while coef:
if coef & 1:
resultX, resultY = addition(currentX, currentY, gx, gy, a, b, prime)
currentX, currentY = addition(currentX, currentY, gx, gy, a, b, prime)
coef >>= 1
Let's unroll this loop:
- Current (x,y) is set to G
- Start at the least-significant bit
- If the bit is odd:
-- Then set Result = Current(x,y) + G [for the first iteration this means G+G]
- Set CurrentX += G [again, for the first iteration, it is G+G].
Do you see the problem here?
As you go through all of the bits, you are *adding* G to itself, this will make G, 2G, 3G, and so forth. You have to multiply the CurrentX by 2 each time, to get G, 2G, 4G, 8G, 16G,... 128G.
And each time the bit is odd, you are adding another G to the result which is already full of G's you're adding in succession, when you should set result = 0 in the initialization, and then you add it to Current (x,y). That is to say, Result += Current(x,y).
Binary expansion on private keys doesn't work without multiplication.