This paper comprehensively introduces the mathematics theory for elliptic curve encryption based on ONBover Fm2, like the ONB denotation of element over Fm2, the elliptic curve over Fm2, and some computing rules. Based onthe theoretical introduction, an ECC-based encryption scheme is designed. The mechanism for key exchange is de-scribed in details for further applications. Underlying the given theoretical analysis and protocol description, an ECCsoftware is implemented. The software is characterized by excellent security as well as high efficiency.
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