Abstract: A secure network coding algorithm against the omniscient adversaries was presented. While the adversary can eavesdrop all links and jam z} links, the algorithm transforms the source news with sparse matrix to enhance the data anti wiretapping capacity. In order to detect and eliminate pollution attacks,thc receiver uses list decoding algorithm to recover the source news. The theoretical analysis and simulations both confirm that this algorithm can be designed and implemented in polynomial time, resistant eavesdropping and pollution attacks. At the same time, this algorithm can also make the standard random network coding to achieve the weakly secure condition at a high probability, increase the en- coding rate and reduce the occupied memory space. Furthermore, only the source and destination need to be modified, and intermediate nodes implement a classical distributed network code.

Key words: Network coding, Omniscient attack, Sparse matrix, List decoding, Weakly secure, Encoding rate