Strongly Secure Linear Network Coding

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  • HARADA Kunihiko
    Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo
  • YAMAMOTO Hirosuke
    Department of Complexity Science and Engineering, Graduate School of Frontier Science, The University of Tokyo The Institute of Electronics, Information and Communication Engineers

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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 Sr=(S1, S2, …, Sr) 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 Si 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 (Si1, Si2, …,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 the case of k<h-r.

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