# secp256k1 curve parameters
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
a = 0
b = 7
Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

# Point addition and subtraction functions
def point_add(P, Q):
    if P == Q:
        return point_double(P)
    if P is None:
        return Q
    if Q is None:
        return P
    lam = ((Q[1] - P[1]) * pow(Q[0] - P[0], p-2, p)) % p
    x = (lam * lam - P[0] - Q[0]) % p
    y = (lam * (P[0] - x) - P[1]) % p
    return (x, y)

def point_sub(P, Q):
    if Q is None:
        return P
    # instead of using p - Q[1], use -Q[1] % p to correctly compute y coordinate
    Q_neg = (Q[0], (-Q[1]) % p)
    return point_add(P, Q_neg)

# Point doubling function
def point_double(P):
    if P is None:
        return None
    lam = ((3 * P[0] * P[0] + a) * pow(2 * P[1], p-2, p)) % p
    x = (lam * lam - 2 * P[0]) % p
    y = (lam * (P[0] - x) - P[1]) % p
    return (x, y)

def is_valid_point(point):
    # Check that the point is not the point at infinity
    if point is None:
        return False
    
    x, y = point
    # Check that the coordinates are within the allowed range
    if x < 0 or x >= p or y < 0 or y >= p:
        return False
    
    # Check that the point lies on the curve
    return (y*y - x*x*x - a*x - b) % p == 0

def decompress_point(compressed_key):
    if compressed_key.startswith(b'\x02') or compressed_key.startswith(b'\x03'):
        x = int.from_bytes(compressed_key[1:], byteorder='big')
        y_sq = (x * x * x + a*x + b) % p
        y = pow(y_sq, (p+1)//4, p)
        if (y*y) % p == y_sq:
            return (x, y)
        else:
            return None
    else:
        return None

def compress_point(point):
    x, y = point
    prefix = b'\x02' if y % 2 == 0 else b'\x03'
    return prefix + x.to_bytes(32, byteorder='big')

def point_subtraction(compressed_keys):
    P = None
    for compressed_key in compressed_keys:
        Q = decompress_point(compressed_key)
        
        # Check that the point is valid on the curve
        if not is_valid_point(Q):
            return None
        
        if P is None:
            P = Q
        else:
            P = point_sub(P, Q)
        
        # Check that the resulting point is not the point at infinity
        if P is None:
            return None
    
    if is_valid_point(P):
        return compress_point(P)
    else:
        return None

compressed_keys = []
file1 = open('file1.txt', 'r')
for line in file1:
    compressed_keys.append(bytes.fromhex(line.strip()))
file1.close()

file2 = open('file2.txt', 'r')
for line in file2:
    compressed_keys.append(bytes.fromhex(line.strip()))
file2.close()

result = point_subtraction(compressed_keys)

if result:
    file3 = open('result.txt', 'a')
    file3.write(result.hex() + "\n")
    file3.close()
else:
    print("The subtraction result is not a valid point on the curve.")