Security Analysis on "An Authentication Code Against Pollution Attacks in Network Coding"
This work exposes critical flaws in a proposed security scheme for network coding, which is important for researchers and practitioners in secure communication networks, though it is incremental as it builds on prior analysis.
The paper identifies a security vulnerability in Oggier and Fathi's authentication code for network coding, showing that malicious nodes can easily perform pollution and substitution attacks due to the near-linear nature of the authentication tag, and it demonstrates how to remove a restrictive condition (H ≤ M) that increased computational costs.
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.