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[[Network coding]] has been shown to optimally use [[Bandwidth (computing)|bandwidth]] in a network, maximizing information flow but the scheme is very inherently vulnerable to pollution attacks by malicious nodes in the network. A node injecting garbage can quickly affect many receivers. The pollution of [[network packet]]s spreads quickly since the output of (even an) honest node is corrupted if at least one of the incoming packets is corrupted.
An attacker can easily corrupt a packet even if it is encrypted by either forging the signature or by producing a collision under the [[hash function]]. This will give an attacker access to the packets and the ability to corrupt them. Denis Charles, Kamal Jain and Kristin Lauter designed a new [[homomorphic encryption]] signature scheme for use with network coding to prevent pollution attacks.<ref>{{Cite journal |citeseerx = 10.1.1.60.4738 |title = Signatures for Network Coding |year = 2006 |url = https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.60.4738 |archive-url = https://web.archive.org/
The homomorphic property of the signatures allows nodes to sign any linear combination of the incoming packets without contacting the signing authority. In this scheme it is computationally infeasible for a node to sign a linear combination of the packets without disclosing what [[linear combination]] was used in the generation of the packet. Furthermore, we can prove that the signature scheme is secure under well known [[Cryptography|cryptographic]] assumptions of the hardness of the [[discrete logarithm]] problem and the computational [[Elliptic curve Diffie–Hellman]].
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