New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding

TL;DR

This paper introduces new parameters for linear codes, RDIP and RGRW, to characterize universal security and error correction capabilities in secure network coding, independent of underlying network codes.

Contribution

It defines RDIP and RGRW parameters and demonstrates their role in expressing universal security and error correction in linear code-based network coding.

Findings

RDIP and RGRW characterize universal security and error correction.

Existing schemes are analyzed using RDIP and RGRW.

Security performance is independent of underlying network codes.

Abstract

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.