The continuous growth of media-rich content calls for more efficient and secure methods for content delivery. In this paper, we will address the optimal  linear network coding  (LNC) design for  secure unicast streaming  against passive attacks, under the requirement of  information theoretical security  . The objectives include 1) satisfying the information theoretical security requirement, 2) maximizing the transmission rate of a unicast stream, 3) minimizing the number of additional random symbols, and 4) minimizing the total bandwidth cost of content delivery. To fulfill the first three objectives, we formulate an  information theoretically secure unicast streaming  (ITSUS) problem, and then solve it by transforming it to a maximum network flow problem with node-capacity constraints. Based on the solution of the ITSUS problem, we develop an efficient algorithm that can find the optimal transmission topology with minimum bandwidth cost in a polynomial amount of time. With the optimal transmission topology, we investigate the design of both  deterministic  LNC and random LNC. For the  deterministic  LNC design, we not only prove that it achieves the four objectives but also analyze the size of required finite field. Moreover, for the random LNC design, we analyze the probability that a random LNC scheme satisfies the information theoretical security requirement. Finally, extensive simulation experiments have been conducted, and the results demonstrate the effectiveness of the proposed algorithms.
['Jin Wang', 'Jianping Wang', 'Kejie Lu', 'Yi Qian', 'Naijie Gu']
On the Optimal Linear Network Coding Design for Information Theoretically Secure Unicast Streaming