A public cryptosystem based on the generated data in extension set

Assume X^# is an extension set in the domain U. Let X ^A, X^B be the positive domain of X^# in which X^A⊂X^#, X^B⊂X^#, and X^A≠X^B. X^A={x₁^A , x₂^A, ..., x_n^A}, X ^B={x₁^B, x₂^B, ..., x_n^B}. ∀x₁^A, x₁ ^B∈N⁺, |X^A|⩾4, |X^B |⩾4. By using the accumulated generating operation, we can obtain a mathematical model from X^A and X^B. From the mathematical model we also derive the sets of X´_A and X´ _B. Both X´_A and X´_B are the extended domains of X^#. There exist polynomials p^A(x), p ^B(x); and p^AB(x) from X´_A, X´_B , and X^AB, respectively. Based on the p^A(x), p^B(x), and p^AB(x), we propose a new public cryptosystem. In the presented system, we have a public cryptography system from generated data in extension set X^#, a public cryptosystem from two generated data in extension set X^#, and a public cryptosystem from hybrid generated data in extension set X^#. The proposed model is a secure system. Both sides in the communication system can depend on the proposed cryptosystem to fulfill the cryptography of the to-be-transmitted file and de-cryptograph of the cryptograph