Quote from: mcdouglasx on October 21, 2023, 10:24:22 PM

Quote from: alek76 on October 21, 2023, 05:47:43 PM

The comma can be moved in any direction

It's not just moving the comma, it's reducing the target.
from
1185429467683753
to
785429467683753

Quote from: alek76 on October 21, 2023, 05:47:43 PM

Can you do the same with the public key?

yes.

Quote from: alek76 on October 21, 2023, 05:47:43 PM

Even if you can, it doesn't give you the range of the private key.

If you perfect your division technique
and you manage to reduce enough, you could for example.

1185429467683753

If you manage to reduce to

1439467683753

1185429467683753-1439467683753
1183990000000000

obtaining the first 3 digits of your goal..Discarding the 3 digits that follow, which would be the error range.

Basically this technique is based on reducing pubs without losing the last digits of the pk so that when you subtract you identify the first digits.
Then, once you have the first digits, you have the basis to continue.

Main question is, how can we guess the first few digits? If even if we guess the 4 first digits correctly, the fifth digit would cause a problem if we make a mistake.

Something to demonstrate, for example if we guess the last 2 hex chars of the target, we can divide by a 3 digit number, but if we do that, we'd need to generate 256 keys and can only divide up to 1024, so we'll have 256 keys divided by 1024, then we will have to generate 256 keys as a guess for each one of those first 256 keys, well just now writing this I realize we can indeed guess the last 2 chars and divide by 1024 and continue until we reach a very small range easily brute force able. Or do we need to guess more than 2 ending characters to divide by 1024?

Disclaimer, I take no responsibility for any damages caused by my published studies, I am an independent researcher and publish my findings on public domain.