def gcm_add(x, y):
    return x ^ y

def gcm_multiply(x, y, poly):
    z = 0
    for _ in range(poly.bit_length()):
        if y & 1:
            z ^= x
        hi_bit_set = x & (1 << poly.bit_length() - 1)
        x <<= 1
        if hi_bit_set:
            x ^= poly
        y >>= 1
    return z

def incr(x):
    y=1%(2^32)
    wyn = x+y
    if wyn >= 2^32:
        wyn=1%(2^32)
    return wyn

a = 0b0001
b = 0b0101
print(a,b)
print(bin(a),bin(b))
polynomial = 0xE1000000000000000000000000000000

result = gcm_multiply(a, b, polynomial)
print("GCM Multiplication Result:", bin(result))

result = gcm_add(a, b)
print("GCM Addition Result:", bin(result))

print(incr(1))
print(incr((2^32)-1))