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Suppose I want to create an arbitrary tree deriving from one master secret, with an arbitrary structure, with some branches being arbitrary different crypto-currencies (e.g. BTC/ETH/XRP/...).

Is this always possible? Are there any currencies that won't be supported by such a private key generation scheme?

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As long as they utilize a form of public key cryptography, I think the answer is yes. My understanding is that BIP32 was meant to be a standard for Bitcoin, but not the only possible implementation of a hierarchy structure for deterministic key pair generation. The examples given in the standard are, however, specific to elliptic curve used by Bitcoin:

we will assume the public key cryptography used in Bitcoin, namely elliptic curve cryptography using the field and curve parameters defined by secp256k1

This means that it would work for other types of public key cryptography, though you may have to tweak the generation functions for different size keys (other than 32 bit private keys and 33 bit compressed public keys). Of course the security of the arbitrary scheme depends on the design, but that wasn't what this question was asking.

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