<p>"Improbable" is an understatement.</p>

<p>There are 2<sup>256</sup> possible keys.  In the entire universe, there are estimated to be "<strong><em>only</em></strong>" 2<sup>100</sup> atoms.</p>

<p>So the odds of someone else ending up with the exact same address/key as you is far, far less than the same atom, out of the entire universe, being randomly picked twice.</p>

<p>If you are worried about an address collision, here are things that should be more worrisome:</p>

<ul>
<li>Gamma ray burst wiping out all life on earth.</li>
<li>Sun unexpectedly going Supernova</li>
<li>Rogue Blackhole swallowing the solar system</li>
<li>An asteroid hitting the earth <em>at the same time</em> as nuclear war breaks out.</li>
</ul>

<p>On the list of things to worry about, an address collision just does not show up.</p>

<hr>

<p>You say that "millions of people use Bitcoin and Bitcoin Wallets that use their own addresses use several addresses per day".  </p>

<pre><code>  100 Million of people 
  100 addresses per day
  365 days / year
* 200 years
-------------
Less than 1 Billion addresses used in the foreseeable future.
</code></pre>

<p>1 billion is about 2<sup>30</sup>.
Which means that in 200 years, the chance of a collision is somewhere around 1 in 2<sup>256-30</sup> or, 1 in 2<sup>226</sup>, which is <em>still</em> way more than atoms in the universe.</p>

<p>You're easily safe for at least 200 years. </p>

CC BY-SA 3.0
2018-01-12T23:41:07.193Z
[Slightly less than 2^256](https://bitcoin.stackexchange.com/questions/38108/order-of-group-of-points-of-secp256k1) keys, but 2^160 addresses and forgery only requires matching the address. Still infeasible.
dave_thompson_085
CC BY-SA 3.0
2018-01-13T00:31:38.583Z
How do you protect your paper wallet from mice nibbling on the paper?  As far as probabilities go, I'd be far more concerned with that than random number hits.
Cort Ammon
CC BY-SA 3.0
2018-01-13T00:33:00.087Z
Did you account for the birthday paradox in your last section?  I think the real probability of any collision occurring (for anyone, not just you) is 2^96.  We're at least getting down to the number of atoms in the universe.  Or, if we prefer to think in positive terms, the probability of *someone* having a collision happen in the next 200 years is equivalent to *you* winning the Powerball lottery 4 times in a row.
Cort Ammon
CC BY-SA 3.0
2018-01-13T15:29:14.707Z
Also, studying the [Large Bitcoin Collider](https://lbc.cryptoguru.org/trophies) project might make it seem more of a 'real' problem than one might distil from this answer.
bzeaman
CC BY-SA 3.0
2018-01-16T20:28:13.817Z
https://motherboard.vice.com/en_us/article/nzpv8m/the-large-bitcoin-collider-is-generating-trillions-of-keys-and-breaking-into-wallets  "the project has generated over 3,000 trillion private keys and ... has found ***three*** that contain bitcoin.";   "the brute force strategy they're using poses no threat to anybody's bitcoin."
abelenky
CC BY-SA 3.0
2018-01-16T21:02:00.210Z
@abelenky [More than 3 (10+)](https://lbc.cryptoguru.org/trophies) as of the writing of this comment.
Nate Diamond
CC BY-SA 3.0
2018-01-16T21:55:10.563Z
Nope, I only see 3.  The rest you see all note they are part of the "Puzzle Transaction", a sequence of addresses that was deliberately created as a puzzle in a non-secure manner, and is meant to be solved.
abelenky
CC BY-SA 3.0
2018-01-12T21:56:17.443Z
2018-01-12T22:23:48.867Z
2018-01-12T22:23:48.867Z
abelenky
<p>The generation of private keys is made randomly. Therefore, it is possible for someone to generate the same private key as you did. In your question, you <strong>heavily insisted</strong> that you did not want an answer on how improbable this is. The answer is : <strong>You cannot protect your paper wallet from someone having incredible chance and getting the same number generated as you did</strong>.If you do not trust the way private keys are generated, you should take a look at <a href="https://learncryptography.com/cryptanalysis/why-is-2-256-secure" rel="noreferrer">this article</a>.</p>

<blockquote>
  <p>So – for all those doubting the security of 2^256 collision chances, there’s the number: There is a 1 in over 115 quattuorvigintillion (that’s a 78 digit number) chance of finding a collision. This number is bigger than the number of atoms in the perceivable universe</p>
</blockquote>

