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Let's assume that we only have the bip32 derived btc address, no private or public key. Is it possible to find out its index used for the bip32 generation?

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BIP 32 does not derive addresses but derives a series of private keys from which corresponding addresses are then calculated. So there are multiple layers of obfuscations here that would make the index recalculation impossible. First, Bitcoin addresses do not reveal anything about the associated private key (ECC and hash protected) and second, the private key related to the address is in itself derived from the master private key through a function that hashes multiple inputs of which one of them is an index number. Since hash functions and ECC are one-way, there is no way to back calculate this data.

  • Awesome, thanks for the quick & in-depth reply! – cptproto Sep 14 '19 at 8:03
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One of the privacy properties of BIP32 is that given two public keys (or even private keys), you cannot even tell whether they were generated from the same xpub or two distinct xpubs. This implies you certainly can't tell their index.

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