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Keys & Addresses

Unique numbers used for sending and receiving batches of bitcoins.

What is a private key, a public key, and an address?

To send and receive money in bitcoin you need an “account number” and a “password”.

In bitcoin we call these a public key and a private key.

Here are your account details. Welcome to Bitcoin.

However, this “account number” is awkwardly long number. So to make life easier we create a condensed version of this public key, and we call it our address.

You’ll see how hideous the public key is in a moment.

And that’s the role of the private key, the public key, and the address.

Where do keys and addresses come from?

Private Key

It all starts with the private key, which is just a randomly generated number:

But because this number is so large, computers (and bitcoin) like to work with it in hexadecimal format:

Hexadecimal numbers are shorter than decimal numbers because they also use the letters a,b,c,d,e and f

And there we have a private key… just a big random number (in hexadecimal format).

Private Key ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db2

A private key can be any number between 1 and 115792089237316195423570985008687907852837564279074904382605163141518161494336.

Public Key

You use your private key to create your public key.

But first of all, this public is going to be seen by other people. Therefore, when we use the private key to create our public key, we don’t want it to be possible for anyone to figure out what our private key was.

Because after all, the private key protects our bitcoins.

Even though the public key is made from the private key, we don’t want anyone to be able to work backwards from it.

Fortunately we can use a special type of mathematical function to achieve this.

We just shove the private key in to it (which is a number after all), and the function spits out a public key (a new number).

Now, there are two benefits of using this particular function:

  1. This function returns a public key that is mathematically connected to our private key. This will come in handy when we want to send bitcoins in a transaction.
It’s like starting with a key and creating a padlock from it.
  1. Even though the public key is connected to the private key, it’s not possible to figure out what the private key is from the public key. And this is why we use this particular mathematical function… because it’s a “one-way” function.

And ta-da, thanks to our random number and this function, we now have a pair of keys that we can use to send and receive money in bitcoin.

Private Key ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db2
Public Key 02b4632d08485ff1df2db55b9dafd23347d1c47a457072a1e87be26896549a8737


Oh yeah, that public key is hideous isn’t it. Nobody is going to enjoy typing that out, so let’s make it more practical and call it an address.

Thank goodness for that!

All we’ve done here is compress the public key, and used a format that doesn’t make use of any characters that look similar to each other when written down (i.e. no “0”, “O”, “I” or “l”).

So no, it still doesn’t quite roll off the tongue, but it is an improvement.

And that’s all an address is – a shorter/easier version of the public key.

Private Key ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db2
Public Key 02b4632d08485ff1df2db55b9dafd23347d1c47a457072a1e87be26896549a8737
Address 1EUXSxuUVy2PC5enGXR1a3yxbEjNWMHuem

Due to the way the public key has been compressed, it’s not possible to work out the public key from the address.

Do I have to remember all 3 of these keys?

Because your public key and address are worked out from your private key, you can get away with just saving your private key.

Remember, your public key (and address) are worked out from your private key.

So if worst comes to worst, if you ever need to send your address to someone, you can just work it out from your private key.

In everyday life, it’s practical to keep note of your private key and address, because your address is what you give to people when you want to receive bitcoins.

What happens if I lose my private key?

Well then you’re fu lly out of luck.

It’s impossible to work out your private key from either your public key or address, so if you lose your private key, it’s lost.

And if you haven’t got the private key for an address, any bitcoins located at that address will be locked there forever.

How’s that for security?

By Greg Walker,

Last Updated: 25 Aug 2020
  • 25 Aug 2020: Updated private key pages to indicate that a private key can be any number between 1 and (n-1) and not between 1 and (n), where n=115792089237316195423570985008687907852837564279074904382605163141518161494337 and is the order of the curve.
  • 30 Mar 2020: corrected base58 chars removed
  • 28 Mar 2020: updated html for h1 headers and subheadings - now dynamic from yaml
  • 28 Mar 2020: updated html for h1 headers and subheadings
  • 15 Oct 2019: updated CSS and router to use pandoc 2.7 (from 1.19)
  • 09 Oct 2019: renamed browser to explorer, glossary to guide, and guide to beginners
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Hey there, it's Greg.

I'll let you know about cool website updates, or if something seriously interesting happens in bitcoin.

Don't worry, it doesn't happen very often.