Quote from: kTimesG on Today at 05:27:44 PM

Quote from: Valera909 on Today at 11:41:05 AM

I’ve got a basic grasp of modular arithmetic, but initially interpreted the situation differently — like, the point −𝑃 −P kinda feels “greater” than 𝑃
P, especially when you look at it through the lens of inversion over the 𝑦 y-axis. 📉📈

Now here’s the spicy bit 🌶️:
If you start walking from − 𝑃 −P, incrementing the private key by 1 each time (i.e., checking for some 𝑘 k where 𝑘⋅𝐺=𝑃 k⋅G=P), you'll actually hit the point 𝑃 P relatively quickly — because they’re connected through the curve’s group order.
But if you go the other way — starting at 𝑃
P, trying to reach −𝑃
−P via +1 steps — you'll have to walk almost the entire group order. 🚶‍♂️🔁

That means direction matters, and that’s something we might be able to leverage. This method gives a hint about the sign or orientation of the point. 👀🧭

🤔 I'm wondering — are there any libs or implementations that let you determine which of two points is “closer to 0” or gives clues about their directional relationship?

Nothin' about this ChatGPT response makes any sense.

There is no point "closer" to 0. The associated point at infinity doesn't exist on the curve, it's an abstract construct, part of the mathematical group. It has no value to be compared against. It's undefined.

There's no such thing as orientation of a point. They're all modular coordinates, under the same field. It makes no sense to talk about signs. We can only speak about the Y parity, but a parity does not mean that a value is above or below some median value, so there is no way to extract any information about the "sign", or the "low"/"high" values based on parity. Let alone extract any information about any relation to some other point.

The scalars of a point and its opposite always have two possible differences, one of them less or equal to N - 1 / 2, the other one the difference to N itself. There is no way to tell whether the shorter difference is going from P to -P, or from -P to P, when the scalars are unknown.

This thread's goin' nowhere lately, only junk questions, n00b code, and fantasies about solving a problem that requires up to 2 million dollars to solve (using the fastest possible methods and hardware) on google colab. wtf Cheesy

AI-generated
23%

AI-generated & AI-refined
0%

Human-written & AI-refined
0%

Human-written
77%