Strongly Secure Linear Network Coding

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-i1, S-i2, ... , Sir-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 case of k < h-r.