基于最大秩距离码的私钥加密方案

Jordan和Rao基于纠错码提出了一种私钥加密方案，通过安全性分析可知，基于大数选举方法，此方案中的秘密矩阵能有效地获得。Gabidulin于1985年提出了秩距离码及最大秩距离码的理论，由于秩范数和秩距离码的特点，利用秩距离码构造密码系统，可用比较小的参数获得比较大的工作因子。Gabidulin,Paramonov和Tretjakov基于最大秩距离码提出了一种新的McEliece公钥密码系统，该文基于最大秩距离码提出了与其稍有不同的一种私钥加密方案。讨论了它的可行性及安全性，并证明了它比基于最大秩距离码的上述公钥密码系统更安全。

One Kind of Secret Code Encryption Scheme Based on Maximum Rank Distance Codes

Based on error correcting codes, a kind of secret code encryption scheme was put forward by J.P.Jordan and T.R.N.Rao. By analyzing security of the scheme based on the method of majority voting, it was shown that the secret matrix of the scheme could be obtained in an efficient way. E.M.Gabidulin introduced the theory of maximum rank distance codes in 1985. The method of determining the minimum rank distance of a given code had been given. By introducing the concept of linearized polynomial, similar to error correcting codes, some kinds of maximum rank distance codes have been constructed, and their coding and decoding problem had been studied. Because of characteristics of rank norm and rank distance codes, relatively large work factor can be obtained by making use of relatively little parameters if cryptosystem is constructed based on rank distance codes. By improving the McEliece public key cryptosystem based on error correcting codes and by utilizing maximum rank distance codes, E.M.Gabidulin, A.V.Paramonov and O.V.Tretjakov put forward one new public key cryptosystem. It was shown that relatively large work factor can be obtained by using relatively small parameters and the memory space of keys can be decreased. By combining the idea of the secret code encryption scheme suggested by J.P.Jordan and T.R.N.Rao with the idea of the new McEliece public key cryptosystem based on maximum rank distance codes put forward by E.M.Gabidulin, a new kind of secret code encryption scheme is proposed in this paper, which is based on maximum rank distance codes and there is a little bit of difference between it and that scheme suggested by Gabidulin etc. Feasibility and security of the scheme are discussed and it is proved that for sufficiently large parameters, it is infeasible by an exhaustive search to obtain the private key in the scheme proposed in this paper. Moreover, because of characteristics of rank norm and rank distance codes, the method of majority voting that is used for security analysis of secret code encryption scheme based on error correcting codes has no effect on the secret code encryption scheme based on maximum rank distance codes. All kinds of existing decoding methods have no effect on the secret code encryption scheme based on maximum rank distance codes. Therefore, the scheme in this paper is more secure than the above mentioned public key cryptosystems based on maximum rank distance codes.