Creating same priv. key two times

[Bitdonator]

After I made a paper wallet for long-term saving,
I start thinking about posibility that somone can create same priv. key
in their wallet in the future.

I know that posibility for this is very small, but it exist.
If someone want to create billions and billions private keys,
he can generate someone address with positive balance.

What you people think about that? This can become a big problem
for Bitcoin in the future... no?

I am a little scared 

[Amph]

it was already said multiple times that collision probability is so slim that it is more feasible for the universe to explode right now instead

anyway by splitting your balance among several addresses, you can prevent that you lose a big portion of it in the unlikely event that an unimaginable collision will come out...

[Hexcoin]

After I made a paper wallet for long-term saving,
I start thinking about posibility that somone can create same priv. key
in their wallet in the future.

I know that posibility for this is very small, but it exist.
If someone want to create billions and billions private keys,
he can generate someone address with positive balance.

What you people think about that? This can become a big problem
for Bitcoin in the future... no?

I am a little scared 

im thinking of that too, in the future it is possible to generate private keys for used address but when i knew the total possible address im thinking im could be dead if that thing happens. i've read somewhere in this forum than all possible address is greater than the number of dust in the world

[OnkelPaul]

So you bought this account just recently?
No way you could have been a bitcointalk member for 2 years without ever reading this frequently (asked/answered) question.

The risk is non-zero, but small enough that you don't need to bother (unless you're using software with a broken random number generator). If you bother about duplicate private keys, you should bother more about the possibility of being eaten alive by an ice bear or drowning in a soup bowl - both events are much more likely.

Onkel Paul

[Muhammed Zakir]

Given your example of 1 billion users at 10 addresses each:

There are 2^160 or about 1,460,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible addresses
In your scenario, 1,000,000,000 people are using 10 addresses each for a total of 10,000,000,000 possible addresses
10,000,000,000 / 2^160 should yield the probability of a collision occurring
10,000,000,000 / 2^160 = 0.00000000000000000000000000000000000000684

So the chances of a collision occurring in your scenario are approximately 0.000000000000000000000000000000000000684%

See why we don't consider collisions an issue?

The probability of a collision is found by a standard formula: p = 1 - k! / N^k-1(N-k)!, where k is the number of hashes generated (100x10¹⁰x10³) and N is the number of possible hashes (2¹⁶⁰).

This is a difficult number to calculate, but there is a good approximation: p = 1 - e^-k(k-1)/2N

But even that value is difficult to compute because of the precision needed. Here is another approximation p = k²/2N.

So the answer is that the probability of at least one collision is approximately 7x10^-19 or 0.00000000000000007%


See: http://preshing.com/20110504/hash-collision-probabilities

Ok, new data, will recalc everything:

• probability of getting struck by lightning in any given year: 1/280000.
• probability of taking a shit at any given point in time: 1/(60*24) = 1/1440 (assuming you take a crap every day and the actual process takes 1 minute)
• probability of getting struck by lightning while taking a crap in any given year: 1/(280000*1440) = 1/1.47E11 = 2.48E-9
• probability of taking a crap while being in a situation where being struck by lightning can actually occur = 1/1440 = 0.25 = 1.74E-4
• probability of finding a collision: 1E-65
• getting hit by lightning while taking a crap for how many years in a row is equally probable as finding a collision: log(1E-65) / log(1.74E-4) = 17.3

is my math roughly correct now?

If so, I can say: "Finding a collision is about as likely as being struck by lightning while taking a crap every year for 17 years in a row".

A graphical explanation of bitcoin security https://i.imgur.com/VjtG3.jpg

-snip-
What you people think about that? This can become a big problem
for Bitcoin in the future... no?

I am a little scared 

There is nothing to be scared of. Lucky guy get others' money. Isn't it cool?

[ClamCoin]

The chance is extremely low, you better worry how to keep your paper wallet safe & secure.
If you worry about it, split your bitcoin to multiple addresses or using multi-signature address

So if two people have the same private key, they have the same wallet??

[Bitdonator]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

[Bitdonator]

So you bought this account just recently?
No way you could have been a bitcointalk member for 2 years without ever reading this frequently (asked/answered) question.

The risk is non-zero, but small enough that you don't need to bother (unless you're using software with a broken random number generator). If you bother about duplicate private keys, you should bother more about the possibility of being eaten alive by an ice bear or drowning in a soup bowl - both events are much more likely.

Onkel Paul

No, its my account. I know about bitcoin for 3 years....
but never read / think before about this possible problem.

[ClamCoin]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

[Bitdonator]

Given your example of 1 billion users at 10 addresses each:

There are 2^160 or about 1,460,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible addresses
In your scenario, 1,000,000,000 people are using 10 addresses each for a total of 10,000,000,000 possible addresses
10,000,000,000 / 2^160 should yield the probability of a collision occurring
10,000,000,000 / 2^160 = 0.00000000000000000000000000000000000000684

So the chances of a collision occurring in your scenario are approximately 0.000000000000000000000000000000000000684%

See why we don't consider collisions an issue?

The probability of a collision is found by a standard formula: p = 1 - k! / N^k-1(N-k)!, where k is the number of hashes generated (100x10¹⁰x10³) and N is the number of possible hashes (2¹⁶⁰).

This is a difficult number to calculate, but there is a good approximation: p = 1 - e^-k(k-1)/2N

But even that value is difficult to compute because of the precision needed. Here is another approximation p = k²/2N.

