An improved MFE scheme resistant against SOLE attacks

It has been pointed out that those multivariate public key encryption schemes which are based on Medium Field Equations(MFE) can not resist the second order linearization equation(SOLE) attacks. Elaborate analysis of the attacks helps us to find out the conditions to construct the linearization equations. Then, we redesign the central map such that the linearization equations can not be built in any way. Thus, the proposed scheme based on this central map can withstand the SOLE attacks. The security analysis shows that the improved MFE scheme is a secure public key encryption scheme.