Infinite generating keys based on publish system

In this paper, we combined the public secrete key cryptograph system proposed by Diffie and Hellman, with the infinite generation keys based on grey theory. And we got another related code for cryptograph system. This is a kind of infinite generation keys based on the public key system. This system is much more secret than traditional systems, and it can also be applied in then. According to past researches, Diffe and Hellman had presented the basic concepts of cryptography, based on the discrete logarithm model. Another search in grey field, only a few papers has touch this field. It is the first time that AGO method applied in grey theory in this kind of research. Also, based on the GM(1,1) model, we used finite original code to create an infinite variables code sequence, and we got the code from the known secrete key. In this paper, we define two parameters: cryptography sequence ψ and 3rd order symmetric group S₃ and presented six cryptography models to contribute our system. Based on discrete logarithm model, the secrete value is high to O(e^{C√(ln(p)ln(ln(p)))}) for public system, and it is hard to calculate the sequence by the present computing ability. Therefore, to break into this system by mathematical formula is not possible nowadays. To promote the efficiency, we also develop a toolbox not only to decrease the calculation time, but also to examine the reliability of our system.