How do paper wallets work

[IdMineThat]

I'm curious how the paper wallet generators such as bitaddress.org work. If they can generate offline, doesn't that mean that every possible public key and their corresponding private key already exist, and whoever is capable of programming something like this has all the private keys?

Thanks

[1715349754]

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[hosseinimr93]

If they can generate offline, doesn't that mean that every possible public key and their corresponding private key already exist

You are right. They all do exist.

and whoever is capable of programming something like this has all the private keys?

No one is capable to do so.
There are around 2²⁵⁶ valid private keys and around 2²⁵⁶ valid public keys. It's not possible to generate even 1 trillionth of them, let alone all of them.

It's not that all private keys and all public keys have already been generated and are kept somewhere.  

Any private key is a 256 bit number (or a 64 character number in hexadecimal format). In other words, almost any integer between 1 and 2²⁵⁶ is a valid private key.
Once you request a tool like bitaddress to give you a private key and an address, it generates a random number between 1 and 2²⁵⁶, do some calculations and gives you the private key in WIF format.

Note that the 256 bit space is large enough and it's not possible to generate a private key that has already been generated by someone else.
So, if you generate a private key using a secure tool in a secure device, you can be sure that you are the only owner of that private key.

[BitMaxz]

They do not store any private keys on that tool it generates unique private keys.
Bitaddress.org only contains HTML documents and Javascript it won't work on any browser with disabled javascript.

If you want to deeply check this tool then go to their GitHub to check their respiratory https://github.com/pointbiz/bitaddress.org
You can also check their old thread here https://bitcointalk.org/index.php?topic=43496.0

As you can see it was developed years ago in 2011 and the last update is after 5 years or 2016. If you do not trust their work better use normal or non-custodial wallets like Electrum or Bitcoin core for safety.

[bitmover]

If they can generate offline, doesn't that mean that every possible public key and their corresponding private key already exist

You are right. They all do exist.

A private key is just a random number. All random numbers already exist. Imagine that you pick a random number:

Code:

13840170145645816737842251482747434280357113762558403558088249138233286766301

This is the HEX format of the number, which is a private key in a HEX format:

Code:

1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD

You can read more about private keys here:
https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html

A private key is simply a number, picked at random. Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoins by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoins secured by that key. The private key must also be backed up and protected from accidental loss, because if it’s lost it cannot be recovered and the funds secured by it are forever lost, too.

and whoever is capable of programming something like this has all the private keys?

No one is capable to do so.
There are around 2²⁵⁶ valid private keys and around 2²⁵⁶ valid public keys. It's not possible to generate even 1 trillionth of them, let alone all of them.

It's not that all private keys and all public keys have already been generated and are kept somewhere.  

2²⁵⁶ is a very big number.

To illustrate and to show you how big is that number, take a look at the picture below:


https://www.reddit.com/r/Bitcoin/comments/1ohwvu/bitcoin_your_money_is_secured_by_the_laws_of_the/ccs5g52/?utm_source=share&utm_medium=ios_app

[Miguel 11th]

I have a question also sir as a newbie and curious about this,

If bitaddress.org creates the public key and private key, where we can put that public/private keys? In any wallet/platform?

Thank you

[BitMaxz]

I have a question also sir as a newbie and curious about this,

If bitaddress.org creates the public key and private key, where we can put that public/private keys? In any wallet/platform?

Thank you

You can import private keys to any bitcoin wallet such as Bitcoin Core, Armory, Mycelium, or Electrum and etc...

But be careful in choosing which wallet you are going to use there are many phishing sites and wallets out there that could compromise your private key. Only choose a wallet that is already well-known like what I mentioned above.

[hosseinimr93]

If bitaddress.org creates the public key and private key, where we can put that public/private keys? In any wallet/platform?

You can do that on any wallet supporting importing private keys. But it's not recommended to use any wallet.
The purpose of a paper wallet is to keep the private key offline. If you import the private key of a paper wallet into any online wallet, it would defeat its purpose.

Whenever you want to make a transaction, you can import the private key into an offline computer and sign the transaction there. A good wallet allowing you to do so is electrum.
If you are interested to know how you can make a transaction without the private key touching the internet, you can read the following guide. It should help you know the correct use of a paper wallet.

How to spend from an offline paper wallet using Electrum

[crwth]

I was once like you, thinking it would be possible to generate the duplicate keys caused by someone else. Considering that you can hit the jackpot that has the lost bitcoins in store, but of course, it's all just a dream. Just like what the other member said, that number is so significant that there's no chance that you can recreate it.

If someone could have programmed that, you could bet your life savings that they have already done it, but no. It's just not plausible.

[IdMineThat]

First, thank you for your brains and info.

I think this link is what I was really looking for. The math behind it is what really interests me.
(Quite possible I completely failed at quoting you. Tried to be cool. (I'm probably not))

You can read more about private keys here:
https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html

I was once like you, thinking it would be possible to generate the duplicate keys caused by someone else. Considering that you can hit the jackpot that has the lost bitcoins in store, but of course, it's all just a dream. Just like what the other member said, that number is so significant that there's no chance that you can recreate it.

If someone could have programmed that, you could bet your life savings that they have already done it, but no. It's just not plausible.

It's not that I want to generate duplicate keys, I mean that would be really cool, but it's really for my personal assurance and understanding how it works. I'm just getting into mining, and the entire process really interests me.

Basically... My puny human brain can't possible fathom 2²⁵⁶ or 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935 and the security is derived by that number being so astronomically huge, that nobody can guess your number, unless it's a Douglas Adams book.

