’s possible?



One alternative is creating a multiples multi-signatures wallets. I mean, create three addresses one with (K1 + K2), another with (K1 + K3) and so on. But, it will have multiples address, it is what I'm trying to avoid. Another solution is need all keys (4 of 4), but it will need the signature of the three clients, but it’s not easy and will need to wait everyone sign it.



For the background of the history, I trying to use the OP_RETURN. Everyone can access one single address and view all the information, about the three clients. The OP_RETURN value will be generated by the server (K1) and need to be signed with one of the client (K2, K3, K4). But, the client itself can't be able to create a transaction alone, so K2 + K3 need to be an invalid signature.
You are right, multisig as implemented in Bitcoin right now requires M participants out of N to sign. However, the use case you want is doable with more complex scripting.

For example, K1 + (K2 or K3 or K4) could be done with something like:

&lt;pk1&gt; CHECKSIGVERIFY 1 &lt;pk2&gt; &lt;pk3&gt; &lt;pk4&gt; 3 CHECKMULTISIG

That script can be redeemed with the signature of K1 and a signature of one of K2, K3 or K4.