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In network coding, we discuss the effect of sequential error injection oninformation leakage. We show that there is no improvement when the operationsin the network are linear operations. However, when the operations in thenetwork contains non-linear operations, we find a counterexample to improveEve's obtained information. Furthermore, we discuss the asymptotic rate in alinear network under the secrecy and robustness conditions as well as under thesecrecy condition alone. Finally, we apply our results to network quantum keydistribution, which clarifies the type of network that enables us to realizesecure long distance communication via short distance quantum key distribution.

Secrecy and Robustness for Active Attack in Secure Network Coding and its Application to Network Quantum Key Distribution