# Secure Image Signal Transmission Scheme Using Poly-Polarization Filtering and Orthogonal Matrix
## 5 Security Performance Evaluation  
In this section, the security performance of the PPF-OM scheme is evaluated. First, we assumed the eavesdropper [PERSON] had no information of the parameters \(l\), \(u\), PSs \(\mathbf{P}\), \(\mathbf{P}^{\perp}\), the \(M\times M\) orthogonal matrix, and the modulation mode of the two AM signals. Based on the demodulation procedures of [PERSON], if [PERSON] attempted to recover the information, the first step would include reshaping the received signal vector into the matrix. * It was known that the length of the received image signal vector was \(\frac{2\mu M}{l}\), and if the number of the divisor of \(\frac{2\mu M}{l}\) was \(\vartheta\), there were at least \(\vartheta\) matrix reconstruction methods. In addition, \(\frac{2\mu M}{l}\) was adjustable and \(\vartheta\) would increase as \(\frac{2\mu M}{l}\) increased. Moreover, the reshaped matrices \(\mathbf{T}_{\text{E,RH}}\) and \(\mathbf{T}_{\text{E,RV}}\) were composite matrices, and the \(M\times M\) orthogonal matrix \(\mathbf{\Gamma}\) was also unknown, which made it difficult to determine the correct matrix size. When the size of the reshaped matrices \(\mathbf{T}_{\text{E,RH}}\) and \(\mathbf{T}_{\text{E,RV}}\) were incorrect, it was not possible to correctly recover the horizontal and vertical signal component matrices. * If [PERSON] could correctly reshape the received image signal vector into a \(M\times\frac{2\mu}{l}\) matrix, [PERSON] would know \(\mathbf{T}_{\text{E,RH}}\) and \(\mathbf{T}_{\text{E,RV}}\) were composite matrices that should be processed by \(\mathbf{\Gamma}\) in the correct order. As [PERSON] did not have the information about \(\mathbf{\Gamma}\), it needed to search for the correct \(\mathbf{\Gamma}\) and order, as follows: \[\mathbf{F}_{\text{ER}}^{\text{o}}=\left[ \begin{array}{c}\mathbf{\Gamma}_{ \text{E}}^{\text{o}}(\cdot,2)^{\text{H}}\mathbf{T}_{\text{RH}}\\ \mathbf{\Gamma}_{\text{E}}^{\text{o}}(\cdot,2)^{\text{H}}\mathbf{T}_{\text{RH }}\\ \vdots\\ \mathbf{\Gamma}_{\text{E}}^{\text{o}}\left(\cdot,\frac{l}{2}\right)^{\text{H}} \mathbf{T}_{\text{RH}}\end{array} \right],\mathbf{F}_{\text{ER}}^{\text{e}}= \left[ \begin{array}{c}\mathbf{\Gamma}_{\text{E}}^{\text{e}}(\cdot,1)^{\text {H}}\mathbf{T}_{\text{RV}}\\ \mathbf{\Gamma}_{\text{E}}^{\text{e}}(\cdot,2)^{\text{H}}\mathbf{T}_{\text{RV}} \\ \vdots\\ \mathbf{\Gamma}_{\text{E}}^{\text{e}}\left(\cdot,\frac{l}{2}\right)^{\text{H}} \mathbf{T}_{\text{RV}}\end{array} \right]\] (26) According to Equation (26), only \(\left[ \begin{array}{cc}\mathbf{\Gamma}_{\text{ER}}^{\text{o}}&\mathbf{ \Gamma}_{\text{ER}}^{\text{e}}\end{array} \right]\)\(=\)\(\left[ \begin{array}{cc}\mathbf{\Gamma}^{\text{o}}&\mathbf{\Gamma}^{\text{e}}\end{array} \right]\) obtained \(\mathbf{F}_{\text{ER}}^{\text{o}}=\mathbf{F}^{\text{o}},\mathbf{F}_{\text{ER}}^ {\text{e}}=\mathbf{F}^{\text{e}}\). In other cases, H and V components could not be correctly recovered, nor could the two signals be separated through polarization filtering. In addition, a larger \(M\) led to a larger amount of calculation for [PERSON]. Therefore, in this case, the parameters were difficult to determine. * If we assumed that [PERSON] could correctly obtain the matrices \(\mathbf{F}_{\text{ER}}^{\text{o}}=\mathbf{F}^{\text{o}}\) and \(\mathbf{F}_{\text{ER}}^{\text{e}}=\mathbf{F}^{\text{e}}\) while the information regarding PSs was used for processing, the transmission signals were unknown. As \(\mathbf{F}_{\text{ER}}^{\text{o}}\) and \(\mathbf{F}_{\text{ER}}^{\text{e}}\) were mixed matrices of two polarized signals, the first step was to isolate them for demodulation. Thus, [PERSON] must first search for the correct PSs to construct polarization filtering matrices for the signal separation. However, the PSs for each row signal vector were different, and the modulation mode of the two AM signals was unknown. Therefore, even with the right polarization filtering matrices, it would be difficult to determine the correct AM signals. Based on the above analysis, it was difficult to avoid errors in the PSs.