## 3 Proposed Approach  
The proposed approach employs SVD to select that part of each frame of video feed that contains the most significant information. This selected part of the frame is encrypted using PRESENT block cipher [36] for which an 80-bit key is generated using a logistic map. The following are the steps of the proposed approach:  
Given an image M with size \(128\times 128\),  
The image \(M\) is split into non-overlapping blocks, each measuring \(4\times 4\).  
For each block, the singular value decomposition is applied, and the diagonal matrix \(S_{i}\) is extracted, where \(i\) is the block number.  
\[B_{i}(M) =U\cdot S\cdot V^{T}\] \[=U\cdot\begin{bmatrix}S_{1}&0&0&0\\ 0&S_{2}&0&0\\ 0&0&S_{3}&0\\ 0&0&0&S_{4}\end{bmatrix}\cdot V^{T}\]  
For each block, the first singular value is extracted and stored in matrix \(M_{s}\) with size \(N/4\times N/4\). After processing all the blocks, matrix \(M_{s}\) is constructed, and it represents the input to encryption procedure.  
The singular values of the matrix \(M_{s}\) are rounded and converted to binary. Then, the binary values are transformed to a vector, which is decomposed into blocks of size 64 bits that are encrypted.  
Starting from an initial condition \(x_{0}\) and a control parameter \(\mu\), 80 pseudo-random numbers are generated by iterating the logistic map. These numbers are quantified using a threshold \(T\) to construct the encryption key \(K\).  
The encrypted blocks are reshaped, and the encrypted singular matrices are constructed.  
The inverse singular value decomposition is applied to each block to obtain the image with encrypted singular values.  
The pixels of the resulted images are shuffled using the Arnold cat map. The number of iterations of the cat map \(t\) is considered one of the keys of the cryptosystem.  
The secret keys of the scheme are: the initial condition and control parameter \((x_{0},\mu)\) of the logistic map, the threshold \(T\) used for the quantification step of the pseudo-random sequence, and the number of iteration \(t\) of the Arnold cat map. The following are the values used in our experiments:  
* \(x_{0}\) = 987,654,326 and \(\mu\) = 3.993787543;
* The threshold \(T=0.498754632\);
* The number of iterations of the Arnold cat map \(t=66\).  
Figure 7 shows the flowchart of the encryption method, whereas Figure 8 shows the encryption results.  
The encrypted images can be decrypted at the receiver's end using the following procedure:  
1. To restore pixel coordinates, the cat map is iterated \"P-t\" times, where \"P\" is the period of the cat map and \"t\" is the number of iterations in the encryption process.
2. The encrypted image \(M_{e}\) is split into non-overlapping blocks of size \(4\times 4\).
3. Every block is decomposed using singular value decomposition, and the diagonal matrix is extracted.
4. For each block, the first singular value is extracted and stored in a matrix to construct the encrypted singular matrix.
5. The singular values of the encrypted matrix are rounded and converted to binary. The binary values are then transformed to a vector, which is is decomposed into blocks of size 64 bits that are decrypted.  
Figure 8: Result of encryption-procedure employed on standard images: (**a**) aerial; (**b**) lena; (**c**) cameraman; (**d**) jet; (**e**) lake; (**f**) tank.  
Figure 7: Flowchart of the encryption procedure employed.  
The logistic map is used to generate 80 pseudo-random numbers, which are quantified using the threshold \(T\) to construct the decryption key \(K\).  
The blocks are injected along with the key \(K\) into the decryption procedure.  
The decrypted values are reshaped and transformed to singular blocks.  
Finally, the inverse singular value decomposition is applied to each block to obtain the decrypted image.  
Figure 9 shows the flowchart of the decryption method, whereas Figure 10 shows the decryption results.