A New Class of Multivariate Public Key Cryptosystem Constructed on the Basis of Message-Dependent Transformation

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. For constructing the proposed scheme, random transformations X and Ψ are used. The transformation Ψ would yield a breakthrough to a field of multivaliate cryptosystem in a sense that the transformation is dependent on a message. Namely it is a message-dependent transformation on the basis of random coding. We show that the proposed PKC’s, can be secure against the various excellent attacks such as the attack based on the Gröbner bases calculation(Gröbner bases attack, GB attack), Patarin’s attack and Braeken-Wolf-Preneel attack, due to the random transformations using new trap-doors.