60 65 70 75 80 85 90 95 100 q train SRq train ANN SVM PUF Robustness

60 65 70 75 80 85 90 95 100 q train srq train ann svm

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5000 50 55 60 65 70 75 80 85 90 95 100 q train SR(q train ) [%] ANN SVM PUF Robustness PUF Bias (a) Simple Arbiter PUF. 2000 3000 4000 5000 6000 7000 8000 9000 50 55 60 65 70 75 80 85 90 95 100 q train SR(q train ) [%] ANN SVM PUF Robustness PUF Bias (b) 2 -XOR Arbiter PUF. Fig. 1. Box plots of obtained SR ( q train ) of our ML attacks. has freedom to scrutinize the training set, and as we verified that the modeling performance depends strongly on the used training CRPs, 100 different models were created for each experiment. Each model was respectively built and validated on subsets formed by random splits of a training set containing 70% and 30% of the training CRPs. The model with the best validation results was selected to evaluate the success rate using a test set of 5 , 000 previously unseen CRPs. In the Arbiter PUF additive delay model, e.g. as detailed in [5], [7], the response is shown to be linearly dependent on the cumulative XORs of the challenge bits, rather than on the challenge bits directly. Performing this nonlinear operation prior to training the ML algorithms substantially improves their performance: the ANN models use fewer neurons and the SVM models count on fewer support vectors. Consequently, as the models get simpler, fewer training CRPs are required. The results for the ANN and SVM modeling attacks on the simple Arbiter PUF are shown in Fig. 1(a). The used ANNs consist of a single neuron SLP using a threshold comparator as the activation function. The SVM models were based on
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linear kernels with γ = 0 . 1 . The graph shows the box plots of SR ( q train ) for both techniques over all performed experiments on all 20 data sets. Also shown are the Arbiter PUF’s robustness and bias which indicate practical lower and upper bounds for the achievable success rates. On average, SVM yields more accurate Arbiter PUF models than ANN for q train 500 , but ANN outperforms SVM for larger training sets. SVM achieves SR (50) 70% and for q train = 500 , both SVM and ANN are able to predict responses with an accuracy close to 90% . For q train 5 , 000 , ANN is able to perfectly model an Arbiter PUF by achieving success rates arbitrarily close to the PUF’s robustness. The decreasing height of the box plots indicates that the estimation of SR ( q train ) gets more accurate as q train increases. Similarly, the modeling performance of ANN and SVM on 2 -XOR Arbiter PUFs is evaluated. As their behavior is more complex, more training CRPs are required for effective modeling and we use training set sizes ranging from q train = 2 , 000 up to 9 , 000 CRPs, and 1 , 000 CRPs for the test set. Ten models are created for each experiment. The used ANNs consist of two layers with respectively four and one neurons, and respectively using hyperbolic tangent and linear activation functions. The SVM models were based on RBF kernels with ( γ = 10 , σ 2 = 3 . 16 ) for experiments with q train 6 , 000 and on MLP kernels with ( γ = 2 . 7 , κ 1 = 0 . 015 , κ 2 = - 1 . 2 ) for q train > 6 , 000 . Figure 1(b) shows the box plots of the obtained SR ( q train ) for all the experiments for the ANN and SVM models. This shows that SVM performs better than ANN when q train 3 , 000
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