Quote from: DannyHamilton on April 28, 2014, 01:12:54 PM

Quote from: C. Bergmann on April 28, 2014, 12:42:35 PM

Hi, me again with a stupid question about cryptography.

There are 2^160 possible public keys. This is quiet a lot, but it is not infinite.

No. There are 2²⁵⁶ possible public keys.
Public keys are a number between 0 and 2²⁵⁶.

There are 2¹⁶⁰ possible bitcoin addresses. This is because a bitcoin address is a 160 bit hash of a public key.
Bitcoin Addresses are a number between 0 and 2¹⁶⁰ (along with a version byte and 4 checksum bytes).

Quote from: C. Bergmann on April 28, 2014, 12:42:35 PM

But every combination of signs works as a private key, right? I can type
"tt" or I can type
"öööööööööööööööööööösööööööööööööööööööööööööööörtrrrrööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööööössssssssssssssssssssssssssssssssssssssssssskjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj"
And it's a private key.
I can use every word humankind made, every sentence which exists and even every block in every book and every page and so on.
Seems infinite to me.

No.

Valid private keys are 256-bit (2²⁵⁶) numbers between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141

Quote from: C. Bergmann on April 28, 2014, 12:42:35 PM

Isn't the logical solution that every public key must correspond to an infinite number ob private keys?

Since there are nearly 2²⁵⁶ private keys, and only 2¹⁶⁰ Bitcoin Addresses, each Bitcoin address has an average of approximately 2⁹⁶ private keys. I'm not sure if it has been proven yet that both SHA256 and RIPEMD160 are evenly distributed across the result set. If they aren't then some addresses may have additional private keys, while others have a few less.

Ok, thank you, I'm still a bit confused.
When I make a brainwallet on brainwallet.org I can type every passphrase I want, no matter how long it is (I tried it with one of my texts, ~6,000 signs). Ok, this is not a private key, but am I right that there is an infinite number of passphrases like this which fit to every address?

So every adress contains 2^96 public keys and also 2^96 private keys?

Doesn't this reduce the difficulty to bruteforce an adress?