Construction of Extended Multivariate Public Key Cryptosystems

Based on the ideas: “invertible cycle”, “tame transformation” and “special oil and vinegar”, three different nonlinear invertible transformations were constructed separately. Then making use of the idea of the extended multivariate public key cryptosystem, and combining the nonlinear invertible transformations above with Matsumoto-Imai (MI) scheme, three methods of designing extended multivariate public key cryptosystem were proposed. Next, the corresponding encryption and signature algorithms were given. Analysis results demonstrate that the new extended cryptosystems inherit the merit of MI scheme, i.e., efficient computation. Meanwhile, the new extended cryptosystems can also resist the linearization attack, differential attack and algebraic attack.