gistfile1.txt

from Crypto.Util.number import *

# global vars

# Y^2= X + 497X + 1768 mod 9739 

a=497
b=1768
p=9739

O = 'O'

##

def elliptic_add(P, Q):
    # Handle special cases with point at infinity
    if P == 'O':  # Identity element
        return Q
    if Q == 'O':
        return P

    x1, y1 = P
    x2, y2 = Q

    # If x1 == x2 and y1 == -y2 (mod p), the result is the point at infinity
    if x1 == x2 and (y1 + y2) % p == 0:
        return 'O'

    # Compute the slope (lambda)
    if P != Q:
        numerator = (y2 - y1) % p
        denominator = (x2 - x1) % p
    else:
        numerator = (3 * x1**2 + a) % p
        denominator = (2 * y1) % p

    # Compute lambda using modular inverse
    lam = (numerator * inverse(denominator, p)) % p

    # Calculate resulting point coordinates
    x3 = (lam**2 - x1 - x2) % p
    y3 = (lam * (x1 - x3) - y1) % p

    return (x3, y3)

def scalar_mul(P,n):
    Q=P
    R=O

    while n > 0 :

        if n % 2 ==1 :
            R=elliptic_add(R,Q)

        # Q=[2]Q 
        Q=elliptic_add(Q,Q)

        # and n=[n/2]
        n=n//2


    return R
    


P = (2339, 2213)
n = 7863

Q = scalar_mul(P,n)

# Print result
print("Q =", Q)

# Check if Q is on the curve
x, y = Q
on_curve = (y**2 % p) == (x**3 + a*x + b) % p
print("Is Q on the curve?", on_curve)