CC BY-SA 3.0
2018-01-12T20:19:47.163Z
2018-01-12T20:19:47.163Z
Cedric Martens
<p>The idea of ignoring sufficiently small possibilities is fundamental to BitCoin, and if you have a problem with it, then you shouldn't be using BitCoin (or anything else that involves a finite password space). If someone were to simply create a forged transaction from your wallet, put it in a block, and find a hash for that block, being able to do that by random chance would be likelier than picking the same keys as you. Randomly choosing a name and social security number and having it match yours would be likelier. Randomly choosing a credit card number, expiration date, and cvv, and having it match yours would be likelier. You are waaaaaaaaay more likely to lose your BitCoins from your wallet being trampled by a zebra who's been spooked by lightning hitting someone who just won the lottery than from someone randomly choosing the same keys.</p>

<blockquote>
  <p>If you consider this a "stupid question", it apparently isn't, because Google has literally no results whatsoever about this. </p>
</blockquote>

<p>That logic is valid only if it is reasonable to expect Google to have answers to every stupid question.</p>

CC BY-SA 3.0
2018-01-12T23:24:35.067Z
2018-01-12T23:24:35.067Z
Acccumulation
<p>The <a href="https://lbc.cryptoguru.org/about" rel="nofollow noreferrer">Large Bitcoin Collider</a> was already mentioned in a comment, but it is worth mentioning in an answer also.</p>

<p>These are a group of people out there doing this now, going through random BTC private keys looking for wallets with money in them. So far they have found private key for three wallets, worth 0.0079 BTC, 0.0001 BTC and 0.00001 BTC. In addition they've found several keys related to a <em>puzzle transaction</em>, which apparently used intentionally guessable keys.</p>

<p>Their current search speed is 1550 Mkeys/s. If you have a single wallet with a random private key, this means that by average you'll be hit once every 3 · 10³¹ years. So for an individual user, the statistical risk is insignificant. There are 15 millions wallets with money in them, so even the chance of hitting <em>any</em> wallet is just once every 2 · 10²⁴ years. <strong>Their hits so far are much higher than this</strong>, which suggests not all keys are as random as one would expect. Someone may have even made the addresses intentionally for LBC to find, but no-one knows.</p>

<p><strong>The real risk</strong> is in your random generator that you used to generate your private key. A few years back, Debian's OpenSSL package <a href="https://en.wikipedia.org/wiki/Random_number_generator_attack#Debian_OpenSSL" rel="nofollow noreferrer">had a very bad random generator bug</a>. This made it trivial to guess all private keys generated with it, yet it took two years until the problem was publicly detected. I would be somewhat wary of using less commonly used or experimental software to generate private keys, a single bug could make the wallet easy to compromise.</p>

<p>But as long as you use a well designed software to generate the key, you should be safe.</p>

CC BY-SA 3.0
2018-01-13T19:56:47.407Z
2018-01-13T19:56:47.407Z
jpa
<p>What all of url don't realise is that is not impossible for hackers to brute the crap out of private keys, with computer processing increasing rapidly it's definitely not IMPOSSIBLE, to put the record straight, but then again that's vulnerability as being around since computers started to exist.</p>

CC BY-SA 3.0
2018-01-13T14:39:42.220Z
Yes, it is impossible.
abelenky
CC BY-SA 3.0
2018-01-13T12:56:03.260Z
2018-01-13T12:56:03.260Z
JoeyB
<p>Since millions of people use Bitcoin and Bitcoin Wallets that use their own addresses use several addresses per day, it is obvious that generators can generate the same characters for the Bitcoin address multiple times. So please therefore simply tell me how one would prevent others from accessing or spending the coins that are stored at my paper bitcoin address.</p>

CC BY-SA 3.0
2018-01-12T21:24:45.613Z
"that is improbable so therefore who cares": **This is the entire point!** Cryptography never makes anything truly impossible, but it can make it so improbable that you no longer worry about it happening.  You have to understand and accept this before you can go on to understand anything else.
Nate Eldredge
CC BY-SA 3.0
2018-01-12T23:40:20.580Z
My first Google result for "bitcoin address duplication" is https://bitcoin.stackexchange.com/questions/23268/what-if-duplicate-wallet-addresses-are-created which links to two additional dupes.
dave_thompson_085
CC BY-SA 3.0
2018-01-12T23:43:01.207Z
The point of ignoring probabilities here makes literally no sense. You could just as sensibly ask about physical money you held simply flying away spontaneously due to random atomic vibrations and quantum physics. Yes, it could happen, no, it wont.
Vality
CC BY-SA 3.0
2018-01-13T02:14:08.937Z
I could also spontaneously combust. Statistically SOMETHING could trigger it (I agree, super unlikely... but still). I don't carry a fire extinguisher with me just in case (and I assume you don't)... it's all about risk management and understanding what "1 in a trillion" (or whatever) really means. I am aware that in the world of bitcoin, it's FAR LESS than 1/trillion btw...
Patrice
CC BY-SA 3.0
2018-01-13T05:05:44.473Z
I think that "having a probability greater than 0" is a poor definition of "possible". After all, the probability that I will grow wings and become an airplane tomorrow is greater than 0, but that isn't the sort of thing you'd call *possible*, is it? So, don't be so sure that it's *possible* for someone else to end up with the same private key that you ended up with.
Sophie Swett
CC BY-SA 3.0
2018-01-13T12:13:20.177Z
try to focus on the question, not the rant. the current ‘question’ is 90% rant.
Aganju
CC BY-SA 3.0
2018-01-13T22:31:15.863Z
@Raven: try to edit your question into open–ended wording, and you might make it easier for the community to find a proper answer. Maybe the question should be „how possible is it to duplicate an address randomly“. There are roughly 20 posts on this forum here and in bitcointalk. They explain the math, and people would be more than happy to provide corresponding links. With you wording this is nearly impossible....
pebwindkraft
<wallet><address><security><private-key><coldstorage>
How do I protect my paper wallet from use by a different human who has used a random generator?
Raven
# How do I protect my paper wallet from use by a different human who has used a random generator?

