Universal Secure Error-Correcting (SEC) Schemes for Network Coding via McEliece Cryptosystem Based on QC-LDPC Codes

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 network coding system. The characteristics of the cryptosystem make it does not need to reduce information rate additionally to offer security. The messages \(\mu \) is coded into x with QC-LDPC. x is transmitted through a network where a MDS network coding error-correcting scheme is performed. \(\rho \) links are observed by adversary and t errors occurs in the network. The characteristic of MDS codes make the errors can’t 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 occurs in the intermediate links is not beyond the minimum distance of QC-LDPC codes, the hybrid scheme can perform error-correcting and security simultaneously. The information rate reaches \(\mathrm{{(n}} - 2t)/n\) instead of \(\mathrm{{(n}} - \rho - 2t)/n\) where n is the max-flow min-cut.