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Let's assume another blockchain (blockchain ATH) uses the same protocol to derive addresses from private keys as the one used by Ethereum.

If I see an ETH address then I know for sure that the person who controls it can generate an identical ATH address (unless the private key is held in a hardware wallet or something).

Now, suppose another blockchain (BTH) use a different protocol to derive addresses; as long as I know the one-way function used, is there a way for me to know which BTH address can be derived from the same key as a specific ETH address?

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It really depends on the algorithms used to derive the addresses.

For example all Bitcoin derived cryptocurrencies use the same algorithm to derive the address from the public key RIPEMD160(SHA256(PublicKey)). If you have the bitcoin address then you can determine the corresponding address in any bitcoin derived cryptocurrency, litecoin, dogecoin, etc. The only difference between them is the representation usually add a prefix with the coin type and a suffix with a checksum.

The same applies to ETH and ETC they both use the same algorithm to obtain addresses from the public key B_{96,255}(KECCAK256(PublicKey)). If you have an ETH address then it will also work as an ETC address.

To derive a ETH address corresponding to a BTC address you will have to break KECCAK256, which is equivalent to a primage attack to KECCAK256 hash function, ie very unlikely in practical terms.

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