Proceedings of CRYPTO 84 on Advances in cryptology
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
An explication of secret sharing schemes
Designs, Codes and Cryptography
Randomized metarounding (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Communications of the ACM
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Comprehensive view of a live network coding P2P system
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
Signing a Linear Subspace: Signature Schemes for Network Coding
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Network Coding Fundamentals
Homomorphic MACs: MAC-Based Integrity for Network Coding
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Network coding: a computational perspective
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Information flow decomposition for network coding
IEEE Transactions on Information Theory
The encoding complexity of network coding
IEEE Transactions on Information Theory
Minimum-cost multicast over coded packet networks
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
Secure Network Coding on a Wiretap Network
IEEE Transactions on Information Theory
Secure Network Coding for Wiretap Networks of Type II
IEEE Transactions on Information Theory
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Secret sharing has been used in multicast network coding to transmit information securely in the presence of a wiretapper who is capable of eavesdropping a bounded number of network edges. Typically information-theoretic security against the wiretapper can be achieved when multicasting a message by concatenating it with some random symbols and representing them with a carefully chosen network code. In this paper, we revisit a secret sharing approach to network codes. Particularly, we are concerned with whether or not a given network code is secure. We derive a necessary and sufficient condition for a given network code to be secure for a network coding instance. In comparison with previous work, our condition is more explicit in the sense that it is easier to verify. Furthermore, we devise a precise algorithm to transform an insecure network code into a secure one. Our algorithm achieves smaller secure code alphabet size over previous work.