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Let's say I'd go through all the transactions in my wallet, write down their block-heights and store this list somewhere insecure.

Could my privacy or security be compromised by this in any way (assuming an attacker knows it is a list of block-heights for all of my wallet's transactions)?

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Yes, it would weaken your privacy. By knowing when you transacted, an attacker can narrow down the field of which possible outputs you own, thus increasing their capability to trace your past and future transactions.

jtgrassie
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