# Audio Encryption Algorithm Based on Chen Memristor Chaotic System

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## Abstract

**:**

## 1. Introduction

## 2. Model and Dynamic Analysis of a Novel Memristor Chaotic System

#### 2.1. Chen Chaotic System Model Based on Magnetically Controlled Titania Memristor

#### 2.2. System Bifurcation and Maximum Lyapunov Exponent

#### 2.3. Multivariable Complexity Chaos Diagram

## 3. The Encryption Algorithm

#### 3.1. Preliminaries

#### 3.1.1. Chaotic Sequence Preprocessing

#### 3.1.2. Audio Signal Preprocessing

#### 3.2. The Encryption Process

#### 3.2.1. Scrambling

**Step 2**of Section 3.1.1) to get ${R}^{\prime}$, ${G}^{\prime}$, ${B}^{\prime}$.

#### 3.2.2. Shuffling

## 4. Experimental Simulation and Safety Analysis

#### 4.1. Key Sensitivity Analysis

#### 4.2. Statistical Characteristic Analysis

#### 4.2.1. Histogram

#### 4.2.2. Correlation Analysis

#### 4.3. Spectral Analysis

#### 4.4. Antidifferential Attack Analysis

#### 4.5. Root Mean Square (RMS) and Crest Factor (CF)

#### 4.6. Peak Signal-to-Noise Ratio and Encryption Efficiency

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Attractor phase diagram: (

**a**) x-y plane of new memristor chaotic system; (

**b**) x-z plane; (

**c**) y-z plane; (

**d**) 3D chaotic attractor.

**Figure 5.**Chaotic map of multivariable Multiscale Permutation Entropy (MPE) complexity: (

**a**) system MPE complexity; (

**b**) a–c plane of memristor chaotic system; (

**c**) 3D-MPE chaotic map.

**Figure 7.**Compression and encryption of audio signal: (

**a**) original audio diagram; (

**b**) compressed audio signal; (

**c**) noise suppression; (

**d**) reshaped audio signal; (

**e**) reconstructed audio signal; (

**f**) color audiogram; (

**g**) color encrypted audio map; (

**h**) decrypt audio map.

**Figure 8.**Key sensitivity test: (

**a**) Change Key 1; (

**b**) change Key 2; (

**c**) change Key 3; (

**d**) Correct decryption.

**Figure 9.**Histogram: (

**a**) histogram of original audio signal; (

**b**) histogram of encrypted audio signal.

**Figure 10.**Bar chart of RMS and CF values of original audio and encrypted audio. (

**a**) RMS value (

**b**) CF value.

Filename | Size(MB) | Original Audio Waveform | Encrypted Graph |
---|---|---|---|

Audio 1 | 0.260 | ||

Audio 2 | 0.128 | ||

Audio 3 | 2.56 | ||

Audio 4 | 1.05 |

Filename | Original Audio Data | Encrypted Audio Data | Decrypted Audio Data |
---|---|---|---|

Audio 1 | |||

Audio 2 | |||

Audio 3 | |||

Audio 4 |

**Table 3.**Distribution of adjacent samples of original audio and encrypted audio in horizontal and vertical directions.

Filename | Original Audio | Encrypted Audio | ||
---|---|---|---|---|

Horizontal | Vertical | Horizontal | Vertical | |

Audio 1 | ||||

Audio 2 | ||||

Audio 3 | ||||

Audio 4 |

Filename | Original Audio | Encrypted Audio | Correlation Between Original and Encrypted Audio | ||
---|---|---|---|---|---|

Horizontal | Vertical | Horizontal | Vertical | ||

Audio 1 | 0.9925 | 1.0000 | −0.0012 | $4.5618\times {10}^{-4}$ | 0.0014 |

Audio 2 | 0.9668 | 1.0000 | 0.0013 | $4.5302\times {10}^{-4}$ | 0.0054 |

Audio 3 | 0.9921 | 1.0000 | −$3.2348\times {10}^{-4}$ | −0.0026 | −0.0051 |

Audio 4 | 0.9217 | 1.0000 | 0.0043 | 0.0016 | 0.0021 |

Reference [28] | 0.9445 | – | −0.0081 | – | – |

Reference [29] | 0.9981 | 0.9981 | −0.0094 | 0.0079 | 0.0056 |

Filename | Original Audio Data | Encrypted Audio Data | Decrypted Audio Data |
---|---|---|---|

Audio 1 | |||

Audio 2 | |||

Audio 3 | |||

Audio 4 |

Audio | NSCR | UACI |
---|---|---|

Audio 1 | 99.9268% | 32.8195% |

Audio 2 | 99.9695% | 32.7827% |

Audio 3 | 99.8062% | 32.8285% |

Audio 4 | 99.9786% | 32.8661% |

Reference [10] | 99.9884% | 30.2437% |

Reference [31] | 99.60812% | 36.39705% |

Reference [30] | 99.996% | – |

Audio | Size | RMS (dB) | CF (dB) | Lossless Reconstruction |
---|---|---|---|---|

Audio 1 | 260 KB | 0.1389 | 10.5234 | Yes |

EAudio 1 | 260 KB | 0.5701 | 3.4409 | |

DAudio 1 | 260 KB | 0.1389 | 10.5234 | |

Audio 2 | 128 KB | 0.0536 | 16.4115 | Yes |

EAudio 2 | 128 KB | 0.5686 | 3.4499 | |

Audio 3 | 2.56 MB | 0.1998 | 11.0925 | Yes |

EAudio 3 | 2.56 MB | 0.5675 | 3.4563 | |

Audio 4 | 1.05 MB | 0.0652 | 15.5818 | Yes |

EAudio 4 | 1.05 MB | 0.5693 | 3.4453 | |

Reference [13] | 918 KB | 0.5786 | 4.7621 | Yes |

Reference [32] | – | $\cong 0.6$ | – | No |

Reference [9] | 1.84 MB | 0.6042 | 4.3754 | Yes |

Audio | Size | SNR (dB) | PSNR (dB) | Total (s) | Speed (s/KB) |
---|---|---|---|---|---|

Audio 1 | 260 KB | −12.5183 | 4.6302 | 0.636433 | 0.002448 |

Audio 2 | 128 KB | −20.5570 | 4.8659 | 0.326567 | 0.002551 |

Audio 3 | 2.56 MB | −9.5699 | 4.4186 | 5.342500 | 0.002087 |

Audio 4 | 1.05 MB | −18.8850 | 4.8346 | 2.531556 | 0.002411 |

Reference [13] | 304 KB | −28.1400 | 4.3100 | 58.63000 | 0.190000 |

Reference [34] | 439 KB | −22.139432 | 4.7500 | 1.176000 | 0.002679 |

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**MDPI and ACS Style**

Dai, W.; Xu, X.; Song, X.; Li, G. Audio Encryption Algorithm Based on Chen Memristor Chaotic System. *Symmetry* **2022**, *14*, 17.
https://doi.org/10.3390/sym14010017

**AMA Style**

Dai W, Xu X, Song X, Li G. Audio Encryption Algorithm Based on Chen Memristor Chaotic System. *Symmetry*. 2022; 14(1):17.
https://doi.org/10.3390/sym14010017

**Chicago/Turabian Style**

Dai, Wanying, Xiangliang Xu, Xiaoming Song, and Guodong Li. 2022. "Audio Encryption Algorithm Based on Chen Memristor Chaotic System" *Symmetry* 14, no. 1: 17.
https://doi.org/10.3390/sym14010017