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I tried Blue wallet. I created vault using same private key with 3 different passphrases for vault key 1,2, and 3. However, I can only receive the fund, but can’t send it because of an error that says “ can not add duplicate data to array.” My question is that because of the app bug or I created a burn vault that isn’t fully functional?

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It could be a bug in the app, but let's consider what you are telling the app to do.

If you added a passphrase to a single WIF private key via a BIP38 passphrase (simply encrypting the private key) you still have the same resulting public private key pair upon decryption. So you are telling the app to create a multisig wallet with the same public key (which really isn't multisig anymore). Also someone only needs to know one of the passphrases to spend since they all resolve to the same public private key pair.

There is nothing technically wrong with this, you absolutely can add the same public key 3 times, and require 2 to spend. I don't know why you would, but it is "allowed".

I believe the result you are looking for would be more easily achieved with a BIP39 mnemonic and adding a separate passphrase to each. Different passphrases on the same bip39 mnemonic will produce a different public private key pair for each passphrase. This way you actually need the correct amount of passphrases to spend instead of just one.

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