Can we please stop saying that it is improbable to generate an inuse key?

[rme]

Bitcoin addresses (2¹⁶⁰)
1461501637330902918203684832716283019655932542976

Earth Population
7218626512

Bitcoin addresses per person in Earth
202462564713848561306988538198010461031

Thats Two and two quintillion, four hundred sixty two quadrillion, five hundred sixty four trillion, seven hundred thirteen billion, eight hundred forty eight million, five hundred five thousand,  hundred thirty eight hundred-quintillionths

[1714468749]

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[1714468749]

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[1714468749]

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[1714468749]

1714468749

[Remember remember the 5th of November]

Facts and maths are great, but you never know do you!

That's why I've had my vanitygen running on the satoshi wallets since 2011.  

Lol @ vanitygen. I've written a much optimized version. With 30k addresses, it generates AND compares with 33 million keys per second on the CPU. Vanitygen is much slower.

[DeathAndTaxes]

In time there will be collisions because the probability is not 0. However, not only do you have to match an in-use key, that key also has to carry a balance.

In depends on what you mean by "time".  If given an infinite amount of computing power, an infinite amount of storage space and an infinite amount of time.  However under more realistic constrainsts you may never see a 160 bit collision before the heat death of the universe.  So saying "there will be collisions" especially the plural is dubious.  There may eventually be a collision but even that isn't guaranteed.

[DeathAndTaxes]

Facts and maths are great, but you never know do you!

That's why I've had my vanitygen running on the satoshi wallets since 2011. 

Lol @ vanitygen. I've written a much optimized version. With 30k addresses, it generates AND compares with 33 million keys per second on the CPU. Vanitygen is much slower.

Which for the purpose of this dubious scenario is like the guy with a bucket emptying the ocean laughing at the guy with a teaspoon trying to do the same thing.

[Remember remember the 5th of November]

Facts and maths are great, but you never know do you!

That's why I've had my vanitygen running on the satoshi wallets since 2011.  

Lol @ vanitygen. I've written a much optimized version. With 30k addresses, it generates AND compares with 33 million keys per second on the CPU. Vanitygen is much slower.

Which for the purpose of this dubious scenario is like the guy with a bucket emptying the ocean laughing at the guy with a teaspoon trying to do the same thing.

Even so, my version is on the CPU and is therefore much efficient than a GPU which uses more watts. The key to this optimization is that I skip the base58 phase and use the RIPEMD160 hash and compare the bytes in a boolean expression. This way I also don't need to use PCRE ot strcmp. On my i5-4670k I do 33 million keys per second(which are compared to the list of 30k addresses) per thread.

The only downside is this method requires a list of keys in a file, they are supplied in base58 format and inside they are decoded back to their RIPEMD160 states.

[RodeoX]

It is improbable to generate an inuse key. That is a fact.

[Walter Rothbard]

Given enough time some miner will eventually solo mine a series of 1000 blocks, one-second apart.  The probability is not zero, so it'll eventually happen, right?

[drrussellshane]

It is improbable to generate an inuse key. That is a fact.

This ^

It *is* improbable.

[tkbx]

I don't think you fully understand how large 2^256 is:

[imgremoved]http://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg[/imgremoved]

"B-but it's only got 4 digits, it can't be that big!"

[franky1]

i think the OP is trying to make the point that if there are
1000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000
privkeys (i know i know i have not done enough zeros.. its an example)

but a rndom generator only deals with a length of
1000000000000000000000000000000000000000000000

then everyones address would be somewhere between
1 and 1000000000000000000000000000000000000000000000

leaving the other keys above the 1000000000000000000000000000000000000000000000 never touched

[whtchocla7e]

I don't think you fully understand how large 2^256 is:

I don't think you fully understand how insignificant this is to my algorithm.
Oh boy... 

[taturii]

Facts and maths are great, but you never know do you!

That's why I've had my vanitygen running on the satoshi wallets since 2011.  

