Abstract: The current secure network coding has two methods.They are information-theoretic security and cryptography security. Among the encoding methods of information-theoretic security, the encoding scheme of the relay node uses the Random Linear Network Coding（RLNC） to generate the encoding matrix. But this method does not guarantee that the resulting matrix must be full rank and affects the decoding rate. This paper proposes a Multi-Level Network Coding（MLNC） scheme. The scheme uses the triangle matrix to encode source message. On the relay node, the node whose degree is greater than or equal to 2 is used as coding node, using multi-level network coding can make the message encode mix better. The encoding nodes generate the full rank lower triangular matrix and the full rank upper triangular matrix randomly. It uses their product as an encoding matrix. This scheme will ensure encoding matrix must be full rank. The receiving node can successfully decode the data. The result of the Matlab simulation shows that the probability of the coding matrix of MLNC satisfying k-secure can be better than RLNC. And the scheme of MLNC satisfies the theoretic security.

Key words: network coding, diagonal matrix, multi-level network coding, k-security

摘要： 目前安全网络编码的研究有信息论安全和密码学安全两种方法。信息论安全的编码方案中，中继节点编码主要是使用随机线性网络编码（RLNC）生成编码矩阵，但是此方法并不能保证生成的矩阵一定满秩，从而影响方案的解码率。提出了一个多级网络编码（MLNC）方案，该方案通过在源端使用对角矩阵对消息进行编码，以降低编码复杂度；在中继节点，让入度大于等于2的节点作为编码节点，使用多级的网络编码使混淆效果更好，编码节点随机生成满秩的下三角矩阵和上三角矩阵，用它们的乘积作为编码矩阵，这样能保证编码矩阵满秩，接收节点可以成功解码。Matlab仿真结果表明，MLNC编码矩阵达到k-安全概率优于RLNC编码矩阵，并证明MLNC方案满足信息论安全。

关键词: 网络编码, 对角矩阵, 多级网络编码, k-安全