Neural network-based models are at the core of state of the art techniques in many fields. Most critically, they are increasingly embedded into systems that take autonomous decisions in place of persons, such as in self-driving cars [Wu2017SqueezeDetUS, deepxplore] or in robots . The value of those embedded models is then not only due to the costs implied by research and development, but also because of their critical interaction with their environment. First attacks on neural-based classifiers [BIGGIO2018317] aimed at subverting their predictions, by crafting inputs that are yet still perceived by humans as unmodified. This leads to questions about the security of applications embedding them in the real word [Kurakin2016AdversarialEI], and more generally initiated the interest of the security community for those problems [DBLP:journals/corr/PapernotMSW16]. Those adversarial attacks are confined in modifying the data inputs to send to a neural model. Yet, very recently, other types of attacks were shown to operate by modifying the model itself, by embedding information in the model weight matrices. This is the case of new watermarking techniques, that aim at embedding watermarks into the model, in order to prove model ownership[Nagai2018, watermarking], or of trojaning attacks [trojannn, stuxdnn] that empowers the attacker to trigger specific model behaviors.
The fact that neural network weights are by themselves implicit (i.e., they do not convey explicit behavior upon inspection as opposed to the source code or formal specification of a software component) expose applications to novel attack surfaces. It is obvious that those attacks will have increasingly important impact in the future, and that the model creators – such as companies – have a tremendous interest in preventing the tampering with their models, specially in embedded applications [deepxplore, 8123567].
In this context, we are interested in providing a first approach to detect the tampering of a neural network-based model that is deployed on a device by the model creator. We stress that one can consider as an attack any action on a model itself (i.e., on its weights) that was not performed by the creator or the operator of that model. To illustrate the practical effect of the tampering with a model, we present on Figure 1 a scenario of a fitted model (leftmost image) over two classes of inputs (blue and yellow dots). After a slight manipulation of few weights of the model (attack described in the Figure caption), we can observe the resulting changes in the model decision boundaries on the rightmost image. The attack caused a movement of boundaries, that had the consequence at inference time to return some erroneous predictions (e.g., blue inputs in the yellow area are now predicted as part of the wrong class). Those wrong predictions might cause safety issues for the end-user, and are thus due to the attack on the originally deployed model.
1.1 Practical illustration of an attack: a trojaned classifier
We motivate our work through a practical attack, using the technique proposed by Liu et al. in [trojannn]. The goal of the attack is to inject a malicious behaviour into an original model, that was already trained and was functional for its original purpose. The technique consists in generating a trojan trigger, and then to retrain the model with synthesized datasets in order to embed that trigger into the model. The trigger is designed to be added to a benign input, such as an image, so that this new input triggers a classification into the class that was targeted by the attacker. This results in a biased classification triggered on demand, with potentially important security consequences. The model is then made available as an online service or placed onto a compromised device; its behavior facing user requests appears legitimate. The attacker triggers the trojan at will by sending to the model an input containing the trojan trigger.
A face recognition model, known as the VGG Face model[Parkhi15], has been trojaned with the technique in [trojannn] and made available for download111https://github.com/PurduePAML/TrojanNN
by the authors of the attack. We access both this model and its original version. In order to visualize the effects of the tampering on that model due to the trojaning, we propose a simple forensic technique consisting in measuring the variation between the weight tensors of the model before and after the attack. Figure2 presents a matrix form of a heatmap of this variation (leftmost columns are entry layers of the model, while rightmost ones are output ones). We observe that the attack indeed exposes a visible trace in the weights (and that the position of modified weights, on intermediates layers, is consistent with the objective pursued by the authors in [trojannn]).
Those visible modifications in the weights do not indicate, a priori, to which extent the accuracy has been modified (as depicted on Figure 1 where blue inputs get the orange label and vice-versa), as neural-based models have highly implicit behaviours. One then has to pass a test dataset through the classification API to assess the accuracy change. The authors report an average degradation of only over the original test data, for the VGG Face trojaned model. In other words, both models exhibit a highly similar behaviour (i.e., similar classifications) when facing benign inputs.
As a countermeasure to distinguish both models, an approach is compute such a variation or, in a more straightforward approach, to compute hashes of their weights (or hashes of the memory zone where the model is mapped) and compare them . However, this approach requires a direct access to the model.
