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I am wondering if is there is a way I can check if two different addresess belong to the same prvKey (wallet, person)... since there is a hash function involved in the process from getting the Address from the prvKey, I am guessing it is not posible, given two addresses know for sure if they were generated from the same prvKeys.. But I find hard to make a less intiuitive argument, any help?

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You can look up and use the stake address to determine this. Stake address is unique to wallet and linked back to all payment addresses. Here is an example (use CardanoScan or other method to expose stake address). Two wallet addresses:

addr1q87xqs5duasp4ehuec9gasy9qptt7zhweg046gh9pa7nmax6yxvvxd5qhurea4rvlj6a8c35twc0654l48avkn79z3mq46yfdm

addr1q9rmevy4rsnvzmhj0xfljdqhm9u2zmr9y34rqeytd3qky5k6yxvvxd5qhurea4rvlj6a8c35twc0654l48avkn79z3mq8kpjld

Have the same stake address:

stake1u8dzrxxrx6qt7pu763k0edwnug69hv8a22l6n7ktflz3gaspch4jv

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    Note: stake addresses and payment addresses are not necessarily derived from the same master seed. Most wallet software will do this by default, so the above example can work in linking addresses that share the same stake key. However, a shelley address can be built from payment and stake keys that live on completely different merkle trees. If you have more than one stake address, or non-shelley addresses, you would need to use cardano-db-sync
    – zhekson
    Feb 24, 2022 at 14:32
  • what if there is no stake address? Feb 24, 2022 at 15:19
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    @DaveStrider then this method also would not work. I think the best way to do this would be to list all transactions associated with a wallet's extended account key (beginning in acct_xvk.....) using a wallet software like cardano-wallet
    – zhekson
    Feb 24, 2022 at 16:40

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