Convolutional Chaotification Model With Hardware Implementation

When high-dimensional (HD) chaotic systems are used in practical applications such as signal detection and secure communication, they often suffer from limited robustness and dynamical degradation under finite-precision implementation. To address these issues, this article proposes a convolution-based chaotification model that transforms a seed map into a higher dimensional chaotic system through convolutional coupling and feedback. Theoretical analysis shows that all Lyapunov exponents (LEs) can remain positive within appropriate parameter ranges. Based on this model, three new chaotic maps are derived, which exhibit higher dynamical complexity and stronger resistance to parameter estimation attacks and dynamical degradation than most compared systems. A field-programmable gate array (FPGA)-based hardware platform is further developed to implement the proposed maps, where three hyperchaotic (HC) sequences are generated simultaneously. In addition, a pseudorandom sequence generator driven by finite-precision chaotic states is designed, and at 16-bit precision, only the derived sequences from the proposed system pass all TestU01 tests among the compared systems. Finally, the finite-precision chaotic state sequences are applied to a secure communication system, which achieves lower bit error rates (BERs) under different signal-to-noise ratios (SNRs) and spreading factors.