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I've read a couple blog entries and tutorials on how to spend BTC that are "stored" on a piece of paper.
They all suggested importing the private key into e.g. blockchain.info's wallet (or any equivalent)
and wipe ALL coins from that address. But why should I not continue using it?

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Once your import the key, the key now exists in two places: your paper and your wallet. Because of this, you've lost the advantage that a paper wallet has for cold storage. What you now have is a paper backup of one of the keys stored in your hot wallet. Any risks of a hot wallet now also apply to your paper wallet.

In addition, there is the inherent privacy issues with re-using a Bitcoin address, regardless of how that wallet is stored. There aren't many advantages to re-using addresses, and this case is no exception. If you still need a paper wallet after importing one, you should really create a new one.

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The reason paper wallets are secure is because they aren't connected to the internet and aren't easily accessible to anyone but you because you're supposed to store a paper wallet where no one else can get it (e.g. hide it or store it in a safe if you own one anyways, for example because you own other valuables or a gun).

The very moment you enter your private key into a computer which is connected to the internet, you lose this advantage. You are willing to do this to make use of your money, that's not the topic.

However, if you do that, things are even worse than if that money was in a wallet on a computer connected to the internet or an online wallet all along because you will feel a need to dispose of the piece of paper the private key is written on. You might just throw it into the bin. And here is, where people's paranoias when it comes to large amounts of valuables comes into play.

If someone comes across the piece of paper your wrote your private key on, you can assume your money to be gone unless you transferred it to a different address. This even can happen if you burn the paper in an openly accessible fire, though that of course reduces the chance greatly. If you smear the ash by stepping onto the burned piece of paper and dragging your foot along the ground, you should be very safe, and realistically, the chance of someone stealing your private key after you burnt the piece of paper is very small, too. However, the chance of someone stealing your money if you merely throw the piece of paper away, should be regarded as very real.

It's a lot easier to tell people to transfer their money to a different address than to burn a piece of paper. A lot of people will not actually burn the piece of paper but they will transfer the money to a different address if asked to. After the transfer happened, that piece of paper can be regarded as declassified.

Furthermore, this saves creators of HD wallet software from a having to implement a feature which allows the import of a single address permanently.

To make things worse, if a HD wallet offers such a feature, it losses a major feature: The way, HD wallets are set up, they can create a virtually arbitrary number of private keys + addresses from very little data to begin with. Deterministically. That's what the "D" in "HD" is for. Such wallets can be restored using a seed which often is represented in form of a sequence of a few English words.

A HD wallet software can guarantee the user to be able to create the same private keys + addresses again on a separate installation. This way, a user only has to back up their wallet's seed and will be able to get access to their money again if their HDD fails, a crypto trojan encrypts their wallet, or their computer explodes. If a wallet software, however, allows the user to permanently import a private key which has not been created deterministically from the seed, the user won't get that private key back from the seed. They have to hold on to that key themselves.

Compelling a user to back up that one key is much harder than just telling them to transfer the money to an address the wallet generated and to keep the seed of that wallet backed up.

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