Simple CRC toy examples to try to figure out parameters of the one used in ISO 14443

crc.py

def str2int(s):
  i = 0
  for c in s:
    i = (i << 1) + (1 if c == '1' else 0)
  return i

def xor(a, b):
  return ['1' if aa != bb else '0' for aa, bb in zip(a, b)]

def inv(a):
  return ['1' if aa == '0' else '0' for aa in a]

def space(s, length=8):
  pieces = [s[0+i:length+i] for i in range(0, len(s), length)]
  return ' '.join(pieces)

def divide(data, poly):
  poly = poly.lstrip('0')
  shift = 0
  data = list(data)
  
  print(space(''.join(data)))
  while(len(data) > (len(poly) - 1)):
    print(f' {shift:2d} {str2int(data[:len(poly) - 1]):04x} {str2int(reversed(data[:len(poly) - 1])):04x}')
    if data[0] == '1':
      print(space(shift * '0' + ''.join(data)) + f'  {str2int(data[:len(poly) - 1]):02x}')
      print(space(shift * ' ' + poly))
      print(space(shift * ' ' + len(poly) * '-'))

      for i in range(len(poly)):
        data[i] = '0' if data[i] == poly[i] else '1'
      print(space((shift + 1) * ' ' + ''.join(data[1:len(poly)])))
    data = data[1:]
    shift += 1
  
  normal = data
  inverse = inv(data)
  reverse = reversed(data)
  revinv = inv(reversed(data))

  mask = str2int((len(poly) - 1) * "1")

  print(shift * ' ' + ''.join(data[:len(poly)]) + f'  {str2int(normal):02x} i:{str2int(inverse) & mask:02x} r:{str2int(reverse):02x} ri:{str2int(revinv) & mask:02x}')
  return data

def spec(data):
  crc = 0xffff
  for b in data:
    b = (int(b) ^ crc) & 0xff
    b = (b ^ (b << 4)) & 0xff
    crc = (crc >> 8) ^ ((b << 8) & 0xffff) ^ ((b << 3) & 0xffff) ^ ((b >> 4) & 0xffff)
    print(f'{crc:04x}  {bin(crc)}')
  crc = ~crc & 0xffff
  print(f'{crc:04x}')

divide(16 * '1' + 8 * '0' + 16 * '0', '10001000000100001')
spec(bytes.fromhex('000000'))
print()
spec(bytes.fromhex('0faaff'))
print()
spec(bytes.fromhex('0a123456'))