# Define the EllipticCurve class
class EllipticCurve:
    def __init__(self, a, b, p):
        self.a = a
        self.b = b
        self.p = p

    def contains(self, point):
        x, y = point.x, point.y
        return (y * y) % self.p == (x * x * x + self.a * x + self.b) % self.p

    def __str__(self):
        return f"y^2 = x^3 + {self.a}x + {self.b} mod {self.p}"

# Define the Point class
class Point:
    def __init__(self, x, y, curve):
        self.x = x
        self.y = y
        self.curve = curve

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y and self.curve == other.curve

    def __ne__(self, other):
        return not self == other

    def __add__(self, other):
        if self.curve != other.curve:
            raise ValueError("Cannot add points on different curves")

        # Case when one point is zero
        if self == Point.infinity(self.curve):
            return other
        if other == Point.infinity(self.curve):
            return self

        if self.x == other.x and self.y != other.y:
            return Point.infinity(self.curve)

        p = self.curve.p
        s = 0
        if self == other:
            s = ((3 * self.x * self.x + self.curve.a) * pow(2 * self.y, -1, p)) % p
        else:
            s = ((other.y - self.y) * pow(other.x - self.x, -1, p)) % p

        x = (s * s - self.x - other.x) % p
        y = (s * (self.x - x) - self.y) % p

        return Point(x, y, self.curve)

    def __sub__(self, other):
        if self.curve != other.curve:
            raise ValueError("Cannot subtract points on different curves")

        # Case when one point is zero
        if self == Point.infinity(self.curve):
            return other
        if other == Point.infinity(self.curve):
            return self

        return self + Point(other.x, (-other.y) % self.curve.p, self.curve)

    def __mul__(self, n):
        if not isinstance(n, int):
            raise ValueError("Multiplication is defined for integers only")

        n = n % (self.curve.p - 1)
        res = Point.infinity(self.curve)
        addend = self

        while n:
            if n & 1:
                res += addend

            addend += addend
            n >>= 1

        return res

    def __str__(self):
        return f"({self.x}, {self.y}) on {self.curve}"

    @staticmethod
    def from_hex(s, curve):
        if len(s) == 66 and s.startswith("02") or s.startswith("03"):
            compressed = True
        elif len(s) == 130 and s.startswith("04"):
            compressed = False
        else:
            raise ValueError("Hex string is not a valid compressed or uncompressed point")

        if compressed:
            is_odd = s.startswith("03")
            x = int(s[2:], 16)

            # Calculate y-coordinate from x and parity bit
            y_square = (x * x * x + curve.a * x + curve.b) % curve.p
            y = pow(y_square, (curve.p + 1) // 4, curve.p)
            if is_odd != (y & 1):
                y = -y % curve.p

            return Point(x, y, curve)
        else:
            s_bytes = bytes.fromhex(s)
            uncompressed = s_bytes[0] == 4
            if not uncompressed:
                raise ValueError("Only uncompressed or compressed points are supported")

            num_bytes = len(s_bytes) // 2
            x_bytes = s_bytes[1 : num_bytes + 1]
            y_bytes = s_bytes[num_bytes + 1 :]

            x = int.from_bytes(x_bytes, byteorder="big")
            y = int.from_bytes(y_bytes, byteorder="big")

            return Point(x, y, curve)

    def to_hex(self, compressed=True):
        if self.x is None and self.y is None:
            return "00"
        elif compressed:
            prefix = "03" if self.y & 1 else "02"
            return prefix + hex(self.x)[2:].zfill(64)
        else:
            x_hex = hex(self.x)[2:].zfill(64)
            y_hex = hex(self.y)[2:].zfill(64)
            return "04" + x_hex + y_hex

    @staticmethod
    def infinity(curve):
        return Point(None, None, curve)

# Define the ec_mul function
def ec_mul(point, scalar, base_point):
    result = Point.infinity(point.curve)
    addend = point

    while scalar:
        if scalar & 1:
            result += addend

        addend += addend
        scalar >>= 1

    return result

# Define the ec_operations function
def ec_operations(start_range, end_range, target_1, target_2, curve):
    # Define parameters for secp256k1 curve
    n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
    G = Point(
        0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
        0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8,
        curve
    )

    # Open the files for writing
    with open("target1_division_results.txt", "a") as file1, \
            open("target2_division_results.txt", "a") as file2, \
            open("subtract_results.txt", "a") as file3:

        for i in range(start_range, end_range + 1):
            try:
                # Compute the inverse of i modulo n
                i_inv = pow(i, n-2, n)

                # Divide the targets by i modulo n
                result_1 = ec_mul(target_1, i_inv, G)
                result_2 = ec_mul(target_2, i_inv, G)

                # Subtract the results
                sub_result = result_2 - result_1

                # Write the results to separate files
                file1.write(f"{result_1.to_hex()}\n")
                file2.write(f"{result_2.to_hex()}\n")
                file3.write(f"Subtracting results for {i}:\n")
                file3.write(f"Target 1 / {i}: {result_1.to_hex()}\n")
                file3.write(f"Target 2 / {i}: {result_2.to_hex()}\n")
                file3.write(f"Subtraction: {sub_result.to_hex()}\n")
                file3.write("="*50 + "\n")

                print(f"Completed calculation for divisor {i}")
            except ZeroDivisionError:
                print(f"Error: division by zero for {i}")

    print("Calculation completed. Results saved in separate files.")

if __name__ == "__main__":
    # Set the targets and range for the operations
    curve = EllipticCurve(0, 7, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
    target_1 = Point.from_hex("0230210C23B1A047BC9BDBB13448E67DEDDC108946DE6DE639BCC75D47C0216B1B", curve)
    target_2 = Point.from_hex("02F6B787195159544330085C6014DBA627FF5B14F3203FF05D12482F76261F4FC3", curve)
    start_range = 2
    end_range = 10

    ec_operations(start_range, end_range, target_1, target_2, curve)