Bitcoin address

[Basel636ghazal]

Assuming a btc address begins with bc
Like this address
bcxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
and assuming x is a number or a letter
so there are 1.78689910E + 62 potentially created addresses
how recurrence does not occur when creating BTC addresses?
and after creating 1.78689910E + 62 address what will happen?

[mocacinno]

Well... a bech32 address is basically a hash of the public key that's derived from the private key.

So, if you find a private key where the hash of the public key is equal to an address that was previously funded, you'll be able to spend the funds funding said address EVEN if the funds don't actually "belong" to you.

What you are talking about is key collision... It's theoretically possible, however, the odds are sooooooooo small, they're so close to 0 that in reality you can assume key collision is impossible IF the private key was generated properly.

In other words: it's not like you're "receiving" an address from a central institution, and if this institution runs out of addresses to pass out there'll be problems. The correct situation is:

• your wallet generates a completely random private key (or it derives a private key from a master private key)
• your wallet derives the public key from the private key
• your wallet hashes the public key and the endresult is your address

Here's an interesting read as to how bech32 addresses are generated: https://bitcointalk.org/index.php?topic=4992632.0

[Basel636ghazal]

the odds are sooooooooo small, they're so close to 0 that in reality you can assume key collision is impossible IF the private key was generated properly.

Why the odds is close to 0?
And after creating 1.78689910E + 62 address i think there can be more than one private key or mnemonic phrase that leads to the same address

[mocacinno]

Why the odds is close to 0?
And after creating 1.78689910E + 62 address i think there can be more than one private key that leads to the same address

https://github.com/JeanLucPons/VanitySearch

A vanitygen program like this one (GPU) can create up to ~200.000.000 private keys => addresses per second.

https://bitcointalk.org/index.php?topic=24268.msg41803506#msg41803506

the address space is 2^160

This means it would take your gpu
23171956451847141650870193314249 years to generate all private key => addresses

Since the sun will exist
11000000000 years,
It'll take about 21.065.414.956.224.674.228.063 suns to scan the keyspace.

Even if you want to scan only 1% (so you have a 1% chance of finding a funded address'es private key) and you own 1 million GPU's, it'll still take the lifetime of 210654149562246 suns

So, yes, i'd call those odds close to 0

Things change when you use a flawed RNG.

[Basel636ghazal]

https://github.com/JeanLucPons/VanitySearch

A vanitygen program like this one (GPU) can create up to ~200.000.000 private keys => addresses per second.

https://bitcointalk.org/index.php?topic=24268.msg41803506#msg41803506

the address space is 2^160

This means it would take your gpu
23171956451847141650870193314249 years to generate all private key => addresses

Since the sun will exist
11000000000 years,
It'll take about 21.065.414.956.224.674.228.063 suns to scan the keyspace.

Even if you want to scan only 1% (so you have a 1% chance of finding a funded address'es private key) and you own 1 million GPU's, it'll still take the lifetime of 210654149562246 suns

So, yes, i'd call those odds close to 0

Things change when you use a flawed RNG.

Oh great
Thanks for the clarification