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In secure network coding, there is a possibility that the eavesdropper canimprove her performance when she changes (contaminates) the information on theattacked edges (active attack) and chooses the attacked edges adaptively(adaptive attack). We analyze the security for network code over such types ofattacks. We show that active and adaptive attacks cannot improve theperformance of the eavesdropper when the code is linear. Further, we give anon-linear example, in which an adaptive attack improves the performance of theeavesdropper. We derive the capacity for the unicast case and the capacityregion for the multicast case or the multiple multicast case in severalexamples of relay networks, beyond the minimum cut theorem, when no additionalrandom number is allowed as scramble variables in the intermediate nodes. Noprior study compared the difference of the capacity and the capacity regionbetween the existence and the non-existence of randomness in the intermediatenodes under these network models even with non-adaptive and non-active attacks.

Secure Network Code for Adaptive and Active Attacks with No-Randomness in Intermediate Nodes