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If I send them the change output of a transaction they received from me, wouldn't they assume that it was that, a change output, and have good heuristic that tells them how much money the original output that I send the first transaction had? And assume that output they received came from an original withdrawal from an exchange they know about, from colluding in EAE attack.

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If I send them the change output of a transaction they received from me, wouldn't they assume that it was that, a change output, and have good heuristic that tells them how much money the original output that I send the first transaction had?

Not really. Just because you sent them an amount, they have no knowledge of the total input amount you used to fund the transaction and thus no knowledge of how much goes to the (possible) change output. So at best it's "this user sent us amount X and possibly owns a new output with an unknown amount" after the first tx, and after the second "it's possible that this second tx is spending an output from the first tx, if true, some or all of the funds came from that output". If they're making the assumption it is the true spend, and there's no other input ring and no new change output, only then can they assume to know how much was in the output.

And assume that output they received came from an original withdrawal from an exchange they know about, from colluding in EAE attack.

If they are colluding with another exchange they'd already know how much an original output owned. They still wouldn't know for certain which output(s) funded the tx, though they'd have a pretty good idea, if they are colluding that is.

If you are using two separate KYC exchanges and are concerned with them colluding, you can sweep_single on your received outputs (change or otherwise).

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