基于随机线性码的快速矩阵嵌入方法

Fast Matrix Embedding Based on Random Linear Code

矩阵嵌入将编码思想引入隐写过程,用病灶携带秘密信息,通过寻找校验矩阵的陪集首确定最小修改向量,提高隐写安全性.如何以较低的计算复杂度找到陪集首是矩阵嵌入设计的核心.针对小嵌入率下的隐写,该文讨论了将汉明码矩阵引入到随机线性码矩阵的可行性,进而提出了一种新的校验矩阵结构.在此基础上,以一定的计算复杂度限制为前提,以最大化嵌入效率为目标,给出了矩阵的最优化构造方法.实验结果表明,新方法相比已有矩阵嵌入方法在嵌入效率和嵌入速度上都有所提高,适合实时性要求高的隐写应用.

Matrix embedding （ME） encodes cover objects and secret messages with an error correction code and modifies the cover data according to the coding result. The modification vector is the coset leader of error correction codes and the messages are conveyed by the syndrome. How to find the coset leader with lower computational complexity is the core of ME design. To improve the embedding efficiency and embedding speed of small payloads ME, this paper discusses the feasibility of introducing Hamming codes into the parity check matrix （PCM） of random linear codes, and proposes a new PCM structure. On this basis, an optimization scheme is proposed which can adaptively generate a PCM to accommodate to the given cover length and provide the best performance while guaranteeing the desired computational complexity. Experimental results show that this new method achieves higher embedding efficiency and faster embedding speed than previous fast ME methods, and is more suitable for real-time steganogaphic systems.