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

We analyze the security for network code when the eavesdropper can contaminate the information on the attacked edges (active attack) and can choose the attacked edges adaptively (adaptive attack). We show that active and adaptive attacks cannot improve the performance of the eavesdropper when the code is linear. Further, we give an non-linear example, in which an adaptive attack improves the performance of the eavesdropper. We derive the capacity for the unicast case and the capacity region for the multicast case or the multiple multicast case in several examples of relay networks, beyond the minimum cut theorem, when no additional random number is allowed as scramble variables in the intermediate nodes. Index Terms secrecy analysis, secure network coding, adaptive attack, active attack