So the answer is that the probability of at least one collision is approximately 7x10^-19 or 0.00000000000000007%


See: http://preshing.com/20110504/hash-collision-probabilities

Ok, new data, will recalc everything:

• probability of getting struck by lightning in any given year: 1/280000.
• probability of taking a shit at any given point in time: 1/(60*24) = 1/1440 (assuming you take a crap every day and the actual process takes 1 minute)
• probability of getting struck by lightning while taking a crap in any given year: 1/(280000*1440) = 1/1.47E11 = 2.48E-9
• probability of taking a crap while being in a situation where being struck by lightning can actually occur = 1/1440 = 0.25 = 1.74E-4
• probability of finding a collision: 1E-65
• getting hit by lightning while taking a crap for how many years in a row is equally probable as finding a collision: log(1E-65) / log(1.74E-4) = 17.3

is my math roughly correct now?

If so, I can say: "Finding a collision is about as likely as being struck by lightning while taking a crap every year for 17 years in a row".

A graphical explanation of bitcoin security https://i.imgur.com/VjtG3.jpg

-snip-
What you people think about that? This can become a big problem
for Bitcoin in the future... no?

I am a little scared 

There is nothing to be scared of. Lucky guy get others' money. Isn't it cool?

Muhammed thank you for all this info =)

[Bitdonator]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Yes, this site is real.
Do we have to worry?

maybe yes, maybe no 

[ClamCoin]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Yes, this site is real.
Do we have to worry?

maybe yes, maybe no 

But with a private key you can acces the wallet or not?

[Bitdonator]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Yes, this site is real.
Do we have to worry?

maybe yes, maybe no 

But with a private key you can acces the wallet or not?

You have acces only to ballance in that address, not all bitcoins
from addresses placed in same wallet

[medUSA]

So you bought this account just recently?
No way you could have been a bitcointalk member for 2 years without ever reading this frequently (asked/answered) question.

I have been on the forum a long time, have seen this brought up frequently. I KNOW the standard answer is "extremely unlikely". It doesn't mean  I am convinced by this standard answer. "Extremely unlikely" doesn't bring much sense of safety to be honest.

I understand why OP is suddenly worried after 2 years of using bitcoin. Because 2 years is about the time when he accumulates enough bitcoin to be worried about loosing it.

Someone already create www.directory.io
but I think this site is only prank

So is it his website real or just fake?
Do we have to worry about is?

It's fake. I have read from somewhere that the site only calculates the address from keys when someone click on the link.

[OnkelPaul]

So you bought this account just recently?
...
Onkel Paul

No, its my account. I know about bitcoin for 3 years....
but never read / think before about this possible problem.

I was basically kidding you :-)
(although a bought account seemed like a remote possibility, too)

The info posted by Muhammed Zakir is pretty extensive and should answer all the concerns around "possibilities".
One thing that must be understood about low probabilities is that astronomically low probabilities (for example, for private key collisions) are for all practical purposes equal to "can't happen", but mathematically they are still not zero. This often confuses people who never deal with really large numbers.

Onkel Paul

[shorena]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Its real, but you dont have to worry about it. They dont have a database with all keys (there is not enough storage space on the planet for that), they just generate them on the fly.

The chance is extremely low, you better worry how to keep your paper wallet safe & secure.
If you worry about it, split your bitcoin to multiple addresses or using multi-signature address

So if two people have the same private key, they have the same wallet??

No, wallet is the software that handles the private keys for you.

[ClamCoin]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Its real, but you dont have to worry about it. They dont have a database with all keys (there is not enough storage space on the planet for that), they just generate them on the fly.

The chance is extremely low, you better worry how to keep your paper wallet safe & secure.
If you worry about it, split your bitcoin to multiple addresses or using multi-signature address

So if two people have the same private key, they have the same wallet??

No, wallet is the software that handles the private keys for you.

So the website is useless?

Or for what do they use private keys than?

[shorena]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

So is it his website real or just fake?
Do we have to worry about is?

Its real, but you dont have to worry about it. They dont have a database with all keys (there is not enough storage space on the planet for that), they just generate them on the fly.

The chance is extremely low, you better worry how to keep your paper wallet safe & secure.
If you worry about it, split your bitcoin to multiple addresses or using multi-signature address

So if two people have the same private key, they have the same wallet??

No, wallet is the software that handles the private keys for you.

So the website is useless?

Well you can use it to generate private keys if you want. Its also very informative with the right information and you can test yourself how likely it is to find a used private key.

Or for what do they use private keys than?

They dont store any private keys, thus they cant use them. Thats the "fake" part others are talking about. You go to a specific page e.g. 1 and have there listed the private keys from #0 to #19 because they show 20 (the actual number is probably different) keys per page. If you pick the 3rd key from the top of page 42 you have the private key that is representing the number 20*42+3 = 843. Private keys are just that, numbers. Your chance to find a used private key while browsing that page is very low. The keys on the first few pages are the exception because some people thought it was a smart idea to use the private key #1 or #8 or #13 or #17 or #42 or #666 or any other number humans tend to apply higher meaning to.

[Bitdonator]

This website also generate and publish private keys.  www.coinfind.cf
New archive with 100,000 priv. keys are published every day.

But seems like this is for good reason, creator of that website
drop some BTC to 5 addresses for others to find.

 

[pooya87]

Someone already create www.directory.io
but I think this site is only prank

Its good that guy who make this site didnt
implement address search option

This website also generate and publish private keys.  www.coinfind.cf
New archive with 100,000 priv. keys are published every day.

But seems like this is for good reason, creator of that website
drop some BTC to 5 addresses for others to find.

 

directory.io is an old prank.
it doesn't actually contain all of the private keys despite the fact that it might seems like it.
it creates private keys on the spot as you brows through the pages.

go to https://brainwallet.org/ and you can do this too, put 0000000000000000000000000000000000000000000000000000000000000001 in the "Secret Exponent" section and add +1 every time for bijillion times and you have all the private keys too.

p.s. stop visiting shady websites, you are going to be infected by malware or something.