Post
Topic
Board Bitcoin Technical Support
Merits 19 from 4 users
Re: Address without public key and private key?
by
DannyHamilton
on 07/03/2025, 16:14:35 UTC
⭐ Merited by LoyceV (6) ,vapourminer (6) ,ABCbits (5) ,Catenaccio (2)
maybe ratio 1:2 between hash sha256 with hash RMD160

There are 2256 possible SHA256 results when hashing the public key

There are 2160 possible RIPEMD160 results when hashing the SHA256 hash result.

Since there are more SHA256 results than there are RIPEMD160 results, there must be some SHA256 results which, when hashed with RIPEMD160 will provide identical results (this is known as the pigeonhole principal).

Dividing the number of possible SHA256 results by the number of possible RIPEMD160 results, we find that, on average, each RIPEMD160 result can be computed from 296 different SHA256 results. That implies that there is an average of 296 valid private keys for each address computed with RIPEMD160 (that's 1 : 296 ratio, and not the 1:2 ratio that you suggested).

The odds of finding any one of those 296 private keys is vanishingly small. It just isn't going to happen. With nearly 2256 valid private keys,  and only 296 of them being valid for a given address, you have a 0.0000000000000000000000000000000000000000000000684% chance of a collision on each attempt.

That's a probability of 1 / 2160.