Quote from: archyone on September 05, 2020, 10:33:20 AM

If the formula is always the same, All public keys will also always be the same! "Where am I wrong?

(dx, dy, c, R.x, R.y, Q.x Q.y, P.x, P.y)Can someone explain to me what are this?

I think Rx and Ry are the coordinates of the public key, right?

ok, I will try to explain as simply as possible because it is true that I myself struggled to understand the system.
So it is a question here of adding 2 points (not the same). In this example we use :

first point: (all values are in décimal for a better comprehension)

X coordinate: 21262057306151627953595685090280431278183829487175876377991189246716355947009 (it is Qx)
Y coordinate: 41749993296225487051377864631615517161996906063147759678534462689479575333124 (it is Qy)
The Private key for this point is 0000000000000000000000000000000000000000000000000000000000000008

second point to add:

X coordinate: 89565891926547004231252920425935692360644145829622209833684329913297188986597 (it is Px)
Y coordinate: 12158399299693830322967808612713398636155367887041628176798871954788371653930 (it is Py)
The Private key for this point is 0000000000000000000000000000000000000000000000000000000000000002

So to add the 1st point to the second we use the formula : (here modulo is 115792089237316195423570985008687907853269984665640564039457584007908834671663 )

dx = (Q.x - P.x) % modulo
dy = (Q.y - P.y) % modulo
c = dy * invert(dx) % modulo
R.x = (c*c - P.x - Q.x) % modulo
R.y = (c*(P.x - R.x) - P.y) % modulo

in our example we have

dx = (21262057306151627953595685090280431278183829487175876377991189246716355947009 - 89565891926547004231252920425935692360644145829622209833684329913297188986597) % modulo
dx = 47488254616920819145913749673032646770809668323194230583764443341328001632075

dy = (41749993296225487051377864631615517161996906063147759678534462689479575333124 - 12158399299693830322967808612713398636155367887041628176798871954788371653930) % modulo
dy = 29591593996531656728410056018902118525841538176106131501735590734691203679194

invert of dx = 70279122268919195963430815486314537773961171454828771794853116552210630553734

c = dy * invert(dx) % modulo
c = 16132032934385503768504319366562120314980927452732756733183380715276156205226

So the new point (8 + 2)

R.x = (c*c - P.x - Q.x) % modulo
R.x --> X coordinate of (8+2) = 72488970228380509287422715226575535698893157273063074627791787432852706183111

R.y = (c*(P.x - R.x) - P.y) % modulo
R.y --> Y coordinate of (8+2) = 62070622898698443831883535403436258712770888294397026493185421712108624767191

If we check these coordinates, we find that it corresponds to the private key: 000000000000000000000000000000000000000000000000000000000000000a (10)

There you go, I hope I was as clear as possible and apologies for my broken English ^^

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Good explanation ... I understood perfectly