8. Conclusion
In this paper, we have investigated the optimal design of weakly secure NC under wiretapping attack, where we focused on the scenario that there are multiple unicast streams between the same source and destination nodes. Our objectives include (1) maximizing the STR under the weakly secure requirement, and (2) minimizing the size of the finite field, on which the weakly secure NC is defined. To address the issue, we have applied a novel approach that integrates weakly secure NC design with transmission topology construction. In particular, we first defined the problem and analyzed its behaviors, including the characteristics of an optimal transmission topology, the maximal STR, and the NP-hardness of the problem. Based on the understandings of the problem, we developed an optimal algorithm that is practically solvable when the capacity between the source and destination nodes is small, and we developed two efficient heuristic algorithms for general case to achieve the above two objectives. We then devised deterministic and random coding schemes that can achieve the maximal STR, given a transmission topology, where we also studied the relationship between the transmission topology and two major system factors: (1) the size of the finite field, and (2) the probability of a random code is weakly secure. Then, another heuristic algorithm is developed for the transmission topology which can reduce the size of the finite field and increase the probability of a random code is weakly secure. Finally, we have conducted extensive simulation experiments and the results show that the the proposed heuristic algorithms achieve good performance in various scenarios.