Lol @ vanitygen. I've written a much optimized version. With 30k addresses, it generates AND compares with 33 million keys per second on the CPU. Vanitygen is much slower.

2^256 is approx. 10^77, the age of our universe is 4x10^17 s approx. Even if you had a trillion machines (10^12) generating 100 million addresses per second since the big bang you would cover the 0.00000000000000000000000000000000000000001% of the 256 bit configuration space. It is more likely that a frappuccino pass through Mark Karperles by tunnel effect.

Edit: if we only consider the 160-bit space corresponding to the public key hash. The same trillion machines working since the Big Bang would only cover the 0.000000000001%, so it can be safely said that generating used keys is improbable.

[Peter R]

In time there will be collisions because the probability is not 0. However, not only do you have to match an in-use key, that key also has to carry a balance.

I don't think people realize how much is "possible" if you only include P=0 events as impossible.  

For example, the laws of physics are reversible.  Video record someone "breaking" the triangular group of pool balls, as the balls scatter into an unorganized state.  Now play this recording backwards and watch the balls all converge to the organized triangle, popping the cue ball back against the player's cue.  Calculate the physics of every collision for the "backwards event" and you'll see that no laws of physics were violated.  The "backwards event" is possible.  

But you won't be able to make it happen!!

For any event that can happen (e.g., cracking an egg), the backwards event can also happen with some probability (uncracking an egg).  It is just so vastly improbable that physicists assume it will never happen and call this the "Second Law of Thermodynamics."  But it's not a law at all--it's just a bold statement that extremely unlikely events do not actually happen.  

[franky1]

do you know the probability of life being created on any planet in the universe.
now
multiply that by the probability of that life being more then just a 1 celled organism
multiply that by the probability of that life having different abilities, such as swimming, flying walking
multiply that by the probability of that life gaining intelligence to communicate with each other (like birds)
multiply that by the probability of that life gaining intelligence to communicate with each other to such an extent that they can work together to do things.
multiply that by the probability of that life gaining intelligence to communicate with each to learn how to make objects like axes and clubs(Neanderthals)
multiply that by the probability of that life gaining intelligence to develop even further to then make computers to automate tasks

now you probably have a very large number, which is right.. we are an improbable number, that many things had to combine in the right way for it to happen.

... yet 7 billion of us all have the same ability to walk talk and build.

,, nothings impossible, just improbable

[RodeoX]

I don't think any of us have to worry. This can be mitigated by the much greater probability that there is pirate gold buried in your backyard. The chances of a treasure chest in your yard from a privateer must be many times greater than an encryption collision. So relax, if your key is generated by another peer you can just start looking for the treasure.

[Beliathon]

There are more possible private keys than there are grains of sand on Earth.

Is a collision possible? Certainly.

Is it going to happen in your lifetime? Not a chance.

The chances of a treasure chest in your yard from a privateer must be many times greater than an encryption collision. So relax, if your key is generated by another peer you can just start looking for the treasure.

I think I'm in love with you.

[Lauda]

People still realize how wide the spectrum is for a collision. Therefore we must use words like improbable.
Let me steal something: Now ←-------------- Very Soon -------- Soon -------- Soon-ish ---------------→ End of Time
Now, it's possible that one collision might Soon-ish.

The chances of a treasure chest in your yard from a privateer must be many times greater than an encryption collision. So relax, if your key is generated by another peer you can just start looking for the treasure.

Good one, mate.

[BadBear]

You should be much more worried about being hit by an asteroid.

[Skoupi]

Facts and maths are great, but you never know do you!

That's why I've had my vanitygen running on the satoshi wallets since 2011.  

Dat genius

[Ekaros]

I think vector of attacking a the RNG is much more interesting...

That is probable attack vector if you know the implementation and hardware. I don't think many use truly random generation in key generation... At current levels of power and computing this isn't feasible, but it might be at some point...