## 3 Methodology
### Receiver
#### 3.2.2 Side Channel Attack Detection
The pointwise convolution operations \(p_{t}\) were applied to \(\hat{D}\) and are given as follows:  
\[p_{t}=\sum_{q=0}^{q-1}\hat{D}.\widetilde{B}(0.0,q,\hat{q}) \tag{29}\]  
Here, \(\widetilde{B}\) signifies the pointwise filter and \(\hat{q}\) signifies the output channel index. After that, the adaptive convolution operation was applied to \(p_{t}\) and is expressed as follows:  
\[\widetilde{A}=\sum p_{t}*w(i,u,\hat{q}) \tag{30}\]  
Here, \(\widetilde{A}\) signifies the output of the convolution layer and \(w\) signifies the adaptive weights. * _Pooling Layer_: Here, the maximum pooling method was applied, considering the parameters. The pooling equation is calculated as follows: \[\Psi_{p}=max(\widetilde{A})\] (31) Here, \(\Psi_{p}\) signifies the pooling layer's output. * _Fully connected layer_: Here, the flattening was initially performed using the outcome of the pooling layer to reshape the multi-dimensional input into a one-dimensional vector. The equation of the flattened layer is expressed as follows: \[F_{l}=flat(\Psi_{p})\] (32) Here, \((F_{l})\) implies the flattened layer and \((\Psi_{p})\) implies the flattening of the maximum pooling layer. Lastly, the obtained output given to the Fully Connected Layer (FCL) was derived as follows: \[v_{imp}=\frac{\sum S}{nm}\]0 (33) In this context, \((\pi)\) denotes the output of the FCL, \(w^{*}\) and \(b^{*}\) represent the weight and bias of the FCL, respectively, and \(\sigma\) is the sigmoid activation function. The final output was then obtained and is presented as follows: \[v_{imp}=\frac{\sum S}{nm}\]1 (34) Here, \((\hat{O})\) signifies the output layer outcome, and \(w^{out}\) and \(b^{out}\) signify the output layer weight and bias. Therefore, the predicted outcome is represented as \(\mu\). The algorithm for the ADS-CNN is given as follows (Algorithm 2):
* _Comparison with Standard CNN's_: To demonstrate the advantages of the proposed ADS-CNN architecture, we compared it with conventional Convolutional Neural Networks (CNNs) [25; 26] in terms of structure and efficiency. Traditional CNNs typically use standard convolution and pooling operations across multiple layers, which often leads to an increased parameter count and computational overhead. In contrast, ADS-CNN incorporates depthwise separable convolutions, which significantly reduce the number of trainable parameters by decomposing standard convolutions into depthwise and pointwise operations. For instance, a conventional CNN with three convolutional layers (kernel size \(3\times 3\), stride 1, and 64 filters) has approximately 37% more parameters compared to an ADS-CNN of equivalent depth. Furthermore, our ADS-CNN includes adaptive weight mechanisms, where the convolution weights are dynamically adjusted based on input feature characteristics. This contrasts with fixed-weight standard CNNs and improves flexibility in detecting the subtle spatial variations introduced by side-channel attacks. In our implementation, the ADS-CNN architecture uses three convolutional blocks with kernel sizes \(3\times 3\), each followed by ReLU activation and max-pooling layers. The adaptive weights \(w(i,u,\bar{q})\) in Equation (30) are updated during backpropagation using standard gradient descent, but are further modulated based on the local entropy features of the input. As a result, ADS-CNN achieves both higher classification accuracy and lower computational cost during training and inference, particularly for embedded or resource-constrained quantum hardware environments. The attacked signal \((\vec{\mu})\) was discarded when there was an attack on the signal. With the absence of any attack on the signal, the non-attacked \((\mu^{\prime})\) signal was provided for the quantum state measurement, which is discussed in the following section.