5 research outputs found
Secret Sharing and Network Coding
In this thesis, we consider secret sharing schemes and network coding. Both of these fields are vital in today\u27s age as secret sharing schemes are currently being implemented by government agencies and private companies, and as network coding is continuously being used for IP networks. We begin with a brief overview of linear codes. Next, we examine van Dijk\u27s approach to realize an access structure using a linear secret sharing scheme; then we focus on a much simpler approach by Tang, Gao, and Chen. We show how this method can be used to find an optimal linear secret sharing scheme for an access structure with six participants. In the last chapter, we examine network coding and point out some similarities between secret sharing schemes and network coding. We present results from a paper by Silva and Kschischang; in particular, we present the concept of universal security and their coset coding scheme to achieve universal security
Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding
By extending the notion of minimum rank distance, this paper introduces two
new relative code parameters of a linear code C_1 of length n over a field
extension and its subcode C_2. One is called the relative
dimension/intersection profile (RDIP), and the other is called the relative
generalized rank weight (RGRW). We clarify their basic properties and the
relation between the RGRW and the minimum rank distance. As applications of the
RDIP and the RGRW, the security performance and the error correction capability
of secure network coding, guaranteed independently of the underlying network
code, are analyzed and clarified. We propose a construction of secure network
coding scheme, and analyze its security performance and error correction
capability as an example of applications of the RDIP and the RGRW. Silva and
Kschischang showed the existence of a secure network coding in which no part of
the secret message is revealed to the adversary even if any dim C_1-1 links are
wiretapped, which is guaranteed over any underlying network code. However, the
explicit construction of such a scheme remained an open problem. Our new
construction is just one instance of secure network coding that solves this
open problem.Comment: IEEEtran.cls, 25 pages, no figure, accepted for publication in IEEE
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