Homomorphic signatures for network coding: Difference between revisions

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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>http://{{Cite journal |citeseerx.ist.psu.edu/viewdoc/download?doi = 10.1.1.60.4738&rep|title =rep1&type Signatures for Network Coding|year =pdf 2006}}</ref> 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]].
 
==Network coding==
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#(Alternating) <math>e_m(P, P) = 1</math>.
 
Also, <math>e_m</math> can be computed efficiently.<ref>http://{{Cite journal |citeseerx.ist.psu.edu/viewdoc/download?doi = 10.1.1.88.8848&rep|title =rep1&type Improved Weil and Tate pairings for elliptic and hyperelliptic curves|pages =pdf 169–183|year = 2004|bibcode = 2003math.....11391E|last1 = Eisentraeger|first1 = Kirsten|last2 = Lauter|first2 = Kristin|last3 = Montgomery|first3 = Peter L.|arxiv = math/0311391}}</ref>
 
===Homomorphic signatures===