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Aiming at the problem that speech information has a strong correlation in adjacent times and the data type is floating point, the image encryption algorithm of integer type is not suitable for speech encryption. This paper proposed a speech encryption algorithm based on robust chaotic mapping, which mainly utilizes the nonlinearities and dynamics of robust chaos to adapt to the characteristics of speech signals. Furthermore, a new 3D sine robust chaotic mapping (3D-SRCM) model is proposed in this paper, which effectively solves the problems of discontinuous parameter ranges, prone to chaotic degradation and lack of robustness in existing chaotic systems, and improves the robustness and complexity of chaos. In the speech encryption algorithm, the parameters of the chaotic mapping are adjusted according to the changes in speech signal characteristics to generate unique keys for different speech signals. The encryption algorithm compresses and denoises the signal through the Fast Walsh–Hadamard Transform (FWHT) before using chaotic sequences for initial scrambling encryption. Then, the signal is transformed by Discrete Wavelet Transform (DWT) to realize the second round of scrambling and diffusion encryption. This structure increases the security of the encryption algorithm and ensures the efficiency and reliability of the encryption process. The experimental results show that the algorithm has a large key space, good resistance to exhaustive attack, and statistical attack, which can effectively resist chosen plaintext attack. In the decryption process, the algorithm can quickly and accurately decrypt the encrypted speech with good decryption performance. • A speech encryption algorithm based on robust chaos was proposed. • A new 3D-SRCM model is proposed for existing chaotic systems. • The 3D-SRCM model solves chaotic degradation, improving robustness and complexity. • Control parameters were adjusted to adapt to speech signal, linking key and the signal. • In the encryption algorithm, the parameters of the chaotic map are adjusted to fit the speech signal. [ABSTRACT FROM AUTHOR]