Paper wallet safety and randomness

as you know you move around the cursor to create a unique wallet but how safe is it? we talk about new people joining etn everyday and creating a paper wallet takes almost 10 seconds. how random is it? i think it’s not impossible to create someone else’s wallet. i checked bitcoin paper wallet as well on an open source site, it took near 1 minute to create the wallet. can you make an explanation what’s the possibility of create an already existing wallet. it won’t warn if it’s created, you know this is called offline.

Perhaps one of the Electroneum developers will chime in on the exact numbers…

…but in the meantime, think about it this way… what do you think the chances are of someone doing the exact same mouse movements at the exact moment in time (plus any other randomisation it has on top of that) in order to generate the same key?

It’s always good to question things like this… but in this case… the chance of an intersection is at a level that makes it mathematically impossible.

Now obviously that doesn’t cater for user error (i.e. malware on computers, non-official version downloaded or improper storage of the keys etc)… but the generation itself is more than safe.

Hopefully someone like @Chris_ETN or @andrepatta see the thread and offer more specifics…

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absolutely i know it’s a slight possibility but a mathematical expression would be great!

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64 characters of 1234567890 and abcdefghijklmnopqrstuvwxyz gives this amount of possibilities:

1,157,920,892,373,161,954,235,709,850,086,879,078,532,699,846,656,405,640,394,575,840,079,13,129,639,936

What ever gazillions that is!! The wallet address is 128characters which would multiply that amount above A LOT!

So in terms of math this security of this is as good as anything can get in math!

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I wouldn’t worry, our sun will have burnt out long before anyone creates a duplicate. :wink:

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that’s the number of combinations of each wallet. i was talking about moving the cursor in a rectangle area which is way harder to calculate. we should invite a math professor to calculate this lol

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after this happens sun will create a duplicate itself too

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Wow … now thats a number :rofl::rofl::ok_hand:

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I’m sure someone will correct me if I’m wrong, but I believe the mouse movement is just part of the entropy (i.e. additional randomisation). It will also be using a random number generator on top of that…

As i said, super safe :blush:

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didn’t know it is additional that’s great

Basically what you’re doing when you’re moving your mouse is , you’re using a Cryptographically Secure Pseudorandom Number Generator.(CSPRNG)

Let’s say you drew a square using your mouse of sides 100 pixels.
Now , imagine a pixel , a very tiny dot on the screen.
So for a person to draw the exact same square of same dimensions is very very difficult , he’d probably need very very steady hands.
And since a pixel is a minute thing on the screen , there’s a very small probability of another person drawing the same exact pattern.

Now in terms of cryptography ,

As BegaMutex said , you’re using a number generator.

The number generator creates a number.On top of entropy , once a hashing function is applied on top of the generated number , the probability of getting the same number is close to impossible.

Cryptocurrencies use Elliptic Curve cryptography, so the private key you generate is a point on an ellipse and once a hashing function is applied , you get another point on the same ellipse which gives your wallet address.
All the private keys have a unique co-ordinate on the ellipse.
The math works one way , so you can’t have somebody generate your private key from a public key.

As far as until now , there’s been no case where a CSPRNG has generated the same private key and it’s highly , highly unlikely in the future.
And as you said it’s not impossible , but it is very close to impossible.

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To give you another idea ,
The number of possible Bitcoin wallets is greater than the number of atoms in the universe.(10^82)

So you might as well consider the probability to be 0.

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