Abstract: To resist linearization attack and differential attack effectively, a nonlinear invertible transformation based on “tame transformation” was constructed. Incorporated with the Matsumoto-Imai (MI) scheme, a novel extended multivariate public key cryptosystem was proposed. Then, according to the proposed scheme, two practical applications including an encryption scheme and a signature scheme were designed respectively. Analysis results demonstrate that the extended cryptosystem inherits the merit of MI, i.e. efficient computation. Meanwhile, the novel extended scheme can also resist linearization attack, differential attack and algebraic attack.