Strongly Secure Linear Network Coding

In a network with capacity h for multicast, information Xh = (X1, X2, · · · , Xh) 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 i1 , S i2 , · · · , S ir− 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. key words: network coding, secure network coding, linear network coding, secret sharing schemes, strong ramp secret sharing schemes