Paper 2008/316

Signing a Linear Subspace: Signature Schemes for Network Coding

Dan Boneh, David Freeman, Jonathan Katz, and Brent Waters


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. Here, we propose two signature schemes that can be used in conjunction with network coding to prevent malicious modification of data. In particular, our schemes can be viewed as signing linear subspaces in the sense that a signature on V authenticates exactly those vectors in V. Our first scheme is homomorphic and has better performance, with both public key size and per-packet overhead being constant. Our second scheme does not rely on random oracles and uses weaker assumptions. We also prove a lower bound on the length of signatures for linear subspaces showing that both of our schemes are essentially optimal in this regard.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. To appear in PKC 2009
signature schemesnetwork codingpairing-based cryptography
Contact author(s)
jkatz @ cs umd edu
2008-12-23: last of 4 revisions
2008-08-02: received
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Creative Commons Attribution


      author = {Dan Boneh and David Freeman and Jonathan Katz and Brent Waters},
      title = {Signing a Linear Subspace: Signature Schemes for Network Coding},
      howpublished = {Cryptology ePrint Archive, Paper 2008/316},
      year = {2008},
      note = {\url{}},
      url = {}
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