How do I edit my point addition function so that it can directly add G to itself k times for ethereum public key generation?

In my python function, I have a point addition mathematical formula going that can properly calculate a public key from a private key integer. In order to calculate the public key properly, the program just needs to add G to itself k times so it can get to the coordinates of the correct public key.

I just want a mathematical formula that can add G to itself k times instantly.

The code I’m using so far is:

def modinv(a, p):
    """Compute modular inverse of a mod p using extended Euclidean algorithm."""
    return pow(a, p-2, p)


def point_add(P1, P2, p, k):
    """Add two points P1 and P2 on the elliptic curve over the field of size p.
    Optionally, add P2 k times to P1."""
    # If adding P2 k times, set initial result to P1
    result = P1

 # Loop to add P2 k times
    x1, y1 = result
    x2, y2 = P2

    if x1 == x2 and y1 != y2:
        return None  # This means the points add up to infinity (inverse points)

    if x1 != x2:
        # Point addition
        m = (y2 - y1) * modinv(x2 - x1, p) % p
    else:
        # Point doubling
        m = (3 * x1 ** 2) * modinv(2 * y1, p) % p

    x3 = (m ** 2 - x1 - x2) % p
    y3 = (m * (x1 - x3) - y1) % p
    result = (x3, y3)  # Update the result for the next addition

    return result

As you can see in this, the point_add function is just using a formula to add G to itself but it only does it once. When I turn the function into a for loop, it is able to run the function again and again so it will calculate the new public key depending on how many times the function was ran.

I want a mathematical formula that can do this for me, I want the mathematical formula to be able to run this function "k" times instantly (since the private key k is an integer), with the mathematical formula.

I already tried running the function again and again but I don’t want to do this. I want to manipulate the code so that it can be in the mathematical formula to multiply itself by how many times it needs.

You need to sign in to view this answers

Related Post