PURPOSE: A public key encryption system based on a matrix polynomial ring and field is provided, which is used in a very fast PKI construction by overcoming an encryption and decoding speed of the prior encryption system. CONSTITUTION: A size mechanism based on coefficients of a complex polynomial is applied in the public key encryption system. And a size mechanism based on an order of the complex polynomial is applied on the public key encryption system. The public key encryption system is used in an electronic signature method. And a fast key generation time of the public key encryption system is used as one time password.
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