esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Performance Evaluation
### Effect on Faults  
#### 4.1.1 Experimental Setup  
In this subsection, we simulate our proposed architecture RAD defending against internal abnormal status (i.e., link down) and evaluate the architecture from three perspectives as we set up the abnormality.  
* Robustness: Packet Loss Rate (%)
* Agility: Transfer Delay (UDP), Connection Establishment Time (TCP)
* Efficiency: Throughput  
Basically, the general SDN controller (i.e., Floodlight) without RAD sets up the shortest path for routing. We also vary the abnormal level based on the number of downed links.
## 3 Calculation of Seepage Field
### Theoretical Calculation Method for Seepage Field in Shield Tunnel Excavation  
Based on the analysis in Section 3.1, the boundary conditions for steady-state seepage at the tunnel face can be simplified as shown in Figure 5. The longitudinal calculation range \(L\) can be taken as \(3.5D\).  
Without considering the variation in water pressure in the \(x\)-direction and ignoring the impact of anisotropy in the permeability coefficient, the seepage field near the shield tunnel face satisfies the two-dimensional Laplace governing equation:  
\[\frac{\partial^{2}h}{\partial z^{2}}+\frac{\partial^{2}h}{\partial y^{2}}=0 \tag{4}\]  
Assuming sufficient groundwater recharge, a stable groundwater level, and no seepage influence at a distance \(L\) in front of the tunnel, the boundary conditions can be expressed as  
\[\left\{\begin{array}{l}h(z,h_{0})=f_{1}(z)=h_{0}\\ h(z,0)=f_{2}(z)\\ h(L,y)=f_{3}(y)=h_{0}\\ h(0,y)=f_{4}(y)\end{array}\right. \tag{5}\]  
The boundary conditions \(f_{2}(z),f_{4}(z)\) are fitted using numerical calculation results. According to the research by [PERSON] et al. [25], an exponential function can effectively fit the seepage field distribution in front of and above the tunnel face, as shown in Equation (6). The fitting results under the conditions of this engineering case are shown in Table 1 and Figure 6.  
\[\left\{\begin{array}{l}f_{2}(z)=h_{\rm F}(0)+[h_{0}-h_{\rm F}(0)]\cdot\exp( aL/z+b)\\ f_{4}(y)=\begin{cases}h_{\rm F}(y)&0\leq y\leq D\\ h_{\rm F}(D)+[h_{0}-h_{\rm F}(D)]\cdot\exp[c\cdot h_{\rm w}/(y-D)+d]&D<y<h_{0 }\end{cases}\end{array}\right. \tag{6}\]  
Figure 5: Boundary conditions for the steady-state seepage problem at the tunnel face.  
Based on the above analysis, the hydraulic head at any point can be calculated. To improve computational efficiency, a hydraulic head network with a spacing of 0.25 m is established within the potential failure mechanism range in front of the tunnel face. The hydraulic head at any point can be interpolated using the four vertices of the grid to which it belongs. The pore water pressure is given by  
\[u_{i}=\gamma_{w}(h_{i}-y) \tag{9}\]  
where \(u_{i}\) is the pore water pressure at a point in the stratum (kPa), \(h_{i}\) is the total head at that point, and \(y\) is the position head, i.e., the distance from that point to the bottom of the tunnel.  
Figure 8 shows the pore water pressure distribution obtained using the analytical method proposed in this paper.
# Fog Computing: Enabling the Management and Orchestration of Smart City Applications in 5G Networks
## 5 Evaluation Results  
### Unsupervised Outlier Detection  
In Figure 10(a),b, the outcomes of the RC algorithm for the three dimensions regarding PM10, temperature and relative humidity for the bpost Car 1 are shown, with a contamination of 1.0% indicating that the RC algorithm intends to find the 1.0% of samples, which can be considered as abnormal. Similarly, in Figure 10(c),d, the results obtained for the IF outlier detection algorithm with a contamination of 1.0% for the bpost Car 1 are shown. In addition, in Figure 11(a),b, the outcomes of the RC algorithm for the bpost Car 2 are presented, while in Figure 11(c),d, the results obtained from the IF algorithm are shown. As can be observed, clear similarities are present in the results obtained by both algorithms for the two bpost cars. PM10 values above 30 ppm collected by both cars are marked as outliers by both algorithms, which indicates that these samples can be considered as unusual measurements.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Description** \\ \hline \(C\) & Communication range in meters. \\ \(U_{LPWAN}\) & Upload data rate of the LPWAN technology in Mbps. \\ \(D_{LPWAN}\) & Download data rate of the LPWAN technology in Mbps. \\ \(U_{fg}\) & Upload speed between a fog node and the cloud node in Mbps. \\ \(D_{Fog}\) & Download speed between a fog node and the cloud node in Mbps. \\ \(R\) & Number of data samples to be transmitted. \\ \(N\) & Number of bits in each data sample. \\ \(T\) & Transmission time of a packet. \\ \hline \hline \end{tabular}
\end{table}
Table 5: Variables of the fog-cloud infrastructure dimensioning.  
