# ‘Digital Signatures’ in Bitcoin-Payments, and how they assure that only you have control over your Bitcoins.

I will explain the concept of „Digital Signatures“ in Bitcoin-Payments and how they assure that only you, as the only legitimate holder of your Bitcoin, are able to spend them. Illustrations are “house-made”.

So lets imagine you are a merchant who sells some goods. You accept two currencies in your store, US-Dollar and Bitcoin.

When the Bitcoin-Wallet is downloading, on a technical level what is happening, is that the wallet is being generated by the software. In terms of our Bitcoin-Wallet envelope analogy, the software starts with generating the left-side of the envelope. We call this left side the „private key“. This „private key“-left side envelope is unique. That means there is no other left-side of an envelope that looks like yours. The blue pattern on the edge of the envelope illustrate its uniqueness. We will see in a second why this is important. (I will explain in an later article what mathematical function assures, that the envelope is unique).

After, the left-side of the envelope was created, the software starts to create the right-half of the envelope. The right-half is called „public key“. This right-side is not randomly created though. It is being generated from the unique private-key-left-side envelope. So, both halves fit together.

So your Bitcoin wallet consists of these two halves of the envelope; The „private key“-left-half and the „public key“-right-half.

Now you have the real wallet with US-Dollars from Buyer 1 and your „public key“-right-half envelope with Bitcoins from Buyer 2.

What are you doing next? You take the wallet with US-Dollars and the „public key“-right-half envelope with Bitcoins, put them on the street and leave.

Soon a pedestrian walks by. He notices the left-behind wallets and stops. He picks up the real wallet and takes it with him. Afterwards he leaves, without even touching the „public key“-right-half envelope with the Bitcoins in it.

Why is he taking the US-Dollars? He takes the US-Dollars, because he can go with them to the next shop and purchase some goods with it. Why is he not taking the „public key“-right-half envelope with Bitcoins? It is not because the Bitcoins have no value. But because, these specific Bitcoins on the street don’t give the pedestrian any purchasing-power. The reason is, that the Bitcoins (from Buyer 2) are attached to your „public key“-right-half envelope, and they can not be taken out. You may question here: „How about if the pedestrian just takes the „public key“-right-half envelope with the attached Bitcoins and tries to spend them attached together, maybe it is not necessary to take the Bitcoins out of the right-half envelope? Well, here is where one of the key points of Bitcoin-technology comes into the game. The reason why the pedestrian is ignoring the Bitcoins on the street is, that a „public key“-right-half envelope can only receive Bitcoins. That’s its only function. That is the reason why you can make the right-half-envelope public. The only thing people can do when they have your „public key“-right-half envelope, is putting more Bitcoins into it. Nobody can take it out, not even you. Once in, the Bitcoins are attached to the „public key“-right-half envelope forever. The only way to spend these Bitcoins is to add the unique paring „private key“-left-half envelope, which (remember) the „public key“ was generated from. In other words: Bitcoins can only be spent if they come in a full and gapless envelope, which consists of the „private key“-left half and the „public key“-right half of the envelope. That means, everybody accepts only Bitcoins which are enclosed by a full complete envelope, where both halves fit gapless to each other.

So, when I talked about Buyer 2 who paid you in Bitcoins, he actually put a full, gapless envelope (consists of left-side and the matching right-side envelope) with Bitcoins (actually another full envelope Buyer 2 received before) in it, into your „public key“-right-half envelope.

Back to our story. In the next morning you are going back to the place where you left your US-Dollars and Bitcoins on the street, and notice that your Dollars are gone but the right-half-envelope with the Bitcoins from Buyer 2 is still there, as nobody except you (who is the only holder of the matching „private key“-left-side envelope) is able to make a full, gapless envelope. You take the „private key“-left-half envelope, which you hidden before and add it to the right-half-envelope where the full-envelope of Buyer 2 is attached to. Now the full-envelope with Bitcoins from Buyer 2 is in a full-envelope again and can finally be spent.

The fact that you can provide the unique „private-key“-left-half envelope which is the only left-side that fits gapless to the „public key“-right-half envelope, proves that you are the creator of the „public key“-right-half envelope. That means, all Bitcoins which are attached to this right-half envelope (e.g. Bitcoins from buyer 2) belong to you.

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