Reversing Divided Public Keys

Hey everyone. I used Iceland2k's PubDiv to split a pubkey.

Nice! Did it actually work? What’s the next step?

It did work and cut down the range, but how do I get the Privkey back?

You take the public key and divide by 2, or just multiply by a scalar. After that... you need to worry about the fractions.

Not sure that's the way to go. For example, using pubkey from puzzle 35, I ran it and got 1024 keys after reducing by 10. One was 25! Pretty sweet.

How does it give you the right key? If it’s finding the key, you need to explain the math behind it.

It just generates keys in that range. I asked some AI about it, but the explanation was off.

Try checking out albertobsd's ecctools for some concrete examples. It’s a handy library.

If it were that easy, we'd all be rich. Just be careful; shortcuts can wreck your security.

Yeah, but I'm just trying to get a grip on it. The tool is useful, but the inner workings confuse me.

If it reduces the range, it must work somehow. Show us what you did exactly.

I get that, but I just don’t know the divisor or any specifics about the process!

Looks like you’re just guessing. You have to generate enough keys to compare.

So if I divide 52 by 4, I get 13. But without generating enough results, it doesn’t mean anything.

Right, try generating public keys up to 2^130 to see how it works.

What if I just reduce the bits? Like 8. Should be clearer, right?

For sure, reducing by 8 gets you 256 entries. Watch for patterns when you look at your output.

Okay, got it. I’ll test that out and see what I get.

Can someone simplify the equation for me? I don’t get the offsets.

It's not that hard. Original_PVK = Offset_PVK * Total_Offsets + Offset_position 1. Easy peasy.