与低秩纠错编码相结合的多变量加密方案

New multivariate encryption scheme with low rank error-correcting codes

为了探索构造多变量核心映射的新方法,在cubic simple matrix方案基础上,设计了一种利用秩矩阵码的方法来改进原方案的核心映射.主要在隐藏核心映射的相应变换上进行了改进,以低秩奇偶校验(LRPC)码中的校验矩阵设计核心映射,对原方案的核心映射作了一个变换.然后,根据用户身份选定错误向量,作为扰动部分添加到核心映射中,重新构造出了新的核心映射,提出了一种基于LRPC码的多变量加密方案.通过分析可知:新方案的安全性可以归约到求解多变量二次多项式问题和秩最大似然译码问题;在效率上,与原方案相比,密钥量增加不大,但密文扩展率降低了50%.

In order to explore the new way to construct multivariate core mapping,a method was designed by using rank matrix code to improve the original scheme′s core mapping,which based on the cubic simple matrix scheme.The main work was to improve the corresponding transformation of hiding core mapping,which used the check matrix of low rank parity check codes to design the core mapping and made a transformation for the original scheme′s core mapping.Furthermore,an error vector was selected according to users′identity,which was added to the core map as a perturbation.Then a multivariate encryption scheme based on low rank parity check（LRPC）codes was proposed after reconstructing the new core mapping.Finally,through the analysis,it can be seen that the security of the new scheme can be reduced to the problems of solving multivariate quadratic（MQ）equations as well as rank syndrome decoding（RSD）,which increases the scheme′s security.In terms of efficiency,the ciphertext extension rate of the new scheme is reduced by 50% compared with the original one without increasing a lot of key sizes.