Unfortunately, models are not always (easily) accessible, because of their embedding on IoT like devices for instance, as reported in work by Roux et al. . This accessibility problem arise in at least in two contexts of growing popularity: if the model is directly embedded on a device and if the model is located on a remote machine and only exposed through an API. In such cases where the model is only accessible through its query API, one can think about a black-box testing approach [10.1007/3-540-54967-6_57]: it queries the suspected model with specific inputs, and then compares the outputs (the obtained classification labels) with those produced by the original model.
In this paper, we study the efficiency of novel black-box testing approaches. Indeed, while in theory testing the whole model input space would for sure reveal any effective tampering, this would require an impractical amount of requests. For this approach to be practical, the inputs used for querying the model shall be chosen wisely. Our core proposal is then to identify specific inputs whose property is to change classification as soon as the model is tampered with. We call these crafted inputs model markers. Our research question is: how to craft sets of markers for efficient model tampering detection, in a black-box setup?
1.2 Considered setup: black-box interactions
While there exists a wide range of techniques, at the system or hardware level, to harden the tampering with software stacks on a device (please refer to the Related Work), the case of neural network models is salient. Due to the intrinsic accuracy change of the model accuracy after the attack (cf Figure 1), we argue that stealthy, lightweight, and application-level algorithms can be designed in order to assess attacks on a remotely executed model.
We consider the setup where a challenger, possibly a company that has deployed the model on its devices, queries a remote device with standard queries for classifying objects. This is possible through the standard classification API that the device exposes for its operation (paper [stealing] discusses the same query setup for classification APIs of web-services). To a query with a given input object (e.g.
, image, sound file) is answered (inferred) a class label among the set of classes the model has been trained for; this is the nominal operation of a neural classifier. Note that for maximal applicability, we do not assume that the device is returning probability vectors along with classes; such an assumption would make the problem easier, but also less widely applicable (as it is known from previous attacks for stealing models that those probabilities should not be returned, for security hardening facing attackers attempts[stealing, 7958568]).
The contributions of this paper are:
(i) to introduce the problem of tampering detection of neural networks in the back-box setup, and to formalize this problem in Section 2.
to propose three heuristic algorithms to address the challenge of efficient detection, by crafting markers that serve as attack witnesses. Those are compared to a strawman approach. Each have their own scope and efficiency on certain neural networks facing different attacks.
(iii) to extensively experiment those algorithms on the canonical MNIST dataset, trained on three state of the art neural network architectures. We do not only consider the attack of trojaning, but also generalize to any attempt to modify the weights of the remote neural network, through actions such as fine-tuning, compression, quantization, and watermarking. We then validate the efficiency of our approach over five large public models, designed for image classification (VGG16, VGG19, ResNet, MobileNet and DenseNet).
1.2.2 Organization of the paper
The remaining of this paper is organized as follows. We first precisely define the black-box interaction setup in the context of classification, and define the tampering detection problem in that regard in Section 2. The algorithms we propose are presented in Section 3, before they are experimented with in Section 4; the limits of the black-box setup for tampering detection are also presented in that Section. We finally review Related Work in Section 5 and conclude in Section 6.
2 Design rationale
2.1 The black-box model observation setup
We study neural network classifiers, that account for the largest portion of neural network models. Let be the dimensionality of input (feature) space , and the set of target labels of cardinality . Let be a classifier model for the problem222By model, we mean the trained model from a deep neural network architecture, along with its hyper-parameters and resulting weights., that takes inputs to produce a label : .
Definition 1 (Black-box model).
The challenger queries the observed model with arbitrary inputs , and gets in return .
This setup is strictly more difficult than a popular setup where the probability vector is made available to the user, used for instance recently in [stealing], but that turns out to be an attack vector.
We now give a definition of the decision boundary of a model. This definition is required for later defining what are distinguishable models in the black-box setup. This definition is adapted from  for the black-box setup.
Definition 2 (Decision boundary).
Given , an input is on the decision boundary between those two classes if there exists at least two classes maximising the posterior probability: .
The set of points on the decision boundary defines a partitioning of input space into equivalence classes, each class containing input points for which predicts the same label.