***bows in respect***

[Miguel 11th]

If bitaddress.org creates the public key and private key, where we can put that public/private keys? In any wallet/platform?

You can do that on any wallet supporting importing private keys. But it's not recommended to use any wallet.
The purpose of a paper wallet is to keep the private key offline. If you import the private key of a paper wallet into any online wallet, it would defeat its purpose.

Whenever you want to make a transaction, you can import the private key into an offline computer and sign the transaction there. A good wallet allowing you to do so is electrum.
If you are interested to know how you can make a transaction without the private key touching the internet, you can read the following guide. It should help you know the correct use of a paper wallet.

How to spend from an offline paper wallet using Electrum

Thank you Sir! As i'm very intrigued on doing that. So basically those physical bitcoins like in Casacius Coins with value, same thing they redeemed those with this kind of process?

And anyone could sell Physical Bitcoins?

[Poker Player]

Thank you Sir! As i'm very intrigued on doing that. So basically those physical bitcoins like in Casacius Coins with value, same thing they redeemed those with this kind of process?

And anyone could sell Physical Bitcoins?

I think you are confused. There is no such thing as a physical Bitcoin. There are coins that represent Bitcoin, which can be made of gold and other metals, but they are not Bitcoin, and besides, we could say that you have "physical" Bitcoin, if for example you have a paper wallet with the keys that you can import, as explained above, but in reality Bitcoins are not physical. They are not something you can touch.

[BlackHatCoiner]

If you find this interesting then here's something even more interesting:

As said by hosseinimr93, there are around^[1] 2²⁵⁶ valid keys, but the address' length is 160 bits^[2]. This means that there can only be 2¹⁶⁰ valid addresses. If you divide the total valid keys with the total valid addresses, you should get the correspondence of private keys to the same address.

2²⁵⁶ / 2¹⁶⁰ = 2⁹⁶.

This means that there are around 2⁹⁶ different private keys which correspond to the same address. So, each time you generate an address and export the private key, remember that there are more than 79 octillion others which are highly unlikely to be generated from any other person!


[1] The total valid keys aren't exactly 2²⁵⁶, but 2²⁵⁶ - 2³² - 977. It's the prime number P used for secp256k1. The curve is defined over the prime field of ℤ_P.
[2] For simplification let's take 1-of-1 legacy addresses.

[Miguel 11th]

Thank you Sir! As i'm very intrigued on doing that. So basically those physical bitcoins like in Casacius Coins with value, same thing they redeemed those with this kind of process?

And anyone could sell Physical Bitcoins?

I think you are confused. There is no such thing as a physical Bitcoin. There are coins that represent Bitcoin, which can be made of gold and other metals, but they are not Bitcoin, and besides, we could say that you have "physical" Bitcoin, if for example you have a paper wallet with the keys that you can import, as explained above, but in reality Bitcoins are not physical. They are not something you can touch.

I see I get it, sir. They just produce something (eg. metal coins, certificates) loaded with Bitcoins. And sell it to much higher value + loaded bitcoin quantity. Is it possible for a normal guy to make like that sir, but only a metal coin without bitcoin loaded? And how safe is that?

Thank you for the response sir.

[9-planet]

Paper wallet is simply known as a digital wallet, where the developer make it easier to all users, for example Ethereum wallet (ETH) address are one of the simple wallet address you can create through metamask platform and is well secure with private key to every users, and it can bridge across the other smart chain Network.

[hosseinimr93]

I think you are confused. There is no such thing as a physical Bitcoin

Miguel 11th is probably talking about Casascius physical bitcoins. They are something like a paper wallet.
In Casascius coins, there's a paper containing a private key inside the coin and you have to break the coin for accessing that paper.

I see I get it, sir. They just produce something (eg. metal coins, certificates) loaded with Bitcoins. And sell it to much higher value + loaded bitcoin quantity.

I don't think such physical coins are popular these days.
Even Casascius coins are no longer produced. If someone has an undamaged casascius coin now, may be able to sell that at a value higher than bitcoin price on market.

[Miguel 11th]

Thank you for the information, i'm just thinking somehow if how would i connect art with the idea of physical coin. Not something like NFT. Anyway thank you sir! GOd bless

[IdMineThat]

Just wanted to say thank you for everybody's feed back on this. I ended up printing $20 BTC notes for Christmas presents. Half of the people gave me the oh, thanks. Half of the people were really exciited.

Anyways, thanks for your help! It was a fun learning project.

[fillippone]

If they can generate offline, doesn't that mean that every possible public key and their corresponding private key already exist

You are right. They all do exist.

I tell you more, there is a website where you have all the private keys stored.
Try here:
www.keys.lol

If you are luck, you can find the private keys of my wallet, if you are luckier, you can find Micheal Saylor’s.

Read more here:

There are 2^256 private keys out there: how big is that number?

[Lucius]

I ended up printing $20 BTC notes for Christmas presents. Half of the people gave me the oh, thanks. Half of the people were really exciited.

This first half who was a bit disappointed would probably have reacted the same way and if you had given them a $20 bill, they were expecting something a little more expensive and tangible than some piece of paper with codes and numbers. The other half is probably excited to receive a unique gift regardless of its current value, and maybe for some of them, that gift will mean entering the world of Bitcoin.

From personal experience, I realized that there are a lot of people who are interested in Bitcoin, but they do not understand it and often have no one to ask to explain some things to them. Overall, you did a good experiment