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A chaotic orbit generated by a nonlinear system is irregular, aperiodic, unpredictable and has sensitive dependence on initial conditions. However, the chaotic trajectory is still not well enough to be a crypto system in digital secure communication. Therefore, we propose a Modified Logistic Map (MLM) and give a theoretical proof to show that the MLM is a chaotic map according to Devaney's definition. Based on the MLMs, we establish a Modified Logistic Hyper-Chaotic System (MLHCS) and apply MLHCS to develop a symmetric cryptography algorithm, Asymptotic Synchronization of Modified Logistic Hyper-Chaotic System (ASMLHCS). [ABSTRACT FROM AUTHOR]