We can now provide the definition of models distinguishability when queried in a black-box setup, based on the returned labels.
Definition 3 (Models distinguishability).
Two models and can be distinguished in a black-box context if and only if
Note that this implies that their decision boundaries are equivalent on input space . In other words two different supervised classifiers that end up through a training configuration to raise the same decision boundaries on input space , with equivalent classes in each region, are indistinguishable from an observer in the black-box model.
Indistinguishability is trivially the inability to distinguish two models. Since it is generally impossible to test the whole input set , a restricted but practical variant is to consider the indistinguishability of two models with regards to a given set . We name this variant -set indistinguishability.
Since we are interested in cases where is a slight alteration of the original model , it is interesting to quantify their differences over a given set :
Definition 4 (Differences between models).
Given two models , and a set , the distance between and on is defined as: with if , otherwise.
In this light, two -set indistinguishable models and have by definition .
Definition 5 (Model stability).
Given an observation interval in time , and a model observed at time (noted ), model is stable if it is indistinguishable from .
2.2 The problem of tampering detection
Problem 1 (Tampering detection of a model in the black-box setup).
Detect that model is not stable, according to Definition 5.
This means that finding one input so that is sufficient to solve Problem 1. Consequently, an optimal algorithm for solving Problem 1 is an algorithm that provides, for any model to defend, a single input that is guaranteed to see its classification changed on the attacked model , for any possible attack.
Since it is very unlikely, due to the current understanding of neural networks, to find such an optimal algorithm, we resort to finding sets of markers (specific data inputs) whose likelihood to change classification is high as soon as the model is tampered with. Since the challenge is to be often executed, and be as stealthy as possible, we refine the research question: Are there algorithms to produce sensitive and small marker sets allowing model tampering detection in the black-box setup? More formally, we seek algorithms that given a model find sets of inputs of low cost and high sensitivity:
Definition 6 (Tampering detection metrics).
Cost: , the number of requests needed to evaluate
Sensitivity: The probability to detect any model tampering, namely that at least one input (marker) of gets a different label. Formally, the performance of a set can be defined as s.t. .
It is easy to see that both metrics are bound by a tradeoff: the bigger the marker set, the more likely it contains a marker that will change if the model is tampered with. We now have a closer look to this relation.
2.2.1 Cost-sensitivity tradeoff
As stated in previous Section, we assume in this paper that the remote model returns the minimal information, by building our algorithms with solely labels being returned as answers .
Let an original model, and a tampered version of . Consider a set of inputs of cardinality (cost) . Let be the probability that a marker triggers (that is, allows the detection of the tampering). In the experiments, we refer to estimations of as the marker triggering ratio. Assume that given a model tampering the probabilities of each marker to trigger are independent. The overall probability to detect the tampering by querying with of size is the sensitivity . While the challenger is tempted to make this probability as high as possible, he also desires to keep low to limit the cost of such and operation, and to remain stealthy.
In general, we assume the challenger first fixes the desired sensitivity as a confidence level of his decisions (say for instance confidence, ). It turns out that one can easily derive the minimum key size given and :
These relations highlight the importance of having a high marker triggering ratio: there is an exponential relation between and . This relation is illustrated Figure 3, that relates the key size , the marker triggering ratio, and the chosen confidence. Please note the inverted logscale on the -axis. It shows that for (dashed line), markers easily triggered can be checked with a small key (e.g., 6 for ), while markers with a low trigger ratio, require considerably larger keys of markers (458 for for instance).
This short analysis is stressing the importance of designing efficient algorithms that craft markers which have a high chance to be misclassified after the attack; this permits to challenge the model with less markers.
Finally, let us note that the goal of an attacker, beside the successful implementation of his attack (e.g., the embedding of the trojan trigger in the method proposed in [trojannn]), is to have the minimal impact on the model accuracy for obvious stealthiness reason (e.g., the claim for only degradation in [trojannn]). We thus have the classical conflicting interests for the attacker and the challenger: the challenger hopes for a noticeable attack in order to detect it more easily, while the attacker leans towards the perfect attack leaving no trace at all. This motivate the research for the crafting of very sensitive markers, in order to detect even the slightest attacks on models weights.
