Research On MFE Multivariate Public Key Encryption Scheme

Multivariate public key cryptosystem is considered to be able to resist future attacks based on quantum computer, one of several public key cryptosystem whose security is based on a finite field to solve multi-variable polynomial equations as a NPC problem. The system with high efficiency and security, and easy hardware implementation, it has been recognized as a quantum computer age in a secure cryptosystem and digital signature options. MFE is a multivariable public key encryption scheme, it is by Wang et al were presented CT-RSA 2006, is a relatively safe and efficient encryption scheme. In PKC 2007, Ding et al use the second order linearization equation attack method by Patarin to break MFE, Wang Zhiwei et al have carried out two of its improved soon. In this paper, the medium-field multivariate public key encryption scheme and its SOLEs attack is described in detail, and analyze the shortcoming of Zheng et al' improvement, used ideas of increase the sub-center maps and mapping in the center of a new map on the complex and to ensure that the composite of the maps will still enable the public key for the second mapping, By redesigning the original proposal, the center of map, propose two new and improved MFE multivariate public-key encryption scheme. So that an attacker can not be related to the linear equation, and thus resist SOLEs attacks, resolved Wang zhi wei proposed scheme deficiencies. The new analysis shows that the improved scheme can not only resist SOLE attacks, but also to resist attack and Grobner rank-based attacks, Therefore, we have to improve the MFE scheme is a more secure public key encryption scheme of multi-variable.