1. Secure error-correcting network codes with side information leakage.
- Author
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Zhuojun Zhuang, Bin Dai, Yuan Luo, and Vinck, A. J. Han
- Subjects
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INFORMATION technology security , *ERROR-correcting codes , *ERROR correction (Information theory) , *INFORMATION sharing , *DATA transmission systems , *HAMMING weight - Abstract
Incorporating information security and error correction in network coding, which has various applications in communication theory, for example, secret key sharing through a network, is of special interest and has been widely studied. To make a more intensive analysis of secure error-correcting network codes, we investigate how to secure k source symbols transmission in a multicast network against an adversary that can obtain k1 source symbols as side information, eavesdrop µ channels and contaminate d channels. We introduce relative network generalised Hamming weight (RNGHW) with network error correction (NEC), or briefly NEC-RNGHW, to measure the equivocation to the adversary. Network generalised singleton bound on NEC-RNGHW is obtained and code constructions achieving the bound are provided. By these constructions, the maximum rate of a secure linear multicast is n - 2d - &#µ; - k1, where n is the minimum value of the maxflows from a source node to sink nodes. We also characterise the equivocation by the relative profiles of a linear code and a subcode, and tighten the singleton bound on equivocation by the generalised Griesmer bound on relative profiles. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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