An improved signature model of multivariate polynomial public key cryptosystem against key recovery attack

An improved signature model of multivariate polynomial public key cryptosystem to resist the key recovery attack is presented in this paper. Two pairs of public keys are added to design new authentication conditionals for public keys, and then the verification is not only to verify the original external information but also the exact internal kernel information. It requires both the corresponding private key and the exact internal node information to produce an accurate signature, so that a forged signature by key recovery attack cannot pass the verification without the exact private key. To illustrate this, the classic HFE (Hidden Fields Equations) scheme is taken as an example to clarify the signing and verifying process in detail. It provides a useful supplement to the research and designing of secure digital signature schemes in the quantum age.