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The block diagrams of voice encryptiondecryption using the new hyperchaotic process are demonstrated in Fig.8 and Fig.9 respectively.

The voice encryption scheme using the new hyperchaotic system.

The voice decryption scheme using the new hyperchaotic system.

As displayed in Fig.8, the encryption process contains two levels: scrambling level and masking level, where both levels depend on the sequence generated by the proposed scheme. Chaotic scrambling is the process of transforming the original voice signal based on a particular algorithm28,29,30. This transformation can be achieved through various techniques, including mathematical transformations, encryption algorithms, or chaotic systems. In our system, the voice signal is scrambled using the x, y, z, and w sequences generated by the new hyperchaotic system according to the following equation:

$${V}_{s}=vleft(tright)+scramblingStrength*({s}_{1}* xleft(tright){.}^{p}+ {s}_{2} * y{left(tright).}^{p2}+{s}_{3}* z{left(tright).}^{p3} + {s}_{4} * wleft(tright){.}^{p4})$$

(8)

The scrambling equation introduces a more sophisticated algorithm by integrating chaos and nonlinearity into the scrambling process. Where Vs is the scrambled voice signal, v(t) is the original voice signal s1, s2, s3, and s4 represent coefficients, and p1, p2, p3, and p4, represent the power terms associated with each state variable w(t), z(t), y(t), and x(t). The power terms add an element of nonlinearity to the scrambling process, making it more complex and potentially enhancing the algorithms security. Adjusting the power terms allows for fine-tuning the scrambling strength and the degree of nonlinearity introduced into the signal. Where the scrambling strength is set to 0.9, and the values of p1 =p2=p3 =p4 =1. The secret keys used in the encryption process are s1 =s2 =s3 =s4 =1.

Then, to add a complexity to the encrypted signal, the resulted scrambled signal Vs(t) is further masked using the state variables generated from the new scheme producing the encrypted voice signal Ve(t) as follows:

$${V}_{e}left(tright)={V}_{s}left(tright)+(xleft(tright)+yleft(tright)+zleft(tright)+wleft(tright))$$

(9)

In masking level, the complete state variables are used for masking the signal to increase the security level of the proposed system.

The decryption procedure is the vice versa of the encryption procedure, it involves generating an unmask signal by subtracting the same state variables from the encrypted signal producing the signal Vd(t) as follows:

$${V}_{d}left(tright)={V}_{e}left(tright)-(xleft(tright)+yleft(tright)+zleft(tright)+wleft(tright)$$

(10)

The produced signal is then unscrambled according to the following equation:

$${V}_{r}={V}_{d}left(tright)-scramblingStrength*({s}_{1}*xleft(tright){.}^{p}+{s}_{2}*y{left(tright).}^{p2}+{s}_{3}*z{left(tright).}^{p3}+{s}_{4} *wleft(tright){.}^{p4})$$

(11)

The resulting signal Vr(t), represents the recovered voice signal. Assuming that the hyperchaotic systems in both the encryption and decryption systems are identical, have the same initial condition, and synchronized. The recovered signal Vr(t) is like the original voice signal v(t). In our system the values of coefficients terms are 0.1 for s1, s2, and s3, and 1 for s4. While the values of the power terms are 1 for p1, p2, p3, and p4, and 0.5 for the scrambling strength term.

MATLAB program was used to acquire the simulation results. The suggested systems effectiveness and security were evaluated using various tests, including waveform analysis, PRD, SNR, and correlation measurements. The voice signals use eight quantization bits at 8000Hz.

The waveforms obtained from the proposed encryption system are illustrated in Fig.10, the recovered, encrypted, and original voice signals, where the original voice transmission is entirely altered by the encrypted signal. Meanwhile, the recovered and original signals are identical.

Waveform plots for the encrypted, recovered, and original voice signals.

Figure11 depicts the histograms of the encrypted, original, and recovered voice signals. The distributed histogram indicates the randomness of the encrypted voice signal, a stark contrast to the histogram of the original and recovered voice signals, which exhibits a normal distribution, rendering it susceptible to attacks. The analysis reveals that our proposed algorithm provides robust security against various statistical attacks, affirming its efficacy in safeguarding voice communication.

The histograms for the encrypted, recovered, and original voice signals.

The Percentage Residual Deviation (PRD), Signal Noise Ratio (SNR), and Correlation Coefficient (CC) are employed to analyse the proposed schemes immunity against statistical intruders31,32,33. Table 2 displays the values that were computed for various voice signals. The (PRD) is a statistical tool used to measure the deviation between encrypted and original audio signals. Low PRD values suggest a similarity between encrypted and original signals, indicating high fidelity and minimal distortion. Conversely, high PRD values imply significant differences, potentially indicating a decline in signal integrity and increased distortion. Table 2 provides the computed percent residual deviation values for a range of original and encrypted voice signals.

One of the widely considered objective metrics for assessing the strength of the original audio signal is the signalnoise ratio (SNR). The measurements of the SNR in Table 2 are highly negative, indicating an enormous quality of the encrypted speech signals. The correlation coefficient is a numerical correlation measure between -1 and 1. Table 2 provides the calculation for various speech signals. The small value of the (CC) obtained demonstrates how severely jumbled the encrypted signal is in comparison to the original voice signal. The higher PRD values suggest a significant deviation between the encrypted and original signals. The large negative SNR value indicates that the noise power is higher than the signal power, which makes it difficult to detect. On the other hand, near-zero correlation values imply a reduced similarity between the encrypted and original signals.

A keysensitivity analysis has been conducted to assess the responsiveness of the new encryption scheme to slight variations in the key values. A small change in one key, for example, the initial value of the x state variable is changed by 0.000000000000001, will entirely deviate the decrypted signal, as shown in Fig.12, which reflects the immunity of the proposed encryption system against attacks.

Decrypted speech signal with a bit of change in the initial values0.

Utilizing the NIST 80022 test package, which is provided by the US National Institute of Standards and Technology, we examined the randomness of the encrypted speech signal in this test. This research primarily aimsto test the randomness of encrypted and original voice signals. As indicated in Table 3, the tests were used to investigate the degree of randomness ofeach signal. The bit-stream of the original speech signal passed only 2 of the NIST tests. The results also suggest that the encrypted voice signal performs favorably in several statistical tests, meeting the criteria for randomness and passing certain NIST assessments.

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A comprehensive study of the novel 4D hyperchaotic system with self-exited multistability and application in the voice ... - Nature.com