基于贪心算法构成的正交矩阵及保密通信

Orthogonal matrix based on Greedy algorithm and secure communication

提出用贪心算法来构成全正交或类正交矩阵的方法。首先,建立模型,并对该模型进行仿真验证,统计对应列数r一定时的全正交或类正交矩阵数量,进而分析这些矩阵的性质,如唯一性、均衡性、行列正交性以及r变化时的矩阵数量。其次,在此基础上,对其在保密通信中的应用进行了分析和实现,从而说明这种矩阵在保密通信中的可行性和实用性,因其在大小上不受任何限制,数量上较相同列数的walsh矩阵多得多,为保密通信的提供更多的可用密钥序列。

This paper proposed the method of using the Greedy algorithm to generate the orthogonal matrix or Similar orthogonal matrix. First, it built the model, and simulated it. By counting the number of orthogonal matrix or Similar orthogonal matrix when r is constant, it analyzed the characteristics of these matrixes, such as uniqueness, balance, orthogonality and the number of matrix when r changed. Next, based on this, this paper analyzed application of the method in secure communication to illustrate the feasibility and practicality of the matrix. Compared with walsh matrix, the size and quantity of this matrix have many advantages. So, it provides more key sequences for secure communication.