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In this paper, a new class of Public-Key Cryptosystem (PKC) based on Random Simultaneous Equation of degree g(RSE(g)PKC) is presented. The proposed scheme uses a new class of trap-doors based on two classes of transformation, i.e., random transformation and message-dependent random transformation. In this paper, the authors present a new class of PKC whose security depends on the difficulty of the problem of solving a set of random simultaneous equations of degree g. Extensive studies have been made of the PKC constructed based on the Simultaneous Equations of degree g (SE(g)PKC).
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