Figure 11: Outcomes of RC and IF algorithms (blue color: normal samples, red color: abnormal samples) for PM10, temperature and relative humidity values collected by the bpost Car 1. (**a**) RC with 1.0 (3D perspective), bpost Car 1; (**b**) RC with 1.0% (3D planes), bpost Car 1; (**c**) IF with 1.0% (3D perspective), bpost Car 1; (**d**) IF with 1.0% (3D planes) bpost Car 1.  
Figure 12: Outcomes of RC and IF algorithms (blue color: normal samples, red color: abnormal samples) for PM10, temperature and relative humidity values collected by the bpost Car 2. (**a**) RC with 1.0% (3D perspective), bpost Car 2; (**b**) RC with 1.0% (3D planes), bpost Car 2; (**c**) IF with 1.0% (3D perspective), bpost Car 2; (**d**) IF with 1.0% (3D planes), bpost Car 2.
## 5 Stage-Wise Role of SiL and HiL Across Development Phases
### Operational and Methodological Limitations  
Software-in-the-Loop's primary limitation is its lack of physical realism. Although high-fidelity models can simulate inputs, they cannot fully replicate the nuances of hardware timing, signal delays, or environmental noise. Moreover, performance on virtual ECUs may diverge from behavior on physical platforms due to timing discrepancies or resource contention. These limitations may be acceptable in many cases, especially when the development process favors early (unit) testing. Nonetheless, developers must remain aware of the reduced level of realism when interpreting results.  
Hardware-in-the-Loop introduces realism but at the expense of scalability and cost. Setting up and maintaining a HiL bench requires specialized equipment, calibration time,and manual oversight. The iterative process slows down considerably compared to SiL, and hardware availability often becomes a bottleneck.  
Both methods require careful planning to balance depth of coverage against cost, repeatability, and system maturity.
## 5 Experiments
### Position/Pressure Tracking Experiments
In order to verify the influence of varying supply pressure, the load force was set to 1 kN, and the supply pressure was varied according to the curve shown in Figure 13. The displacement tracking errors of the TDDSC, ADRC, and PID control algorithms are shown in Figure 14. It can be seen that the error of the TDDSC algorithm is smaller than those of the ADRC and PID algorithms, which indicates that the TDDCS algorithm can suppress the disturbance caused by the varying supply pressure. For the pressure controller, experiments were conducted to evaluate the tracking accuracies of the TDDSC and PID algorithms. The reference pressure was set to be 4 MPa, while the hydraulic cylinder was moved according to the reference trajectory shown in Figure 8. Figure 15 shows the pressure of the rod chamber. The RMSEs of the TDDSC and PID algorithms are 0.08 and 0.22 MPa, respectively. Due to the nonlinear characteristics of the pressure servo system and the uncertainty of the system, the RMSE of the TDDSC algorithm is less than that of the PID algorithm, which indicates that the designed pressure controller meets the requirements of accuracy. Figure 14: Displacement tracking error as a function of time under varying supply pressure. Figure 12: Tracking errors of the TDDSC and DSC algorithms as a function of time. Figure 8:0 Oil supply pressure as a function of time.
