PAPER WALLETS address and private key are created or were they already created?

[TonyHopper Criptomonedas]

Hello for those who do not know me I have a Youtube channel and I am researching to upload a video tutorial on PAPER WALLETS, it is very easy to create and use your own paper wallet.

The problem is to do it safely that if you take a minimum security measures you can not steal your BTC from your Paper Wallet.

But my question is this: "When I generate my pubic wallet address and my private key at the beginning of the paper wallet, are these addresses already created or are they created by the same paper wallet?"

I do not know if I have explained myself well because my language is Spanish, but it is still difficult to explain the question, because if you are given the option to create your public wallet address and your private key, WITHOUT INTERNET CONNECTION. So my question is if these addresses and passwords are already created before, because if you create them new, how can you create it without an Internet connection?

And if they are accounts created previously or not, another question is how do I know that nobody is going to receive my same private key due to coincidences of life? or that I receive the private key of some other person?


I hope you understand my questions and thanks in advance.

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[TryNinja]

ELI5: You don't need any internet connection because Bitcoin addresses/private-keys aren't stored anywhere (e.g: a server). The website is only using several cryptographic functions to generate a random private key (and public key) for you.

You should definitely read more before making Youtube videos.

https://en.wikipedia.org/wiki/Public-key_cryptography
https://en.bitcoin.it/wiki/Private_key
https://medium.com/@hlopez_/how-are-public-and-private-keys-created-in-bitcoin-f90b2b88f40a

And if they are accounts created previously or not, another question is how do I know that nobody is going to receive my same private key due to coincidences of life? or that I receive the private key of some other person?

You don't know. It's possible but extremely unlikely. The chances of an address collision between 1 billion users at 10 addresses each are approximately 0.000000000000000000000000000000000000684%; [source]

[theymos]

I like this analogy:

Imagine a massive wall of lockers. Each locker is 1mm by 1mm, and the entire wall of lockers is a square 2 light years on each side. When you choose a private key, you pick one of these lockers at random. When someone sends you bitcoins, there's some magical inbox which puts the bitcoins into your locker without telling the sender anything about the location of your locker.

The lockers don't have locks. If someone knew the location of your locker (ie. your private key), then they could just go take what's in it. Similarly, it's possible to choose a locker at random and find that someone has used it already at some point in the past. But there are just so many lockers that in reality it's never going to happen, even if humanity devotes all of its efforts to searching through all of the lockers.

[Piggy]

One other aspect that you should absolutely pay attention to is to generate paper wallet with trusted and established code, there have been cases where the private keys generated where not really randomly generated , either on purpose or because was just a mistake while coding.

So, short story short, doesn't really matter if you are online or offline, if you are using a weak paper wallet generator.

[TonyHopper Criptomonedas]

Thanks for replies i will check that urls to take more information

But my question is still standing: are the bitcoin addresses created as new or have they all been created and given to each new user at random?

[Piggy]

Thanks for replies i will check that urls to take more information

But my question is still standing: are the bitcoin addresses created as new or have they all been created and given to each new user at random?

They all exist already, and you can calculate a random private key out of all the possible one.

This is the total number of addresses that exists:

1 461 501 637 330 902 918 203 684 832 716 283 019 655 932 542 976

[TonyHopper Criptomonedas]

Thanks for replies i will check that urls to take more information

But my question is still standing: are the bitcoin addresses created as new or have they all been created and given to each new user at random?

They all exist already, and you can calculate a random private key out of all the possible one.

This is the total number of addresses that exists:

1 461 501 637 330 902 918 203 684 832 716 283 019 655 932 542 976

THANKS SO MUCH where you find that number of address existing?

[zenrol28]

THANKS SO MUCH where you find that number of address existing?

A bitcoin version 0 public key consists of a prefix "1" + 33 random characters (58 alphanumeric characters from small case, upper case letters and numbers 1-9, where "O" "0" "I" and "l" are excluded). So 33⁵⁸ = total public addresses existing and that would be for version 0 and there are other versions like multisig and segwit addresses. That's what i had read so far from my browsing the internet. You're questions are i think already available, you just have to search them. It might be boring to read them all but if you want to earn views and get paid by that platform, better DYOR and you will be amazed.

[Coding Enthusiast]

I like this analogy:

Imagine a massive wall of lockers. Each locker is 1mm by 1mm, and the entire wall of lockers is a square 2 light years on each side. When you choose a private key, you pick one of these lockers at random. When someone sends you bitcoins, there's some magical inbox which puts the bitcoins into your locker without telling the sender anything about the location of your locker.

The lockers don't have locks. If someone knew the location of your locker (ie. your private key), then they could just go take what's in it. Similarly, it's possible to choose a locker at random and find that someone has used it already at some point in the past. But there are just so many lockers that in reality it's never going to happen, even if humanity devotes all of its efforts to searching through all of the lockers.

