Biblio

Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to ρ packets, and wire-tap up to μ links, all throughout ℓ shots of a (random) linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ℓn'-2t-ρ-μ packets, where n' is the number of outgoing links at the source, for any packet length m ≥ n' (largest possible range), with only the restriction that ℓ\textbackslashtextless;q (size of the base field). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ℓn', and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication.

Today's major concern is not only maximizing the information rate through linear network coding scheme which is intelligent combination of information symbols at sending nodes but also secured transmission of information. Though cryptographic measure of security (computational security) gives secure transmission of information, it results system complexity and consequent reduction in efficiency of the communication system. This problem leads to alternative way of optimally secure and maximized information transmission. The alternative solution is secure network coding which is information theoretic approach. Depending up on applications, different security measures are needed during the transmission of information over wiretapped network with potential attack by the adversaries. In this research work, mathematical model for different security constraints with upper and lower boundaries were studied depending up on the randomness added to the source message and hence the security constraints on linear network code for randomized source messages depends both on randomness added and number of random source symbols. If the source generates large number random symbols, lesser number of random keys can give higher security to the information but information theoretic security bounds remain same. Hence maximizing randomness to the source is equivalent to adding security level.