Systems exploiting network coding to increase their throughput suffer greatly from pollution attacks which consist of injecting malicious packets in the network. The pollution attacks are amplified by the network coding process, resulting in a greater damage than under traditional routing. In this paper, we address this issue by designing an unconditionally secure authentication code suitable for multicast network coding. The proposed scheme is robust against pollution attacks from outsiders, as well as coalitions of malicious insiders. Intermediate nodes can verify the integrity and origin of the packets received without having to decode, and thus detect and discard the malicious messages in-transit that fail the verification. This way, the pollution is canceled out before reaching the destinations. We analyze the performance of the scheme in terms of both multicast throughput and goodput, and show the goodput gains. We also discuss applications to file distribution.
The signature scheme proposed in @cite_5 uses a standard signature scheme based on the hardness of the discrete logarithm problem. The blocks of data are considered as vectors spanning a subspace. The signature is not performed on vectors containing data blocks, but on vectors orthogonal to all data vectors in the given subspace. The signature verification allows to check if the received vector belongs to the data subspace. The security of their scheme holds in that no adversary knowing a signature on a given subspace of data vectors is able to forge a valid signature for any vector not in this given subspace. This scheme requires also fresh keys for every file. Finally, the signature schemes given in @cite_6 follow the approach given in @cite_5 with improvements in terms of public key size and per-packet overhead. The signature schemes proposed are designed to authenticate a linear subspace formed by the vectors containing data blocks. Signatures on a linear subspace are sufficient to authenticate all the vectors in this same subspace. With these schemes, a single public key can be used to verify multiple files.
@cite_5 @cite_6
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Recent research has shown that network coding can be used in content distribution systems to improve the speed of downloads and the robustness of the systems. However, such systems are very vulnerable to attacks by malicious nodes, and we need to have a signature scheme that allows nodes to check the validity of a packet without decoding. In this paper, we propose such a signature scheme for network coding. Our scheme makes use of the linearity property of the packets in a coded system, and allows nodes to check the integrity of the packets received easily. We show that the proposed scheme is secure, and its overhead is negligible for large files. Network coding offers increased throughput and improved robustness to random faults in completely decentralized networks. In contrast to traditional routing schemes, however, network coding requires intermediate nodes to modify data packets en route ; for this reason, standard signature schemes are inapplicable and it is a challenge to provide resilience to tampering by malicious nodes. We propose two signature schemes that can be used in conjunction with network coding to prevent malicious modification of data. Our schemes can be viewed as signing linear subspaces in the sense that a signature *** on a subspace V authenticates exactly those vectors in V . Our first scheme is (suitably) homomorphic and has constant public-key size and per-packet overhead. Our second scheme does not rely on random oracles and is based on weaker assumptions. We also prove a lower bound on the length of signatures for linear subspaces showing that our schemes are essentially optimal in this regard.