Quote from: archyone on May 27, 2020, 05:39:29 AM

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I'm confuse with this part : c = 3*P.x*Px*invert(2*P.y) % modulo
How get invert(2*P.y) = 0xb7e31a064ed74d314de79011c5f0a46ac155602353dc3d340fbeaeec9767a6a6 ??
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As was explained above, the inverse for k by modulo is such value mwhere (m*k) by modulo is equal to 1.
The best way for python is to use library gmpy2 and its function gmpy2.invert(k,p) which returns the inverse value to k by modulo = p. This function is the best for python and approx. 50 times faster than any other self made calculations.

For ubuntu for example you can easily install it:

Code:

sudo apt update
sudo apt install python3-gmpy2

If it is not in repository, you can download gmpy2 from here (pls, check the correct python version): https://www.lfd.uci.edu/~gohlke/pythonlibs/#gmpy

and install it in this way (example for python ver 3.7):

Code:

python -m pip install gmpy2-2.0.8-cp37-cp37m-win_amd64.whl

If you do not want to use the gmpy2 libriary (however it is the best way), you can also use this self made inversion function:

Code:

def egcd (a, b):
   if a == 0:
   return (b, 0, 1)
   else:
   g, x, y = egcd(b % a, a)
   return (g, y - (b // a) * x, x)

def inversion (m, n):
   while m < 0:
   m += n
   g, x, _ = egcd (m, n)
   if g == 1:
   return x % n
else: print (' no inverse exist')

The function inversion requires 2 parameters: m and n, where n is the modulo and m is the number for which you would like to calculate the inverse.