But it is misleading, don't you think?
It is creating the false image that you are "receiving" coins in your key where in fact nothing is being delivered to you, but instead is stored on another place (the blockchain) and has a little link inside of it saying it belongs to your key.

I think a better analogy would be to call it a wall of keys like in a parking lot and the parking lot.
There is the same wall but it contains keys on it. then there is the parking lot (the blockchain) that contains cars (the transaction outputs). When someone sends you a car ("bitcoin"), they don't send it to "the wall" instead they send it to the "parking lot" and only change the key that opens the door of that car.

If someone knows where the key for a particular car in the parking lot is, they can go to that wall, take the key, open the car door and drive away.

[LoyceV]

I like this analogy:

Imagine a massive wall of lockers. Each locker is 1mm by 1mm, and the entire wall of lockers is a square 2 light years on each side. When you choose a private key, you pick one of these lockers at random. When someone sends you bitcoins, there's some magical inbox which puts the bitcoins into your locker without telling the sender anything about the location of your locker.

I like your analogy, but I think your math is off (or was it an estimate as a figure of speech)?
2 lightyear equals 1.892 * 10¹⁹ mm. A square wall gives 3.58 * 10³⁸ lockers.
There are 2¹⁶⁰ different Bitcoin addresses, which equals 1.46 * 10⁴⁸ possibilities.

As large as your locker wall is, you'll need 4 billion of those walls!

Allow me to create another analogy: imagine using quite large cubes as lockers, 1.2 meter on each sides. Now, build a cube instead of a wall, and it will be 1 lightyear on each side.
Try to imagine the size: 1 lightyear is 63240 times larger than the distance from the earth to the sun.

[theymos]

Any analogy is going to be imperfect and incomplete.

There are 2¹⁶⁰ different Bitcoin addresses, which equals 1.46 * 10⁴⁸ possibilities.

If someone is trying to attack the system, then the security is as if there are 2¹²⁸ distinct private keys, even though private keys are actually 256 bits long and pubkey-hashes are 160 bits long. Sometimes I say that there appear to be 2²⁵⁶ lockers, but that many of them actually share their internal spaces with many others (via wormholes/magic).

[LoyceV]

If someone is trying to attack the system, then the security is as if there are 2¹²⁸ distinct private keys, even though private keys are actually 256 bits long and pubkey-hashes are 160 bits long.

That does explain the factor 4 billion difference, but I don't understand why the security would be based on 2¹²⁸ and not 2¹⁶⁰.
Is that assuming 4 billion used addresses?

[theymos]

I don't understand why the security would be based on 2¹²⁸ and not 2¹⁶⁰.
Is that assuming 4 billion used addresses?

Partially it's because we're talking about two different situations. I'm thinking mainly of someone actively trying to attack ECDSA, and the lockers symbolize private keys, not addresses or public keys. You seem to be thinking mainly about two people accidentally generating the same address.

In symmetric crypto, if there are no other weaknesses, then a key length of N bits means that you have to search through O(2^N) keys in order to break the cipher. There is no faster way on classical computers. This sort of perfect cipher is used as the security standard for all crypto; when someone says that something has 128 bits of security, they mean that it has the same security as a perfect symmetric cipher with 128-bit keys. My analogy is meant to illustrate that breaking Bitcoin's ECDSA is roughly O(2¹²⁸).

All asymmetric crypto has worse security efficiency than the perfect symmetric cipher. In the case of elliptic-curve crypto, a key length of N bits implies an equivalent security (vis-à-vis the perfect symmetric cipher) of no more than N/2 bits because there are known algorithms for solving the underlying elliptic-curve discrete logarithm problem in O(sqrt(n)) on classical computers. (Also, it's completely broken on quantum computers.)

If you're interested in an attacker who only has an address to work with, without any ECC stuff (ie. unused addresses), then 2¹⁶⁰ is a reasonable number. If you're considering collisions, which cannot usually be useful to an attacker, then 2¹⁶⁰ is OK, but then you need to consider the birthday problem. If someone really wanted to find a collision, then it probably can be done in a human lifetime, but almost certainly they would collide two of their own addresses, not one of theirs with someone else's.

[TheArchaeologist]

But my question is still standing: are the bitcoin addresses created as new or have they all been created and given to each new user at random?

There is no massive database (or something like that) which holds all possible private keys and a new address is taken from there. Instead an address is generated at random, something which you could/should do locally.

In short and a bit simplified:
Truly Random Input -> SHA-256 -> Private Key
Private Key -> ECDSA ->Public Key
Public Key ->Add some  checks -> Encode with Base58 -> Bitcoin Address

If the input is truly random there is no way two of the same Private Keys will be generated. So go ahead, you can literally generate million of keys/addresses yourself to use without even a slight risk of finding one which has been found/used before.