Machine-Learning Assisted Side-Channel Attacks on RNS ECC Implementations Using Hybrid Feature Engineering

Abstract

Machine learning-based side-channel attacks have recently been introduced to recover the secret information from protected software and hardware implementations. Limited research exists for public-key algorithms, especially on non-traditional implementations like those using Residue Number System (RNS). Template attacks were proven successful on RNS-based Elliptic Curve Cryptography (ECC), only if the aligned portion is used for templates. In this study, we present a systematic methodology for the evaluation of ECC cryptosystems with and without countermeasures (both RNS-based and traditional ones) against ML-based side-channel attacks using two attack models on full length aligned and unaligned leakages. RNS-based ECC datasets are evaluated using four machine learning classifiers and comparison is provided with existing state-of-the-art template attacks. Moreover, we analyze the impact of raw features and advanced hybrid feature engineering techniques. We discuss the metrics and procedures that can be used for accurate classification on the imbalanced datasets. The experimental results demonstrate that, for ECC RNS datasets, the efficiency of simple machine learning algorithms is better than the complex deep learning techniques when such datasets are limited in size. This is the first study presenting a complete methodology for ML side-channel attacks on public key algorithms.

A Appendix

Machine Learning Algorithms In this paper, four different classifiers are used to create the training model for the leakage information of a device under test. Hereby, each classifier is described in brief and the important parameters for profiling SCAs are specified.

Support Vector Machine (SVM). Support Vector Machines are one of the most popular algorithms used for classification problems in different application domains, including side-channel analysis [19, 33, 57]. In SVM, n-dimensional data is separated using a hyperplane, by computing and adjusting the coefficients to find the maximum-margin hyperlane, which best separates the target classes. Often, real-world data is very complex and cannot be separated with a linear hyperplane. For learning hyperplanes in complex problems, the training instances or the support vectors are transformed into another dimension using kernels. There are three widely used SVM kernels; linear, radial and polynomial. To tune the kernels, hyperparameters like ‘gamma’ and cost ‘C’ play a vital role. Parameter ‘C’ acts as a regularization parameter in SVM and helps in adjusting the margin distance from the hyperplane. Thus, it controls the cost of misclassification. Parameter ‘gamma’ controls the spread of the Gaussian curve. Low values of ’C’ reflect more variance and lower bias; however, higher values of ‘C’ show lower variance and higher bias. However, higher gamma leads to better accuracy but results in a biased model. To find an optimum value of ‘C’ and ‘gamma’, gridsearch or other optimization methods are applied.

Random Forest (RF). In Random Forest, data is formed by aggregating the collection of decision trees [12]. The results of individual decision trees are combined together to predict the final class value. RF uses unpruned trees, avoids over-fitting by design, and reduces the bias error. Efficient modeling using random forests, highly depends on the number of trees in the forest and the depth of each tree. These two parameters are tuned for an efficient model in this study.

Multi-layer Perceptron (MLP). Multi-Layer Perceptron is a basic feed-forward artificial neural network that uses back-propagation for learning and consists of three layers: input layer, hidden layer, and a output layer [52]. Input layer connects to the input feature variables and output layers return back the predicted class value. To learn the patterns from the non-linear data, non-linear activation function is used. Due to the non-linear nature of side-channel leakages, MLP appears to be the best choice, in order to recover secret information from learning patterns of the signals.

Convolutional Neural Network (CNN). Convolutional Neural Network is a type of neural network which consists of convolutional layers, activation layers, flatten layer, and pooling layer. Convolutional layer performs convolution on the input features, using filters, to recognize the patterns in the data [42]. The pooling layer is a non-linear layer, and its functionality is to reduce the spatial size and hence the parameters. Fully connected layers combine the features back, just like in MLP. There are certain hyperparameters related to each layer, which can be optimized for an efficient trained model. These parameters include learning rate, batch size, epochs, optimizers, activation functions, etc. In addition to these, there are a few model hyperparameters which can be used to design an efficient architecture. It should be noted that the purpose of this study is not to propose the architecture design of the CNN, but to analyze and test the existing CNN design on the RNS-based ECC dataset. Therefore, the focus is on tuning the optimized hyperparameters rather than modeling hyperparameters.

Hyperparameters tuning for SVM, RF, MLP, CNN For the training phase, we tuned the hyperparameters for SVM, RF, MLP and CNN using gridsearch to obtain the best possible model, as shown in Table 2.

Table 2. Parameter tuning for SVM, RF, MLP and CNN

The best parameters are chosen for each classification method and they are shown in Table 3.

Table 3. Best parameters for SVM, RF, MLP and CNN