def crc(nachricht,polynom = '10011'):
    """
    zu der 'nachricht' und zu dem 'polynom' (Strings aus 0 und 1) wird
    die CRC-'Prüfsumme' berechnet (String aus 0 und 1)
    """
    lp = len(polynom)
    ln = len(nachricht)
    for j in range(lp-1):
        nachricht = nachricht+'0'
    nachricht = list(nachricht)
    schieberegister = nachricht[:lp]
    for i in range(ln):
        if schieberegister[0] == '1':
            for j in range(lp):
                if schieberegister[j] == polynom[j]:
                    schieberegister[j] = '0'
                else:
                    schieberegister[j] = '1'
        if i < ln-1:
            schieberegister = schieberegister[1:lp]+list(nachricht[lp+i])
    return ''.join(schieberegister[1:])


if __name__ == '__main__':
    n='1001110100011101' # Test-Nachricht, 16Bit-lang
    crcn = crc(n)
    print(n, crc(n))
    print('Einerbündel')
    for i in range(len(n)):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        g = ''.join(m)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')
    print('Zweierbündel')
    for i in range(len(n)-1):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        if m[i+1] == '1':
            m[i+1] = '0'
        else:
            m[i+1] = '1'
        g = ''.join(m)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')
    print('Dreierbündel,alle Bits verändert')
    for i in range(len(n)-2):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        if m[i+1] == '1':
            m[i+1] = '0'
        else:
            m[i+1] = '1'
        if m[i+2] == '1':
            m[i+2] = '0'
        else:
            m[i+2] = '1'
        g = ''.join(m)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')
    print('Dreierbündel,nur Außen-Bits verändert')
    for i in range(len(n)-2):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        if m[i+2] == '1':
            m[i+2] = '0'
        else:
            m[i+2] = '1'
        g = ''.join(m)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')
    print('Viererbündel,alle Bits verändert')
    for i in range(len(n)-3):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        if m[i+1] == '1':
            m[i+1] = '0'
        else:
            m[i+1] = '1'
        if m[i+2] == '1':
            m[i+2] = '0'
        else:
            m[i+2] = '1'
        if m[i+3] == '1':
            m[i+3] = '0'
        else:
            m[i+3] = '1'
        g = ''.join(m)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')
    print('Fünferbündel,alle Bits verändert')
    for i in range(len(n)-4):
        m = list(n)
        if m[i] == '1':
            m[i] = '0'
        else:
            m[i] = '1'
        if m[i+1] == '1':
            m[i+1] = '0'
        else:
            m[i+1] = '1'
        if m[i+2] == '1':
            m[i+2] = '0'
        else:
            m[i+2] = '1'
        if m[i+3] == '1':
            m[i+3] = '0'
        else:
            m[i+3] = '1'
        if m[i+4] == '1':
            m[i+4] = '0'
        else:
            m[i+4] = '1'
        g = ''.join(m)
        print(n,crcn)
        crcg = crc(g)
        print(g,crcg)
        if crcg == crcn:
            print('Kollision')