New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding
This work addresses security and reliability issues in network coding for communication systems, but it is incremental as it builds on prior results by Silva et al. and focuses on theoretical analysis.
This paper tackles the problem of analyzing security performance and error correction capability in universal secure network coding based on arbitrary linear codes, and it introduces new parameters (RDIP and RGRW) to express these properties, with applications to existing schemes.
The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper considers the secure network coding based on arbitrary linear codes, and investigates its security performance and error correction capability that are guaranteed independently of the underlying network code. The security performance and error correction capability are said to be universal when they are independent of underlying network codes. This paper introduces new code parameters, the relative dimension/intersection profile (RDIP) and the relative generalized rank weight (RGRW) of linear codes. We reveal that the universal security performance and universal error correction capability of secure network coding are expressed in terms of the RDIP and RGRW of linear codes. The security and error correction of existing schemes are also analyzed as applications of the RDIP and RGRW.