In this paper, an efficient method for the construction of nonlinear component in order to improve the confusion effect in cryptosystems is proposed. It is based on linear fractional transformation, 2D Logistic-adjusted-Sine map and Gray code. The proposed approach is able to generate random integer sequences with high efficient nonlinearity in the generated values. The cryptographic analyses prove that the proposed substitution box method is of high performance and can be used with great potential for prominent prevalence in designing symmetric cryptosystems and copy right protection. Detailed experiment results are given to verify the feasibility of the proposed nonlinear component.