Secure network coding with minimum overhead based on hash functions

In order to achieve complete security in networks with network coding, it has been shown that at least k original information symbols must be substituted with k uniformly distributed random symbols chosen from the same code field, where k is the maximum number of independent coding vectors accessible to the adversary. Thus, sender nodes must dedicate a portion of the bandwidth to transmit noise, which could cause a significant signaling overhead. In this letter, we propose a scheme that requires only one noisy symbol to be embedded in the original information symbol vector to achieve complete secrecy. This scheme utilizes hash functions to generate different random noisy symbols by using the only uniformly distributed random symbol and the information symbols. It has two main advantages: (a) complete security is guaranteed regardless of the number of independent coding vectors acquired by the adversary; and (b) signaling overhead to obtain complete security is minimized.