Post
Topic
Board Development & Technical Discussion
Merits 1 from 1 user
Re: zero point of secp256k1
by
NotATether
on 20/12/2021, 04:30:35 UTC
⭐ Merited by BlackHatCoiner (1)
I'm not 100% sure for this, but you can't subtract this way in ECC.

Think of this. 1*G - 1*G would be equal with 1*G + (-1)*G, right? But, -1 is outside the range. In finite fields, -1 is equal with N-1 which is 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364139.

So, what you really do is 1*G + (N-1)*G which is N*G. Apparently, k*G + (-k)*G is always N*G, but I need this to be confirmed. Anyway, check: How to subtract two points on an elliptic curve?

Subtracting a point by itself always leads to zero because one of the points is at the top of the Y axis, the other is on the bottom of the Y axis but has the same X coordinate so they just have a flipped Y coordinate.

Since subtraction is just negative addition, and point addition just finds the third point on the curve that forms a line with the other two points, when you're subtracting a point from itself that third, intermediate point does not exist so it passes through the infinity point that's in three-dimensional space, which is how you arrive at the 0G result. It would not be equal to -1G.