Quote from: no name on December 03, 2013, 01:46:26 PM

I have one brainwallet question for crypt/math gurus, please.

I found that 2^256 private keys, they only map to 2^160 unique wallet addresses. Could SHA-256(whatever) map whole set of possible private keys or only its subset? And what is dimension of that subset?

I'm googled few days but without success.

thanks in advance!

I don't know if anyone has determined yet if the result set of SHA-256 actually includes every number from 0 to 2²⁵⁶. I suppose it may be possible that there are some private keys that SHA-256 will never create no matter what input is used.

Furthermore, since addresses are the result of finding an ECDSA public key from the private key, then calculating RIPEMD-160(SHA-256(public key)), and it's possible that any of those three functions (ECDSA, RIPEMD, SHA) may have result sets that do not include every number in their respective ranges, it is quite possible that the complete result set of addresses that can be generated from using SHA-256 to create a private key is less than 2¹⁶⁰ possibilities.