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The relationships of chaotic functions and cryptography are investigated in this paper. 128-bit symmetric keys are derived from some chaotic function, called simple logistic function (SLF), for suitable parameters. An improved algorithm of discretization of SLF is introduced and applied to the design of block encryption ciphers and key schedules with proper parameters and initial values. These are chosen by the Lyapunov exponent method for testing chaos. Dynamic S- Boxes of such block ciphers are generated. Security analysis is also given to these S-Boxes.