# Machine Learning and Deep Learning Based Model for the Detection of Rootkits Using Memory Analysis
## 2 Background
### Deep Learning (DL) in Memory Analysis  
DL, particularly Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), has shown promise in memory analysis. CNNs can learn visual patterns, such as graphical user interface components, within memory dumps [10]. As we cannot use CNN, we will consider the data obtained from the analysis step which is in numerical format. Furthermore, DL models trained on memory dumps can automate the identification of malware signatures, the extraction of code injection attempts, and the recognition of malicious payloads embedded in memory. These models can process large amounts of memory data in real time, enabling a rapid response to emerging threats. RNN, especially LSTM (Long Short-Term Memory), models are effective in capturing sequential patterns, which is crucial for detecting complex attacks such as multi-stage malware. Refs. [7; 11] have shown that the LSTM success rate/accuracy is better when compared to CNN; that is why we have selected this model for our research. A brief description of LSTM is given below:  
* **Long Short-Term Memory (LSTM):** LSTM is a specialized recurrent neural network tailored for sequential data. Its unique architecture, with forget, input, and output gates, enables it to retain information and capture temporal patterns [11]. The equations given below show that the new state depends on the previous states. The new cell state is a combination of the previous cell state and the updated cell state. The output gate is calculated in the following steps.  
1. Forget Gate:  
\[f_{t}\ =\ \sigma(W_{f}\cdot[h_{t-1},x_{t}]+b_{f}) \tag{2}\]  
2. Input Gate:  
\[\tilde{C}_{t} =\tanh(W_{c}\cdot[h_{t-1},x_{t}]+b_{c}) \tag{3}\] \[i_{t} =\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i}) \tag{4}\]  
3. Cell State Update:  
\[C_{t}\ =\ \tanh(W_{C}\cdot[h_{t-1},x_{t}]+b_{c}) \tag{5}\]  
4. New Cell State:  
\[C_{\text{new}}\ =\ f_{t}\cdot C_{t-1}+i_{t}\cdot C_{t} \tag{6}\]  
5. Output Gate:  
\[o_{t} =\sigma(W_{o}\cdot[h_{t-1},x_{t}]+b_{o}) \tag{7}\] \[h_{t} =o_{t}\cdot\tanh(C_{t}) \tag{8}\]  
where:  
\(f_{t}:\) Forget gate output (0 to 1)  
\(i_{t}:\) Input gate output (0 to 1)  
\(\tilde{C}_{t}:\) Candidate cell state  
\(C_{t}:\) Updated cell state  
\(C_{\text{new}}:\) New cell state  
\(o_{t}:\) Output gate output (0 to 1)  
\(h_{t}:\) Hidden state (output)  
\(W_{f},W_{i},W_{c},W_{o}:\) Weight matrices  
\(b_{f},b_{i},b_{c},b_{o}:\) Bias vectors  
In Equation (2) The forget gate determines what information to discard from the cell state. The input gate determines in Equations (3) and (4) what new information to store in the cell state.The cell state is updated in Equation (5) using the input gate and candidate cell state. Finally, the output gate determines what part of the cell state is exposed as the hidden state in Equations (7) and (8).  
In memory analysis, LSTM's ability to learn from historical sequences makes it adept at identifying complex threats such as rootkits and malware. Its capacity to remember and analyze historical memory events equips it to automate the detection of subtle anomalies and threats in memory analysis.