Strongly Secure Linear Network Coding

摘要

In a network with capacity h for multicast, information X~h = (X_1, X_2, ... , X_h) can be transmitted from a source node to sink nodes without error by a linear network code. Furthermore, secret information S~r = (S_1, S_2,... ,S_r) can be transmitted securely against wiretappers by k-secure network coding for k ≤ h-r. In this case, no information of the secret leaks out even if an adversary wiretaps k edges, i.e. channels. However, if an adversary wiretaps k+1 edges, some S_i may leak out explicitly. In this paper, we propose strongly k-secure network coding based on strongly secure ramp secret sharing schemes. In this coding, no information leaks out for every (S_1, S_2, ... , S_(r-j)) even if an adversary wiretaps k + j channels. We also give an algorithm to construct a strongly k-secure network code directly and a transform to convert a nonsecure network code to a strongly k-secure network code. Furthermore, some sufficient conditions of alphabet size to realize the strongly k-secure network coding are derived for the case of k < h- r.