# FDBP-InSAR: An Efficient Algorithm for InSAR Imaging via Frequency Domain Back Projection
###### Abstract  
High-quality focusing with accurate phase-preserving is a significant and challenging step in interferometric synthetic aperture radar (InSAR) imaging. Compared with conventional frequency-based imaging algorithms, the time-domain back-projection algorithm (TDBPA) can greatly ensure the accuracy of imaging and phase-preserving by point-to-point coherent integration but suffers from huge computational complexity. In this paper, we propose an efficient InSAR imaging method, called a frequency-domain back-projection algorithm (FDBPA), to achieve high-resolution focusing and accurate phase-preserving of InSAR imaging. More specifically, FDBPA is utilized to replace the traditional point-to-point coherent integration of TDBPA with frequency-domain transform. It divides the echo spectrum into uniform grids and transforms the range compression data into the range frequency domain. Phase compensation and non-uniform Fourier transform of the underlying scene are implemented to achieve image focusing in the wavenumber domain. Then, the interferometric phase of the target scene can be preserved by accurate phase compensation of the target's distance. FDBPA avoids the repetitive calculation of index values and point-to-point coherent integration which reduces the time complexity compared with TDBPA. The characteristics of focusing and phase-preserving of our method are analyzed via simulations and experiments. The results demonstrate the efficiency and high-quality imaging of the FDBPA method. It can improve the imaging efficiency by more than three times, while keeping similar imaging accuracy compared with TDBPA.  
InSAR; back projection; frequency domain; imaging algorithm; high-quality focusing; phase preserving +
Footnote †: journal:  
Article
## 3 Description of the Method
### Surface Generation  
Upon establishing the station curves, a set of \((n+1)\)\(\times\)\((m+1)\) discrete points on the surface can be generated based on the equations of station curves, \(k=1\), \(2\), \(\ldots\), \(n\) and  
Figure 16: The uv grid lines of the upper surface: (**a**) uv grid lines generated by cross-sectional method; (**b**) uv grid lines generated by isoparametric method.  
Figure 17: A station curve of the upper surface.  
\(l=1,2,\ldots,m\). A (\(p\),\(q\))-order B-spline tensor product surface is then established to interpolate these discrete points in the following form:  
\[\mathbf{Q}_{k,l}=\mathbf{F}(u_{k},\;v_{l})=\sum_{i=0}^{n}\sum_{j=0}^{m}N_{i,p}(u _{k})N_{j,q}(v_{l})\mathbf{P}_{i,j}=\sum_{i=0}^{n}N_{i,p}(u_{k})\left(\sum_{j=0} ^{m}N_{j,q}(v_{l})\mathbf{P}_{i,j}\right) \tag{41}\]  
By establishing that \(\mathbf{R}_{i,l}=\sum\limits_{j=0}^{m}N_{j,q}(v_{l})\mathbf{P}_{i,j}\), the following is obtainable:  
\[\mathbf{Q}_{k,l}=\sum_{i=0}^{n}N_{i,p}(u_{k})\mathbf{R}_{i,l} \tag{42}\]  
where the surface interpolation problem is transformed into a curve interpolation problem. By employing curve interpolation methods, \(n+1\) curve interpolations can be performed to solve \(\mathbf{R}_{i,l}\), and similarly, \(m+1\) interpolations can be applied to \(\mathbf{R}_{i,l}\) to obtain the surface control points. Substituting these control points into Equation (41) yields the appropriate interpolated surface.  
For the construction of the transom, spray rail, and deck using governing surfaces, since the two boundary curves used to construct these surfaces are of the same order and share the same node vector, the usual process of increasing the order and refining the curves can be omitted. Therefore, the governing surface can be directly constructed using the control points of the boundary curves, as in the following form:  
\[\mathbf{F}(u,v)=\sum_{i=0}^{n+1}\sum_{j=0}^{1}N_{i,3}(u)N_{j,1}(u)\mathbf{P}_ {i,j} \tag{43}\]  
where \(\mathbf{P}_{i,0}\) and \(\mathbf{P}_{i,1}\) each denote the control points of the two boundary curves of the surface. The parameter vector \(u\) is identical to the boundary curves, while the node vector in the \(v\) direction is set as \(\mathbf{V}=\) [0,0,1,1].
## 4 Performance Evaluation
### Performance Comparison with Data Augmentation  
The number of ear images in the CIPIC database seems so small that the deep learning model could be overfitted to the training data [30]. Data augmentation can be an alternative to prevent this problem. In this paper, data augmentation techniques, such as zero-phase component analysis (ZCA) [35] and/or image shifting [36], were applied to 30 ear images; thus, the total numbers of training data were increased to 60 after applying ZCA and 90 after applying ZCA combined with image shifting, respectively.  
