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Universal secure error-correcting (SEC) schemes for network coding via McEliece cryptosystem based on QC-LDPC codes

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Abstract

The McEliece cryptosystem based on quasi-cyclic low-density parity check (QC-LDPC) codes is presented to offer both security and error-correction simultaneously in the determined network coding system. The characteristics of the cryptosystem make it does not need to reduce information rate additionally to offer security. The messages u is encoded into x with QC-LDPC. x is transmitted through a network where a network coding error-correcting scheme is performed. \(\rho \) links are observed by the adversary and t errors occur in the network. The characteristic of MDS code make the errors cannot be spread, therefore, the corrupted packets which occur in t links will cause at most t errors in the received messages in the sink. As long as the number of errors occuring in the intermediate links will not exceed the minimum distance of QC-LDPC codes, the hybrid scheme can perform error-correcting and security simultaneously. The information rate reaches \({\mathrm{n}} - 2t\) instead of \({\mathrm{n}} - \mu - 2t\) where n is the max-flow min-cut.

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Acknowledgements

This work is supported by the fundamental research funds for Heilongjiang provincial universities (the study on error spreading depression in network coding), Suihua technology office program (SHKJ2015-015, SHKJ2015-014 ), National Science Foundation of China (61571150), Education Office of Heilongjiang Province Science and Technology Program (2016-KYYWF-0937), Suihua University Program (K1502003).

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Authors and Affiliations

  1. Computer Science Department, Harbin Engineering University, Harbin, China

    Guangzhi Zhang & Shaobin Cai

  2. Suihua University, Suihua, China

    Guangzhi Zhang

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  1. Guangzhi Zhang
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  2. Shaobin Cai
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Correspondence to Guangzhi Zhang.

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Zhang, G., Cai, S. Universal secure error-correcting (SEC) schemes for network coding via McEliece cryptosystem based on QC-LDPC codes. Cluster Comput 22 (Suppl 2), 2599–2610 (2019). https://doi.org/10.1007/s10586-017-1354-x

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  • DOI: https://doi.org/10.1007/s10586-017-1354-x

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