针对有理多变量公钥密码系统（RMPKC）曾被改进的2R分解算法成功攻破这一问题,文中提出了一种RMPKC体制的改进方案.该方案的核心思想是将第一个有理映射的函数次数变为三次,第二个有理映射的函数次数保持不变.文中证明了这种改进方法能够使得2R分解算法的条件不被满足,因此能够抵抗目前的2R分解算法;文中还证明了,当第二个有理映射的函数次数是三次、第一个有理映射的函数次数保持不变时,2R分解算法仍有效.

As the rational multivariate public key cryptosystem（RMPKC） had been broken by an improved 2R decomposition method,this paper proposes an improved RMPKC scheme.In this scheme,the order of the function of the first rational mapping is changed to three while that of the second remains unchanged.Based on this core idea,the requirement for conducting the 2R decomposition attack is not fulfilled.Thus,the current 2R decomposition attack is effectively resisted by the improved RMPKC scheme.It is proved that the 2R decomposition attack is valid when the order of the function of the second rational mapping is changed to three while that of the first remains unchanged.