Tables 6 and 7 compare the RMSEs and LSDs for individual subjects according to the proposed HRTF estimation method with and without data augmentation, respectively, as measured at \(-135^{\circ}\), \(-80^{\circ}\), and \(-45^{\circ}\). As shown in Table 6, the average RMSE went a little higher as the amount of augmentation data increased. In other words, the average RMSE of ZCA + Image Shift-CNN-DNN HRTF was increased by 0.45 dB compared to that of CNN-DNN HRTF. Meanwhile, the average LSD was decreased as the amount of data augmentation increased. Table 7 showed that the ZCA+Image Shift-CNN-DNN HRTF could reduce the average LSD by 0.29 dB compared to CNN-DNN HRTF.
## 3 Experiments and Results
### Experimental Environment and Parameters Setting  
Infrared image dataset is a kind of self-made dataset. These images are taken by infrared imaging equipment. It contains 400 training images and 100 test images. In order to make the experimental results as accurate as possible, the training set should contain as many scenes as possible. In order to synthesize low-resolution images, Gauss filter is used to blur high-resolution images. Due to the small number of samples in the dataset, the original high-resolution image and the blurred low-resolution image are cut to generate more sample pairs. The original image pixel is \(320\times 240\), the cut image pixel is \(32\times 24\) and finally \(4\times 10^{4}\) pairs of training samples are generated. During the training, the learning rate is set to \(10^{-4}\) and the activation function is RELU.  
Among them, MAX is the largest number of regular partial iterations, and the maximum number of iterations has an impact on the reconstruction effect and time. As shown in Figure 5.  
As can be seen from the Figure 5a, the greater the number of iterations, the greater the PSNR values, the better the reconstruction effect. Figure 5b shows that the larger the number of iterations, the longer the time needed to reconstruct the image. Considering comprehensively, the number of iterations in this experiment is set to 50. In practical work, it can be selected according to the needs.  
The experimental environment is as Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Complexity Related Items** & **SRCNN** & **MPSR** \\ \hline Conv1 & (64, 9, 1) & (64, 5, 1) \\ Conv2 & (32, 5, 64) & (64, 3, 64) \\ Conv3 & (1, 5, 32) & (64, 3, 32) \\ Conv4 & None & (4, 3, 32) \\ Input image & \(S_{HR}\) & \(S_{LR}\) \\ Number of parameters & 57,184 & 58,048 \\ Complexity & 3.9 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparisons of model complexity
# Enterprise Security for the Internet of Things (IoT): Lightweight Bootstrapping with EAP-NOOB
## 2 Background
### User Experience with Devices  
To understand how the above standards are implemented in practice, we also looked at the user experience of bootstrapping two off-the-shelf devices. The Philips Hue [4] ecosystem uses the Zigbee Light Link (ZLL) profile. A typical Hue deployment consists of a bridge device, a smartphone application, and up to 50 connected light bulbs per bridge. The bridge acts as a centralized control system that allows for the user to administer connected light bulbs through the application. To set up a new Hue network, users need to connect the Hue bridge to the Internet through their home router. Users then pair their smartphone and the bridge device. This is done by simultaneously tapping a button on the bridge and the smartphone application. The smartphone must be connected to the same home router to which the bridge is attached before initiating the pairing process. Once the pairing process is successfully completed, the bridge can be accessed through the application and used to control the light bulbs that are connected to it. New lights can be added with the application either by performing an automatic search of available devices within range of the bridge, or by manually entering the serial number of the light bulb that the user wishes to connect.