(Asked by: username_0 on 2018-01-12)

Since millions of people use Bitcoin and Bitcoin Wallets that use their own addresses use several addresses per day, it is obvious that generators can generate the same characters for the Bitcoin address multiple times. So please therefore simply tell me how one would prevent others from accessing or spending the coins that are stored at my paper bitcoin address.

**Tags:** wallet, address, security, private-key, coldstorage

> **Comments:**
> **username_1**: "that is improbable so therefore who cares": **This is the entire point!** Cryptography never makes anything truly impossible, but it can make it so improbable that you no longer worry about it happening.  You have to understand and accept this before you can go on to understand anything else.  
> **username_2**: My first Google result for "bitcoin address duplication" is https://bitcoin.stackexchange.com/questions/23268/what-if-duplicate-wallet-addresses-are-created which links to two additional dupes.  
> **username_3**: The point of ignoring probabilities here makes literally no sense. You could just as sensibly ask about physical money you held simply flying away spontaneously due to random atomic vibrations and quantum physics. Yes, it could happen, no, it wont.  
> **username_4**: I could also spontaneously combust. Statistically SOMETHING could trigger it (I agree, super unlikely... but still). I don't carry a fire extinguisher with me just in case (and I assume you don't)... it's all about risk management and understanding what "1 in a trillion" (or whatever) really means. I am aware that in the world of bitcoin, it's FAR LESS than 1/trillion btw...  
> **username_5**: I think that "having a probability greater than 0" is a poor definition of "possible". After all, the probability that I will grow wings and become an airplane tomorrow is greater than 0, but that isn't the sort of thing you'd call *possible*, is it? So, don't be so sure that it's *possible* for someone else to end up with the same private key that you ended up with.  
> **username_6**: try to focus on the question, not the rant. the current ‘question’ is 90% rant.  
> **username_7**: @username_0: try to edit your question into open–ended wording, and you might make it easier for the community to find a proper answer. Maybe the question should be „how possible is it to duplicate an address randomly“. There are roughly 20 posts on this forum here and in bitcointalk. They explain the math, and people would be more than happy to provide corresponding links. With you wording this is nearly impossible....  

---

## 5 answers

### Answer by username_8 on 2018-01-12. Score: 14

"Improbable" is an understatement.

There are 2256 possible keys. In the entire universe, there are estimated to be "***only***" 2100 atoms.

So the odds of someone else ending up with the exact same address/key as you is far, far less than the same atom, out of the entire universe, being randomly picked twice.

If you are worried about an address collision, here are things that should be more worrisome:

* Gamma ray burst wiping out all life on earth.
* Sun unexpectedly going Supernova
* Rogue Blackhole swallowing the solar system
* An asteroid hitting the earth *at the same time* as nuclear war breaks out.

On the list of things to worry about, an address collision just does not show up.

---

You say that "millions of people use Bitcoin and Bitcoin Wallets that use their own addresses use several addresses per day".

```
  100 Million of people 
  100 addresses per day
  365 days / year
* 200 years
-------------
Less than 1 Billion addresses used in the foreseeable future.

```

1 billion is about 230.
Which means that in 200 years, the chance of a collision is somewhere around 1 in 2256-30 or, 1 in 2226, which is *still* way more than atoms in the universe.

You're easily safe for at least 200 years.

