On the optimal flow allocation and information theoretically secure network coding design for multiple multicasts

Summary With linear network coding (LNC), the data packets transmitted in a communication network are coded packets, which are linear combinations of original data packets. Since the coded packets can be useful for multiple destinations in multicast, LNC has been shown as a promising technology to improve the network throughput. On the other hand, the original data packets can be encoded with random symbols and transmitted in the network to make sure that a passive attacker cannot obtain the information of these original data packets when the passive attacker cannot obtain enough coded packets. Therefore, LNC also provides secure transmission without using the traditional encryption and decryption. In this paper, we will study an Information Theoretically Secure Multiple Multicasts (ITSMM) problem with the following objectives: (1) maximizing the secure transmission rate (STR), (2) minimizing the random symbol rate (RSR), and (3) minimizing the bandwidth cost (BC), when the data transmission is information theoretically secure. We firstly theoretically analyze the ITSMM problem, which shows that it is equivalent to a problem of network flow with constraints on each intermediate node. We then formulate the ITSMM problem by 3 linear programmings to get the maximum STR, the minimum RSR, and the minimum BC. After that, we prove the sufficient condition for the size of finite field over which the information theoretically secure linear multicast code (ITSLMC) can be designed. At last, we give extensive simulations, which show that the proposed algorithms are effective and efficient.