  We analyze the security of the authentication code against pollution attacks
in network coding given by Oggier and Fathi and show one way to remove one very
strong condition they required. Actually, we find a way to attack their
authentication scheme. In their scheme, they considered that if some malicious
nodes in the network collude to make pollution in the network flow or make
substitution attacks to other nodes, they thought these malicious nodes must
solve a system of linear equations to recover the secret parameters. Then they
concluded that their scheme is an unconditional secure scheme. Actually, note
that the authentication tag in the scheme of Oggier and Fathi is nearly linear
on the messages, so it is very easy for any malicious node to make pollution
attack in the network flow, replacing the vector of any incoming edge by linear
combination of his incoming vectors whose coefficients have sum 1. And if the
coalition of malicious nodes can carry out decoding of the network coding, they
can easily make substitution attack to any other node even if they do not know
any information of the private key of the node. Moreover, even if their scheme
can work fruitfully, the condition in their scheme $H\leqslant M$ in a network
can be removed, where $H$ is the sum of numbers of the incoming edges at
adversaries. Under the condition $H\leqslant M$, $H$ may be large, so we need
large parameter $M$ which increases the cost of computation a lot. On the other
hand, the parameter $M$ can not be very large as it can not exceed the length
of original messages.
