广义逆公钥密码体制

A Public-Key Cryptosystem Based on Generalized Inverses of Matrices

本文利用一般矩阵具有许多个广义逆的性质,设计出一种公钥密码体制方案。同时利用了纠错码的一些理论,使可纠的错误模式作为对信息进行保护的手段。文中对体制的各种性能指标进行了详细分析,同时对该体制的许多特性与McEliece公钥密码体制进行对比,指出该体制的优点和缺陷。本文还通过对各种可能的攻击的研究,指出这些攻击方法都有着大得难以实现的运算量,从而说明这种体制具有较高的安全性。本文也是矩阵广义逆理论应用于密码学的初次尝试。

According to the property that a matrix has many generalized inverses, a public-key cryptosystem is proposed. Simutaneously, some error-correcting codes are needed and the error pattern is used as the key procedure of keeping information secure. Many properties of this cryptosystem are analysed in detail, and compared with that of McEliece' s cryptosystem, with this the advantages and defects are showed clearly. By studing some possible attacks of this cryptosystem, any attack is showed to be unrealistic, so this cryp-tosystem is showed to be of high security. This paper is , additionally, the first attampt of using the theory of generalizd inverses of matrices in cryptography.