What are the chances of an address collision? and what happens when it does?

[drawingthesun]

Here is a way to get an address collision in just under a minute:

Step 1: Grab every human on the planet.
Step 2: Convert each of their atoms into a little computer that can generate a new Bitcoin address every 1/10^9 seconds (A billion addresses per second)
Step 3: You will consume the entire search space within 30 seconds.
Step 4: Profit.

Workings:
Bitcoin addresses: 2^160.
Amount of atoms in an average size human (70kg): 7 X 10^27 atoms
Human population: 7.22 billion people.
Addresses generated each second: 1 billion.

[molecular]

Here is a way to get an address collision in just under a minute:

Step 1: Grab every human on the planet.
Step 2: Convert each of their atoms into a little computer that can generate a new Bitcoin address every 1/10^9 seconds (A billion addresses per second)
Step 3: You will consume the entire search space within 30 seconds.
Step 4: Profit.

Workings:
Bitcoin addresses: 2^160.
Amount of atoms in an average size human (70kg): 7 X 10^27 atoms
Human population: 7.22 billion people.
Addresses generated each second: 1 billion.

I think you just found ALL POSSIBLE collisions. Congrats on owning all bitcoins, too (present and future).

[smaxz]

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%

that's for the collision of a specific address correct?

what if you were to continually generate addresses (and thus privkeys) hoping to collide with another random address which holds funds.

i would imagine as the pool of addresses used by the general population increases, the chances of collisions occurring will increases likewise.

[BitcoinjunkieZ]

What do you exactly mean by collision?
I mean is there an point out of building adresses without connected to the network? i think no..

[smaxz]

What do you exactly mean by collision?
I mean is there an point out of building adresses without connected to the network? i think no..

build addresses and check balances against any block explorer, import the generated privkey on any collisions to siphon funds.

its cold calling with an extra step but anyone who ran toneloc back in the day will tell you that the law of averages is pretty unrelenting.

[odolvlobo]

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%

that's for the collision of a specific address correct?
what if you were to continually generate addresses (and thus privkeys) hoping to collide with another random address which holds funds.
i would imagine as the pool of addresses used by the general population increases, the chances of collisions occurring will increases likewise.

That is the probability of the same address being generated by two different wallets, assuming that all generated addresses are all used. It is not the same as simply generating an address that is currently in use.

The maximum theoretical probability can be computed. Suppose bitcoins are maximally distributed such that each address holding bitcoins contains only 1 satoshi. There would be 2.1 quadrillion addresses in use (or about 2⁵¹).

The maximum odds of a collision occurring while distributing the 2.1 quadrillion satoshis is approximately (2⁵¹)² / (2 * 2¹⁶⁰), or

1 in 2⁵⁹, or 1 in 576460752303423488

That is an incredibly small number.

Once the satoshis are distributed, the odds of generating a single address that is already in use is 2⁵¹ / 2¹⁶⁰, or

1 in 2¹⁰⁹, or 1 in 649037107316853453566312041152512

These are the highest possible odds of a collision.

Suppose you are trying to steal satoshis by brute force and you hope to crack one of the 2.1 quadrillion addresses per year. What kind of hash rate do you need? Well, you need to check 2¹⁰⁹ private keys per year (31556926 seconds), or

2.1x10²⁵ checks per second

Note that 2.1x10²⁵ is about 24 million times the total Bitcoin hash rate (though the two rates are not directly comparable)

[smaxz]

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%

that's for the collision of a specific address correct?
what if you were to continually generate addresses (and thus privkeys) hoping to collide with another random address which holds funds.
i would imagine as the pool of addresses used by the general population increases, the chances of collisions occurring will increases likewise.

That is the probability of the same address being generated by two different wallets, assuming that all generated addresses are all used. It is not the same as simply generating an address that is currently in use.

The maximum theoretical probability can be computed. Suppose bitcoins are maximally distributed such that each address holding bitcoins contains only 1 satoshi. There would be 2.1 quadrillion addresses in use (or about 2⁵¹).

The maximum odds of a collision occurring while distributing the 2.1 quadrillion satoshis is approximately (2⁵¹)² / (2 * 2¹⁶⁰), or

1 in 2⁵⁹, or 1 in 576460752303423488

That is an incredibly small number.

Once the satoshis are distributed, the odds of generating a single address that is already in use is 2⁵¹ / 2¹⁶⁰, or

1 in 2¹⁰⁹, or 1 in 649037107316853453566312041152512

These are the highest possible odds of a collision.

Suppose you are trying to steal satoshis by brute force and you hope to crack one address per year. What kind of hash rate do you need? Well, you need to check 2¹⁰⁹ private keys per year (31556926 seconds), or

2.1x10²⁵ checks per second

Note that 2.1x10²⁵ is about 24 million times the total Bitcoin hash rate (though the two rates are not directly comparable)

very concise response, thank you..

although it seems we're still looking at thousands of thousands of years before a rational possibility of collision in maximum scenario (without 24x bitcoins current network capabilities;) it's still a bit unsettling that the possibility is out there.

maybe food for thought in not holding all of ones funds in a single address.

[odolvlobo]

although it seems we're still looking at thousands of thousands of years before a rational possibility of collision in maximum scenario (without 24x bitcoins current network capabilities;) it's still a bit unsettling that the possibility is out there.

maybe food for thought in not holding all of ones funds in a single address.

The chances of the Earth being hit by an asteroid are much much much higher. If 1 in 2⁵⁹ unsettles you, then I suggest you start digging a bunker now. I apologize if I just caused you to become unglued.

This video is always appropriate to this discussion: https://www.youtube.com/watch?v=KX5jNnDMfxA

[smaxz]

a privkey rules an address no matter the salt. you can use that privkey to import the addresses funds to any wallet on any computer.

it doesn't hurt or cost anything to split your funds into a few address, thus minimizing your exposure of being struck by lightning in this sort of attack.

[odolvlobo]

a privkey rules an address no matter the salt. you can use that privkey to import the addresses funds to any wallet on any computer.

it doesn't hurt or cost anything to split your funds into a few address, thus minimizing your exposure of being struck by lightning in this sort of attack.

According to this, the odds of you being struck by lightning in the U.S. each year is

1 in 960000

If the entire Bitcoin network devoted all of its hashing power to guessing your private key (assuming 1 million trillion checks per second), then the odds each year of someone generating your private key are

1 in 31557600000000000000000000

In other words, you are 32872500000000000000 times more likely to be struck by lighting.

Even if someone were able to generate 2¹⁰⁹ addresses per year, you are still about 2 billion times more likely to be struck by lightning in a year.

The cost of doing anything to minimize your risk (including even discussing it) is greater than the risk of doing nothing.

[smaxz]

a privkey rules an address no matter the salt. you can use that privkey to import the addresses funds to any wallet on any computer.

it doesn't hurt or cost anything to split your funds into a few address, thus minimizing your exposure of being struck by lightning in this sort of attack.

According to this, the odds of you being struck by lightning in the U.S. each year is

1 in 960000

If the entire Bitcoin network devoted all of its hashing power to guessing your private key (assuming 1 million trillion checks per second), then the odds each year of someone generating your private key are

1 in 31557600000000000000000000

In other words, you are 32872500000000000000 times more likely to be struck by lighting.

Even if someone were able to generate 2¹⁰⁹ addresses per year, you are still about 2 billion times more likely to be struck by lightning in a year.

The cost of doing anything to minimize your risk (including even discussing it) is greater than the risk of doing nothing.

wow you really like writing zero's

what are the odds of being struck by lightning twice in a lifetime? has that happened?

theorizing and intellectual conversation are always a worthy endeavor.