An Improved Medium Field Multivariate Public Key Cryptosystem

The medium field equation (MFE) multivariate public key encryption scheme has the advantages that it uses medium sized field extensions, which makes it encryption or decryption faster. However, it can not resists the second order linearization equation (SOLE) attack presented by Ding, et al in 2007 PKC conference. An improved MFE scheme is proposed in this paper. It not only resist the SOLE attack but also the previously known attack methods. What´s more, an idea is presented. Substitute for a system of quadratic polynomials which operated in a big extension field, we can improve the degree properly over a smaller extension field to obtain stronger security and faster implementation.