So it is stated an outgoing transaction from an address would reveal some of the private key. That's why we don't reuse an address.

Technically address attaching is also a zero amount transaction. But does it reveal any part of the private key?

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No, because when you attach an address, a zero-value transaction is done to the address. I.e. it's an incoming transaction to the target address and doesn't reveal the private key.

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