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As we know, a single private key or seed phrase generates many addresses.

Is it possible for someone to determine that two addresses were derived from the same private key?

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Technically, a private key will only lead to two addresses - one from the hash of the uncompressed public key, and one from the compressed on. Ethereum only uses uncompressed keys, so you only get one address in reality.

When seed phrases are involved, the mnemonic is used to seed the generation of multiple private keys. Each private key is a standalone private key, it is only the derivation step that links them. Given two such private keys that are derived from the same seed, it is not possible to determine that they were actually derived from the same seed. On their own, they look just the same as all other private keys.

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