This work proposes a class of one-dimensional analogue chaotic signals which have perfect statistical properties. A non-invertible transformation is introduced to generate a class of binary (symbolic) chaotic sequences with desired distribution function and correlation function. These binary chaotic secure sequences are proven to have near-ideal linear complexity and infinite large discrete correlation dimension, thus they cannot be reconstructed by linear-feedback shift-register (LFSR) techniques or nonlinear dynamics (NLD) forecasting in finite order.
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Zhou Hong (1997) studied this question.