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I learned that addresses are generated like this: privatekey->publickey->address. so, the uniqueness of the address depends on the uniqueness of private key. And private key is just a random number with a pretty big range. So, we can assume it will be unique, but it is not guaranteed.

In metamask wallet we can see that we have same private key and address for all the networks(e.g: eth, bnb, polygon etc).

So, how it is determined that my eth private key and address is not yet created by another person in any other EVM based network(e.g: polygon, BSC etc). Is there any relation with MAC address while generating the private keys for uniqueness?

If no relation with mac address, if the private key's uniqueness is the big range of random number, then, is there any possibility to match my private key and address with another person?

Does anyone have clear knowledge about this and can share? I will be so grateful.

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No, nothing except a random number is used to generate a private key. There is an extremely small chance that your private key would map to the same address as another private key, and there is also an extremely small chance that someone would randomly generate a private key you currently control. The chances are so small that these scenarios are for all practical purposes assumed to be impossible.

The address for your private key is the same on all of these networks because you are using the same private key, and they are using the exact same signature scheme that Ethereum is - so, your private key maps to the same public key, and the public key is used to generate the address.

You can read more on the chances of private key collissions here:

Ethereum addresses are 160 bit hashes, meaning there are 2^160 possible hashes. Per the birthday problem, the chance of a collision rises to 50% when there are about 2^80 accounts created.

To give you an idea of how unlikely that is, if every person on earth spent all their time doing nothing but generating Ethereum accounts, and they generated one a second, they'd only generate about 2^57 of them. To generate 2^80 and reach a 50% probability of finding a collision, they'd need to keep on generating one per second for about 8 million years.

-- https://ethereum.stackexchange.com/a/4300/105363

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