# A Novel Image Encryption Algorithm Based on Voice Key and Chaotic Map
## 2 Principles of the Proposed Method
### Voice Key Generation Process  
The user's voice-feature information should be extracted as the key for image encryption prior to encryption. The speech signal is a non-stationary time-varying signal, whose characteristics can be analyzed and described in both the time and frequency domains. Here, sets of time-domain and frequency-domain feature parameters are extracted to perform the image encryption operation. The time-domain analysis method is the simplest and most intuitive analysis method. The time-domain speech parameters include short-term average energy, short-term average zero-crossing rate and short-term autocorrelation function. We take the number of peaks of a single-syllable single waveform as the extracted time-domain parameter. It has a corresponding relationship with the average zero-crossingrate and reflects the difference between various dissimilar syllables. The relevant expression is given in Equation (1).  
\[\left\{\begin{array}{l}n_{w}=\frac{\sum_{m=-l_{a}}^{l_{a}+l_{b}}|sgn[z(m)]-sgn[z( m-1)]|}{M\times 4}\\ sgn[z(m)]=\left\{\begin{array}{cc}1&z(m)\geq 0\\ -1&z(m)<0\end{array}\right.\end{array}\right. \tag{1}\]  
In Equation (1), \(L_{a}\) and \(L_{b}\) are the starting and ending positions of a single syllable in the time domain, respectively; \(z(m)\) is the amplitude of the audio position \(m\); and \(M\) is the number of single waveforms of a single syllable. A total of six \(n_{w}\) values calculated by Equation (1) are represented by \(n_{w}1\) to \(n_{w}6\), and these six values participate in the subsequent chaotic encryption calculation.  
The frequency-domain description of voice information is an important feature that reflects the distribution of voice information over different frequencies. Different people have different spectrum distributions of the same syllable. This can be used to distinguish the difference between the pronunciations of various people. Here, discrete fourier transform (DFT) is used to extract the user's voice frequency-domain features. It is a simple and practical method to analyze the voice frequency spectrum characteristics. Its formula is given by Equation (2), as follows:  
\[X(k)=\sum_{n=0}^{N-1}x(n)e^{-j\frac{2\pi}{N}kn}(k=0,\;1,\;2\ldots N-1) \tag{2}\]  
In Equation (2), \(X(k)\) represents the data after DFT transformation; \(x(n)\) is the \(n\)th signal sample; \(N\) is the total number of Fourier transform points; and \(k\) is the ordinal number of the abscissa of the spectrum, which represents the \(k\)th spectrum position. One of the peak frequency values can be selected to participate in the subsequent chaotic encryption calculation. This selection can be based on either a sequential or a magnitude relationship.  
As illustrated in Figure 1, in the first phase of the speech features extraction, the characteristic single waveform corresponding to each single-syllable speech datum is extracted. Subsequently, the single waveform is used to synthesize the repetitive long-term signal waveform, such as a waveform with a synthetic duration of three seconds. The waveform undergoes DFT transformation to extract its frequency-domain data, where the frequency data corresponding to the peak amplitude are considered. In addition, the time-domain feature data of the single-syllable characteristic single waveform are extracted, where the number of crests of the single waveform and the total number of single syllables are considered.  
Figure 1: _Cont._