3 Algorithms for the Detection of Remote Model Tampering
3.1 Reasoning facing black-box model classifications
Since we aim at leveraging a limited set of marker queries to identify the challenged model, and because success probability is involved, let us introduce notions of true and false positives for Problem 1. A true positive refers to a tampered model being detected as such, a true negative corresponds to the legitimate (original) model being recognized as original.
3.1.1 False negatives in tampering detection
Regarding the problem of tampering detection in the black-box setup, a false negative for the detection occurs if an algorithm challenges the model, gets classifications, and conclude that the model has not been tampered with while it was actually the case. The probabilities of failure that we presented on Figure 3 thus constitutes the probability of false negatives.
3.1.2 False positives in tampering detection
In this setup, assuming that the original model has a deterministic behaviour, false positives cannot happen. A false positive would be the detection of an attack that did not occur. Since the challenger had full control over his model before deployment, he knows the original labels of his markers. Any change in those labels is by the problem definition an indication of the tampering and therefore cannot be misinterpreted as an attack that never occurred.
3.2 The strawman approach and three algorithms
The purpose of the novel algorithms we are now presenting is to provide the challenger with a key to query the remote model, that is composed of a set of input markers. Concretely, given an original model , those algorithm generate a set of markers . The owner of the model stores along with the response vector , associated with the markers in :
We assume that is kept secret (unknown to the attacker). When the user needs to challenge a potentially attacked model , it simply queries with inputs in , and compares the obtained response vector with the stored . If the two response vectors differ, the user can conclude that .
|Knowledge Required||Input format||A bunch of inputs||Original weights||Original architecture||Remote weights|
The algorithms are designed to operate on widely different aspects of black-box model querying. Table 1 synthesizes the different knowledge exploited by those algorithms. Cases where the remove model is accessible (i.e., white box testing) can be solved by direct weight comparison or standard software integrity testing approaches , and are not in the scope of this paper.
SM (standing for strawman) represents an intuitive strawman approach, consisting in tracking a sort of ”non-regression” with regards to the initial model deployed on devices. The GRID algorithm (grid-like inputs) is also model agnostic, as it generates inputs at random, that are expected to be distant from real-data distribution, and then to assess boundary changes in a efficient way. Both WGHT (perturbation of weights) and BADV (boundary adversarial examples) take as arguments the model to consider, and a value ; the former applies a random perturbation on every weight to observe which are the most sensitive inputs with regards to misclassification after the attack (in the hope that those inputs will also be sensitive to forthcoming attacks). The latter generates adversarial inputs by the decision boundaries, in the hope to be sensitive to their movements. We now give their individual rationale in the following subsections, and present on Figure 4 an illustration.
3.2.1 The strawman approach (Sm)
This strawman approach uses inputs from the test set as markers in order to assess changes in classification. It is the natural way of reasoning facing the degradation or improvement of a model: in a machine learning task, the accuracy of a trained model at training stepis measured by inferring a test dataset. The training then proceeds to step , and the changes in accuracy are compared with the previous step.
Algorithm 1 then simply returns a key of size , from the random selection of inputs in the provided test set .
3.2.2 Grid-like inputs (Grid)
This algorithm generates markers independently of the model that is to be challenged.
Most generally, in classification tasks, the inputs are normalized before their usage to train the model. Without loss of generality for normalization out of the range, for each of the dimensions of the considered model (e.g., the dimensions of a MNIST image), Algorithm 2
sets a random bit. The rationale is to generate markers that are far apart the actual probability distribution of the base dataset: since the training and tampering with
are willing to preserve accuracy, constraints are placed on minimizing test set misclassification. The consequence is a large degree of freedom for decision boundaries that are far apart the mass of inputs from the training set. We thus expect those crafted inputs to be very sensitive to the movement of boundaries resulting from the attack.
3.2.3 Perturbation of weights (Wght)
The WGHT algorithm takes as arguments the model , and a value . It observes the classifications of inputs in dataset , before and after a perturbation has been applied to all weights of (i.e., a random perturbation of every weight to up to ). Inputs for which label have changed, due to this form of tampering, are sampled to populate key . The rationale is that with a low , the key markers are expected to be very sensitive to the tampering of model . In other words, inputs from are expected to be the most sensitive inputs from when it comes to tamper with the weights of .
