Re: There are 2^256 private keys out there: how big is that number?
⭐ Merited by fillippone (2)
Now, in Bitcoin, I'm thinking of a number between one and 2^160 (in fact, it's a little less, but let's not delve into technical details too much).
there is a tiny mistake here. that "number" that we choose in bitcoin (aka private key) is between 1 and a little less than 2256 then that number is "converted" and "compressed" using one way operations to a smaller size (2160).There is (AFAIK) no really good answer to how many "guesses" we're talking about in this "game".
There are indeed 2^256 private keys (or slightly less), but they translate to a "mere" 2^160 addresses.
More than one private key translates to one address, but it's not as simple as saying "x private keys translate to one address".
HD wallets have further complicated the question of "how many guesses".
This is why I have settled for the lower boundary of 2^160 whenever I explain the probability of guessing a private key.
This is also why I specifically didn't want to delve into the technical details too much
Here's another snippet of wisdom from when I'm trying to explain the odds of guessing a private key:
2^160 is (roughly) the same as a 1 with
Now imagine a Billion people, that's a 1 with 9 zeros.
Now imagine each of those people guessing a Billion times.
That's a 1 with 18 zeros guesses.
You've only managed to reduce the original 1 with
The chances of guessing the right number are still 1 in a 1 with
Even that is technically not completely correct, but it gives people a better idea of what size of numbers we're talking about.
It's easy to continue with things like "let them take a billion guesses every second for a billion seconds" etc.
In short: always convert to base 10 numbers when talking to "normal" people.
They don't understand base 2.
Once people understand what it takes to reduce a number with