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Say I have an online store that accepts bitcoins and want people to be able to contact me through my wallet, because that is ultimately the entity involved in an hypothetical trade.

Can that be done? how?

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Not in any way that is intended by the protocol.

What do you mean by "ultimately the entity involved in a hypothetical trade"? It's just a hash of a public key, the corresponding private key to which you hold.

What is preventing you from having a contact form or e-mail address in the online store?

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    I mean that payments are made to a certain wallet, not to a certain person. An email is delivered to an email address, therefore is not the same level of reliability. If I could send a message o a wallet, I would know for a fact that the person reading is the one that has access to whatever funds I send to that wallet. Using the destination's public key to encrypt an email message would be the equivalent to what I am asking. Either way, your reply answers my question. – Pico Feb 14 '13 at 20:25
  • I think it might be possible to encrypt something with the public key bitcoin uses, but the address is a hash of that key, so it wouldn't work. If I recall correctly, once an address sends money, the public key it was derived from becomes part of the blockchain, so you could then encrypt messages to whoever holds the private key. How and if this is possible probably deserves a separate question, though. – Andrey Fedorov Feb 15 '13 at 1:24
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Bitcoin transactions - at least the part that ends up on the block chain - should only contain whatever is necessary for the world to validate them. Anything else is pushing extra costs (bandwidth, storage) to everyone who wants to run a full node, and isn't necessary.

Of course, that doesn't mean that payments (as in: the full operation that takes places between to trading entities) need to be restricted to just the low-level transaction that ends up on the block chain. The proposed payment protocol (see https://gist.github.com/gavinandresen/4120476) provides a solution to this: transactions take place directly between two entities (and may involve exchanging messages, order ids, refund addresses, ...), and results in a negotiated transaction which can be broadcast on the P2P network.

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