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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def __read_master_key(self):
        '''
        Read in the rotating master authentication key
        '''
        key_user = self.salt_user
        if key_user == 'root':
            if self.opts.get('user', 'root') != 'root':
                key_user = self.opts.get('user', 'root')
        if key_user.startswith('sudo_'):
            key_user = self.opts.get('user', 'root')
        if salt.utils.platform.is_windows():
            # The username may contain '\' if it is in Windows
            # 'DOMAIN\username' format. Fix this for the keyfile path.
            key_user = key_user.replace('\\', '_')
        keyfile = os.path.join(self.opts['cachedir'],
                               '.{0}_key'.format(key_user))
        try:
            # Make sure all key parent directories are accessible
            salt.utils.verify.check_path_traversal(self.opts['cachedir'],
                                                   key_user,
                                                   self.skip_perm_errors)
            with salt.utils.files.fopen(keyfile, 'r') as key:
                return salt.utils.stringutils.to_unicode(key.read())
        except (OSError, IOError, SaltClientError):
            # Fall back to eauth
            return ''