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Strongly Secure Linear Network Coding

Kunihiko HARADA, Hirosuke YAMAMOTO

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Summary :

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.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.2720-2728
Publication Date
2008/10/01
Publicized
Online ISSN
1745-1337
DOI
10.1093/ietfec/e91-a.10.2720
Type of Manuscript
Special Section PAPER (Special Section on Information Theory and Its Applications)
Category
Information Theory

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