> **Comments:**
> **username_2**: [Slightly less than 2^256](https://bitcoin.stackexchange.com/questions/38108/order-of-group-of-points-of-secp256k1) keys, but 2^160 addresses and forgery only requires matching the address. Still infeasible.  
> **username_9**: How do you protect your paper wallet from mice nibbling on the paper?  As far as probabilities go, I'd be far more concerned with that than random number hits.  
> **username_9**: Did you account for the birthday paradox in your last section?  I think the real probability of any collision occurring (for anyone, not just you) is 2^96.  We're at least getting down to the number of atoms in the universe.  Or, if we prefer to think in positive terms, the probability of *someone* having a collision happen in the next 200 years is equivalent to *you* winning the Powerball lottery 4 times in a row.  
> **username_10**: Also, studying the [Large Bitcoin Collider](https://lbc.cryptoguru.org/trophies) project might make it seem more of a 'real' problem than one might distil from this answer.  
> **username_8**: https://motherboard.vice.com/en_us/article/nzpv8m/the-large-bitcoin-collider-is-generating-trillions-of-keys-and-breaking-into-wallets  "the project has generated over 3,000 trillion private keys and ... has found ***three*** that contain bitcoin.";   "the brute force strategy they're using poses no threat to anybody's bitcoin."  
> **username_11**: @username_8 [More than 3 (10+)](https://lbc.cryptoguru.org/trophies) as of the writing of this comment.  
> **username_8**: Nope, I only see 3.  The rest you see all note they are part of the "Puzzle Transaction", a sequence of addresses that was deliberately created as a puzzle in a non-secure manner, and is meant to be solved.  

---

### Answer by username_12 on 2018-01-12. Score: 4

The generation of private keys is made randomly. Therefore, it is possible for someone to generate the same private key as you did. In your question, you **heavily insisted** that you did not want an answer on how improbable this is. The answer is : **You cannot protect your paper wallet from someone having incredible chance and getting the same number generated as you did**.If you do not trust the way private keys are generated, you should take a look at [this article](https://learncryptography.com/cryptanalysis/why-is-2-256-secure).

> So – for all those doubting the security of 2^256 collision chances, there’s the number: There is a 1 in over 115 quattuorvigintillion (that’s a 78 digit number) chance of finding a collision. This number is bigger than the number of atoms in the perceivable universe


---

### Answer by username_13 on 2018-01-12. Score: 3

The idea of ignoring sufficiently small possibilities is fundamental to BitCoin, and if you have a problem with it, then you shouldn't be using BitCoin (or anything else that involves a finite password space). If someone were to simply create a forged transaction from your wallet, put it in a block, and find a hash for that block, being able to do that by random chance would be likelier than picking the same keys as you. Randomly choosing a name and social security number and having it match yours would be likelier. Randomly choosing a credit card number, expiration date, and cvv, and having it match yours would be likelier. You are waaaaaaaaay more likely to lose your BitCoins from your wallet being trampled by a zebra who's been spooked by lightning hitting someone who just won the lottery than from someone randomly choosing the same keys.

> If you consider this a "stupid question", it apparently isn't, because Google has literally no results whatsoever about this.

That logic is valid only if it is reasonable to expect Google to have answers to every stupid question.


---

### Answer by username_14 on 2018-01-13. Score: 1

The [Large Bitcoin Collider](https://lbc.cryptoguru.org/about) was already mentioned in a comment, but it is worth mentioning in an answer also.

These are a group of people out there doing this now, going through random BTC private keys looking for wallets with money in them. So far they have found private key for three wallets, worth 0.0079 BTC, 0.0001 BTC and 0.00001 BTC. In addition they've found several keys related to a *puzzle transaction*, which apparently used intentionally guessable keys.

Their current search speed is 1550 Mkeys/s. If you have a single wallet with a random private key, this means that by average you'll be hit once every 3 · 10³¹ years. So for an individual user, the statistical risk is insignificant. There are 15 millions wallets with money in them, so even the chance of hitting *any* wallet is just once every 2 · 10²⁴ years. **Their hits so far are much higher than this**, which suggests not all keys are as random as one would expect. Someone may have even made the addresses intentionally for LBC to find, but no-one knows.

**The real risk** is in your random generator that you used to generate your private key. A few years back, Debian's OpenSSL package [had a very bad random generator bug](https://en.wikipedia.org/wiki/Random_number_generator_attack#Debian_OpenSSL). This made it trivial to guess all private keys generated with it, yet it took two years until the problem was publicly detected. I would be somewhat wary of using less commonly used or experimental software to generate private keys, a single bug could make the wallet easy to compromise.

But as long as you use a well designed software to generate the key, you should be safe.


---

### Answer by username_15 on 2018-01-13. Score: -1

What all of url don't realise is that is not impossible for hackers to brute the crap out of private keys, with computer processing increasing rapidly it's definitely not IMPOSSIBLE, to put the record straight, but then again that's vulnerability as being around since computers started to exist.

> **Comments:**
> **username_8**: Yes, it is impossible.  

---

