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In this paper, we synthesize substitution boxes by the use of chaotic logistic maps in linear fractional transformation. In order to introduce randomness in the construction of S-boxes, the data from the chaotic system is used in linear fractional transformation to add additional unpredictable behavior. The proposed S-box is tested for its strength in encryption applications. The nonlinearity characteristic of the proposed S-box is studied, and the strength of the cipher is quantized in terms of this property. In addition, the behavior of bit changes at the output of the cipher in comparison with the input is also studied. Similarly, the input/output differential is also evaluated for different bit patterns. The results of statistical analyses show superior performance of the proposed S-boxes.