Quote from: _Counselor on Today at 05:19:09 PM

Quote from: akaki on Today at 03:33:28 PM

Yes, indeed I calculate (-k*G + k*G) as any other EC addition using this function :

Code:

LamAdd = ((b[1] - a[1]) * modinv(b[0] - a[0], P)) % P

As I said before, there is no exists inverse of zero (a[0] = b[0], b[0]-a[0] = 0)

If you modinv() function returning something with a zero argument, this is mean that is a wrong (or simplified - without error checking) implementation of modular multiplicative inverse. And that is why you're getting unexpected strange numbers in result.

Basically, zero-point, or identity point cannot be calculated, it is defined as [0;1;0] in projective coordinates or [P,0] in affine. Due to all of this, addition algorithms should contain something like "if (p1.y != p2.y and p1.x == p2.x) return zero"

Thanks, I updated my modinv function.

conclusion of discussion:

Code:

-k*G+k*G=(0,P) for k€Z, with P = FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F

The N*G result for k=1 is just coincidence.