Proceedings of CRYPTO 84 on Advances in cryptology
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Polynomial time algorithms for network information flow
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Valuable messages and random outputs of channels in linear network coding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Separate network coding for private and common messages from one source to two sinks
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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In a network with capacity h for multicast, information Xh = (X1, X2, ₀, Xh) can be transmitted from a source node to sink nodes without error by a linear network code. Furthermore, secret information Sr = (S1, S2, ₀, Sr) can be transmitted securely against wiretappers by k-secure network coding for k ≤ h-r. In this case, no information of the secret leaks out even if an adversary wiretaps k edges, i.e. channels. However, if an adversary wiretaps k + 1 edges, some Si may leak out explicitly. In this paper, we propose strongly k-secure network coding based on strongly secure ramp secret sharing schemes. In this coding, no information leaks out for every (Si1, Si2, ₀, Sir-j) even if an adversary wiretaps k ± j channels. We also give an algorithm to construct a strongly k-secure network code directly and a transform to convert a nonsecure network code to a strongly k-secure network code. Furthermore, some sufficient conditions of alphabet size to realize the strongly k-secure network coding are derived for the case of k .