# Towards Improving the Durability and Overall Performance of PV-ETICS by Application of a PCM Layer
## 2 En-ActivETICS as a Proposed Solution for Active External Walls
### Climate  
The analyses were carried out for 20 selected locations in Europe (5 in the north, 10 in the centre and 5 in the south). The 12 cities on the list were chosen as cities in the countries that revealed the highest share of the ETICS market. Moreover, due to the high accessibility of solar energy and its conversion, En-ActivETICS is also popular in 3 southern countries (Spain, Italy, Portugal), where typical ETICS is not useful. In addition, to enable the introduction of En-ActivETICS to new markets, 5 more locations in northern and central Europe were tested. All selected locations are listed alphabetically in Table 2. Locations not selected based on the ETICS market potential were additionally marked with the \({}^{\text{ne}}\) symbol. Two Koppen-Geiger climate classes are given for each location. The first one represents the classification of the photovoltaic climate, K-G-P [33], while the second one corresponds to the climates developed for simulation analysis of buildings, K-G-S [34]. Most cities selected for the analysis were classified as Dfb--a cold climate without a dry season and with a warm summer, based on the K-G-S classification. Other identified classes for the analysed locations are Dfc (cold climate without a dry season and with a cold summer), Cfb (temperate climate without a dry season and with a warm summer), Cas (temperate climate with a dry and hot summer) and Bsk (dry and cold steppe climate). Taking into account the indicators for the K-G-P photovoltaic climate, most locations were classified as DM--temperature with medium irradiation. Scandinavian locations were classified as EL--cold with low irradiation--except for Stockholm, which was classified as DL--temperate with low irradiation. Cities on the Iberian Peninsula were classified as DH--temperate with high irradiation--while Geneva was on the border with EM--cold with moderate radiation. Figure 2 shows the locations of 20 cities in Europe. For the numerical simulation, hourly data according to the TMY standard [35] (EnergyPlus Weather Data) was used. The statistical analysis of the ambient temperature and solar irradiation for all 20 locations was performed. Comprehensive data is shown in Figures 3 and 4. The analysis of the ambient temperature is shown in Figure 3. The minimum (T\({}_{\text{min}}\)) and maximum (T\({}_{\text{max}}\)) temperatures were determined for each location. Additionally, the minimum (T\({}_{\text{minDA}}\)) and maximum (T\({}_{\text{maxDA}}\)) average daily temperatures are presented. Moreover, the average daily difference of ambient temperature (T\({}_{\text{ADD}}\)) is given.
###### Abstract  
We present an experimental investigation into the third-order nonlinearity of conventional crystalline (_c_-Si) and porous (_p_-Si) silicon with Z-scan technique at 800-nm and 2.4-\(\upmu\)m wavelengths. The Gaussian decomposition method is applied to extract the nonlinear refractive index, \(n_{2}\), and the two-photon absorption (TPA) coefficient, \(\beta\), from the experimental results. The nonlinear refractive index obtained for _c_-Si is \(7\pm 2\times 10^{-6}\) cm\({}^{2}\)/GW and for _p_-Si is \(-9\pm 3\times 10^{-5}\) cm\({}^{2}\)/GW. The TPA coefficient was found to be \(2.9\pm 0.9\) cm/GW and \(1.0\pm 0.3\) cm/GW for _c_-Si and _p_-Si, respectively. We show an enhancement of the nonlinear refraction and a suppression of TPA in _p_-Si in comparison to _c_-Si, and the enhancement gets stronger as the wavelength increases.  
