Optimizing the selection of the secret parameters for public key cryptosystems by using interval linear programming and fully fuzzy linear programming

One of the basic tasks in public key cryptosystems is to determine the secret parameters. This paper proposes multi-objective interval linear programming and multi-objective fully fuzzy linear programming (FFLP) models to determine the optimum interval numbers and triangular fuzzy numbers (TFNs) of the secret parameters in the public key cryptosystems. The public and private (secret) objective function(s) and constraints can be considered such that the optimum interval numbers and optimum TFNs for the secret parameters can be obtained from which the random selection of the secret parameters can be made for each algorithm's execution. Adapting the general model to the Rivest, Shamir, Adleman (RSA) public key cryptosystem is also illustrated. In the interval programming model for the RSA, the linear combination method combines multiple objective functions into a single objective function, and nonlinear constraints are linearized using the Taylor series expansion method. No multiple objective functions are obtained in the FFLP model of the RSA, but the nonlinear constraints are again linearized using the Taylor series expansion method. The numerical application for the RSA public key cryptosystem is made for both models by considering five cases and twenty-four subcases, and the results are analyzed. To the best of our knowledge, there is no study in the literature that considers interval linear programming and/or FFLP to obtain the optimum interval numbers and TFNs for the secret parameters of the public key cryptosystems. The proposed methodology is systematic and generic and can also be adapted for other public key cryptosystems easily.