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The paper proposes a digital chaotic secure communication by introducing a magnifying glass concept, which is used to enlarge and observe minor parameter mismatch so as to increase the sensitivity of the system. The encryption method is based on a one-time pad encryption scheme, where the random key sequence is replaced by a chaotic sequence generated via a Chua's circuit. We make use of an impulsive control strategy to synchronize two identical chaotic systems embedded in the encryptor and the decryptor, respectively. The lengths of impulsive intervals are piecewise constant and, as a result, the security of the system is further improved. Moreover, with the given parameters of the chaotic system and the impulsive control law, an estimate of the synchronization time is derived. The proposed cryptosystem is shown to be very sensitive to parameter mismatch and hence the security of the chaotic secure communication system is greatly enhanced.