Keywords:third-order nonlinearity; self-focusing; TPA; porous silicon; Z-scan +
Footnote †: journal: Applied Physics Letters
# An Efficient BGV-type Encryption Scheme for IoT Systems
## 3 Introduction of BGV
first, given \(\text{ct}=(c_{0},c_{1},L-1)\) and corresponding secret key \(s\), \(\langle ct,s\rangle=c_{0}+c_{1}\cdot s=\{b\cdot v\)\(+p\cdot e_{0}+m+(a\cdot v+p\cdot e_{1})\cdot s\}\) mod \(q_{L-1}=\{m-a\cdot s\cdot v-p\cdot e\cdot v+p\cdot e_{0}+a\cdot v\cdot s+p \cdot e_{1}s\}\) mod \(q_{L-1}=\{m-pev\)\(+p(e_{0}+e_{1}s)\}\) mod \(q_{L-1}\). Let error be \(-pev+p(e_{0}+e_{1}s)\). If \(0<\text{error}<q_{L-1}\), \(\langle ct,s\rangle\) mod \(p=m\). Second, given \(\text{ct}=(c_{0},c_{1},i-1)\) and secret key \(s\), where \(\text{ct}\) is the product of \(\text{ct}_{1}=(c^{\prime}_{0},c^{\prime}_{1},i)\) and \(\text{ct}_{2}\) = \((c^{\prime\prime}_{0},c^{\prime\prime}_{1},i)\) outputted by Mul, let \(rt_{i}\) be the inverse element of \(t_{i}\) that maps element from \(R_{t_{i}q_{i}}\) to \(R_{q_{i}}\), we have \(\langle ct,s\rangle=c_{0}+s\cdot c_{1}=rt_{i}(t_{i}d_{0}+b_{i}d_{2})+s[rt_{i}(t _{i}d_{1}+a_{i}d_{2})]=d_{0}+sd_{1}+rt_{i}(b_{i}+a_{i}s)d_{2}=d_{0}+sd_{1}+rt_{ i}(t_{i}s^{2}-pe_{i})d_{2}=d_{0}+sd_{1}+s^{2}d_{2}-rt_{i}pe_{i}d_{2}\). Because  
\[d_{0}+d_{1}\cdot s+d_{2}\cdot s^{2}=\{c^{\prime}_{0}\cdot c^{ \prime\prime}_{0}+(c^{\prime}_{0}\cdot c^{\prime\prime}_{1}+c^{\prime}_{1} \cdot c^{\prime\prime}_{0})s+c^{\prime}_{1}\cdot c^{\prime\prime}_{1}s^{2}\}= \{m^{\prime}\prime^{\prime\prime}+v^{\prime}v^{\prime\prime}(pe)^{\(p\cdot\epsilon_{i}-p_{i+1}\cdot s^{2})\bmod p_{i+1}\cdot q_{i}(=q_{i+1})\). Third, move the SwitchModulu operation in Mul from the last step to the first step.  
Because the encryption, decryption, and addition algorithms do not change, we focus on the multiplication algorithm. Given two ciphertexts \(\text{ct}_{1}^{(i)}=(c_{0}^{(1)},c_{1}^{(1)},i)\) and \(\text{ct}_{2}^{(i)}=(c_{0}^{(2)},c_{1}^{(2)},i)\) of the plaintexts \(m_{1}\) and \(m_{2}\), the multiplication algorithm first SwitchModulu them to \(\text{ct}_{1}^{(i-1)}=(c_{0}^{(1)},c_{1}^{(1)},i-1)\) and \(\text{ct}_{2}^{(i-1)}=(c_{0}^{(2)},c_{1}^{(2)},i-1)\) and then SwitchKey the product of \(\text{ct}_{1}^{(i-1)}\) and \(\text{ct}_{2}^{(i-1)}\) to \(\text{ct}^{(i)}=(c_{0},c_{1},i)\) as below: \(c_{0}\leftarrow\{p_{i}c_{0}^{(1)}c_{0}^{(2)}+b_{i}c_{1}^{(1)}c_{1}^{(2)}\}\bmod q _{i}\) and \(c_{1}\leftarrow\{p_{i}(c_{0}^{(1)}c_{1}^{(2)}+c_{0}^{(2)}c_{1}^{(1)})+a_{i}c_{ 1}^{(1)}c_{1}^{(2)}\}\bmod q_{i}\)  
Given the secret key \(s\), we have  
\[\langle ct,s\rangle=c_{0}+s\cdot c_{1}=\{p_{i}c_{0}^{(1)}c_{0}^{( 2)}+p_{i}sc_{0}^{(1)}c_{1}^{(2)}+p_{i}sc_{0}^{(2)}c_{1}^{(1)}+p_{i}s^{2}c_{1}^ {(1)}c_{1}^{(2)}-pe_{i}c_{1}^{(1)}c_{1}^{(2)}\}\bmod q_{i}\] \[=p_{i}(c_{0}^{(1)}+sc_{1}^{(1)})(c_{0}^{(2)}+sc_{1}^{(2)})\bmod q _{i}-pe_{i}c_{1}^{(1)}c_{1}^{(2)}\bmod q_{i}\]  
If the error terms are less than \(q_{i}\), we have \(\langle ct,s\rangle\bmod p=m_{1}m_{2}\). Obviously, the correctness condition is the same as the BGV scheme. **Observation 1**. : _Next, we replace the normal switch key \(\text{epk}_{i}\) with another sublayer's switch key \(\text{epk}_{j}\) in Mul and observe the decryption process.