A new encryption scheme for multivariate quadratic systems

It is regarded as a difficult task to design a secure MPKC fundamental schemes such as an encryption scheme. In this paper we introduce a new central trapdoor for multivariate quadratic (MQ) public-key cryptosystems that allows for encryption, in contrast to time-tested MQ primitives such as Unbalanced Oil and Vinegar or Rainbow which only allow for signatures. The same as UOV or Rainbow, our construction is single field scheme where the central polynomial system is chosen to have a particular structure that enables efficient inversion. After applying this transformation, the plaintext can be recovered by solving a linear system. Our new central trapdoor can use to replace the broken extension field calculation trapdoor and simple matrix encryption trapdoor, thereafter, we use the minus and plus modifiers to inoculate our scheme against known attacks. It is highlight that our encryption scheme is a good explore in the area of multivariate cryptography. Finally, a straightforward Magma implementation confirms the efficient operation of the public key algorithms.