Paper Info
Title
Local-Encoding-Preserving Secure Network Coding
Abstract
Information-theoretic security is considered in the paradigm of network coding in the presence of wiretappers, who can access one arbitrary edge subset up to a certain size, also referred to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">security level</italic> . Secure network coding is applied to prevent the leakage of the source information to the wiretappers. In this paper, we consider the problem of secure network coding when the information rate and the security level can change over time. To efficiently solve this problem, we put forward <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local-encoding-preserving</italic> secure network coding, where a family of secure linear network codes (SLNCs) is called local-encoding-preserving if all the SLNCs in this family share a common local encoding kernel at each intermediate node in the network. We first consider the design of a family of local-encoding-preserving SLNCs for a fixed security level and a flexible rate. A simple approach is presented for efficiently constructing upon an SLNC that exists a local-encoding-preserving SLNC with the same security level and the rate reduced by one. By applying this approach repeatedly, we can obtain a family of local-encoding-preserving SLNCs with a fixed security level and multiple rates. We further consider the design of a family of local-encoding-preserving SLNCs for a fixed rate and a flexible security level. We present a novel and efficient approach for constructing upon an SLNC that exists a local-encoding-preserving SLNC with the same rate and the security level increased by one. Next, we consider the design of a family of local-encoding-preserving SLNCs for a fixed dimension (equal to the sum of rate and security level) and a flexible pair of rate and security level. We propose another novel approach for designing an SLNC such that the same SLNC can be applied for all the rate and security-level pairs with the fixed dimension. Also, two polynomial-time algorithms are developed for efficient implementations of the later two proposed approaches, respectively. Furthermore, we prove that all our three approaches do not incur any penalty on the required field size for the existence of SLNCs in terms of the best known lower bound by Guang and Yeung. Finally, we consider the ultimate problem of designing a family of local-encoding-preserving SLNCs that can be applied to all possible pairs of rate and security level. By combining the constructions of the three families of local-encoding-preserving SLNCs in the paper in suitable ways, we can obtain a family of local-encoding-preserving SLNCs that can be applied for all possible pairs of rate and security level. Three possible such constructions are presented.
Year
DOI
Venue
2020
10.1109/TIT.2020.3011555
IEEE Transactions on Information Theory
Keywords
DocType
Volume
Network coding,Encoding,Information rates,Kernel,Ciphers
Journal
66
Issue
ISSN
Citations 
10
0018-9448
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Xuan Guang102.70
Raymond W. Yeung281.80
Fang-Wei Fu321438.73