Post
Topic
Board Development & Technical Discussion
Merits 3 from 1 user
Re: Maths Q1 - address to key ratio
by
o_e_l_e_o
on 05/01/2021, 12:31:33 UTC
⭐ Merited by ranochigo (3)
Say someone was giving you clues to their private key.  For each character they gave you a couple of options eg, for the fifth position is either 1, 3, f or a.  How many options would they have to give you per position for it to be crackable by brute force?
Well, we can work out a rough idea. Let:

x = number of addresses you can derive from their respective private keys each second
y = length of time in seconds you are willing to wait

Given that a private key has 64 characters, then the number of possibilities for each character would then be given by the 64th root of the product of these two numbers, so 64√(x*y)

For example

Let's say you are running a GeForce RTX 2080 Ti, which can turn 2.5 billion private keys in to their corresponding addresses each second, and you are willing to let this run for two weeks. 14 days * 24 hours * 60 minutes * 60 seconds * 2.5 billion = 3.024*1015 private keys. The 64th root of this number is 1.745, so you wouldn't even be able to exhaust the search space of 2 characters per position in 2 weeks.

264 is 1.845*1019, so again running your GeForce RTX 2080 Ti and checking 2.5 billion keys per second, it would take you ~234 years to check all combinations, or ~117 years if you wanted a 50% chance of finding the correct key.