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Given the blockchain is a public ledger, if user chooses not not change their public key (address) every time they make a transaction, what information can an attacker gain from watching the users behavior?

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If you use the same address for every transaction you receive, then anyone who knows that address is yours (and is watching the blockchain) will have record of your entire history of transactions. You will have zero financial privacy.

Address reuse is also indirectly bad for the users you transact with: anyone who knows the other user's address will now also know that they transacted with you. Approximate time, and the transaction amount will all be public knowledge.

Thankfully, by using a new address for each transaction, it becomes extremely difficult to make such assumptions, as doing so creates a very high level of plausible deniability and uncertainty when attempting blockchain analysis.

Bitcoin privacy is a highly nuanced topic, for a much more in depth explanation see: https://en.bitcoin.it/wiki/Privacy

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