3.2.4 Boundary adversarial examples (Badv)
Adversarial examples have been introduced in early works presented in [BIGGIO2018317] and re-framed in [DBLP:journals/corr/SzegedyZSBEGF13], in order to fool a classifier (by making it misclassify inputs) solely due to slight modifications of the inputs. Goodfellow et al. then proposed [Goodfellow:2015] an attack for applying perturbations to inputs that leads in vast misclassifications of the provided inputs to the attack function (that attack is named the fast gradient sign attack or FGSM). Those crafted inputs yet appear very similar to the original ones to humans, which leads to important security concerns [deepxplore]; note that since then, many other attacks of that form were proposed (even based on different setup assumptions [Papernot:2017:PBA:3052973.3053009]), as well as platforms to generate them333see e.g., https://github.com/tensorflow/cleverhans or https://github.com/bethgelab/foolbox/.
We propose with BADV to leverage the FGSM attack, but in an adapted way. The FGSM attack adds the following quantity to a legitimate input :
with being the gradient of (the cost function used to train model ), and the label of input . captures the intensity of the attack on the input. Approach in [Goodfellow:2015] is interested in choosing an that is large enough so that most of the input batch provided to the FGSM algorithm are misclassified (e.g., leads to the misclassification of of the MNIST test set). We are instead interested in choosing an that is sufficient to create misclassified markers only; the rationale is that the lower the , the closer the crafted inputs are to the decision boundary; our hypothesis is that this proximity will make those inputs very sensitive to any attack of the model that will even slightly modify the position of decision boundaries. In practice, and with Algorithm 4, we start from a low , and increase it until we get the desired key length .
4 Experimental Evaluation
This section is structured as follows: we first describe the experiments on MNIST (along with the considered attacks and parameters for algorithms). We then discuss and experiment the limitations of the black-box setup we considered. We finally validate our take-aways on five large image classification models, in the last subsection of this evaluation.
We conduct experiments using the TensorFlow platform444https://www.tensorflow.org/
, using the Keras library555https://keras.io/.
4.1 Three neural networks for the MNIST dataset
The dataset used for those extensive experiments is the canonical MNIST database of handwritten digits, that consists ofimages as the training set, and of for the test set. The purpose of the neural networks we trained are of classifying images into one of the ten classes of the dataset.
The three off-the-shelf neural network architectures we use are available on the Keras website666https://github.com/fchollet/keras/blob/master/examples/, namely as mnist_mlp
(0.984% accuracy at 10 epochs),mnist_cnn (0.993% at 10) and mnist_irnn (0 .9918% at 900). We rename those into MLP, CNN and IRNN respectively. They constitute different characteristic architectures, with one historical multi-layer perceptron, a network with convolutional layers, and finally a network with recurrent units.
4.2 Attacks: from quantization to trojaning
This subsection lists the five attacks we considered. Excluding the watermarking and trojaning attacks, the others are standard operations over trained models, yet if an operator has already deployed its models on devices, any of those can be considered as attacks, as they tamper with the model that was designed for a precise purpose.
4.2.1 Quantization attack
This operation aims at reducing the number of bits for representing each weight in the trained model. It is in practice widely used prior to deployment in order to fit the architecture and constraints of the target device. TensorFlow by default uses 32-bit floating points, and the goal is convert the model into 8-bit integers for instance. The TensorFlow fake_quant_with_min_max_args function is used to simulate the quantization of the trained neural network. We kept the default parameters of that function (8-bits quantization, with -6 to 6 as clamping range for the input).
4.2.2 Compression attack
A form of compression is flooring; it consists in setting to zero all model weights that are below a fixed threshold, and aims at saving storage space for the model. We set the following threshold value for the three networks: 0.0727, 0.050735 and 0.341 for the MLP, CNN and IRNN networks respectively. Those threshold cause the degradation of network accuracy by about one percent (accuracies after the compression are 0.9749, 0.9829 and 0.9821, respectively).
4.2.3 Fine-tuning attack
Its consists in starting from a trained model, and to re-train it over a small batch of new data. This results in model weight changes, as the model was adapted through back-propagation to prediction errors made on that batch. We used a random sample of inputs from the MNIST test set for that purpose.
4.2.4 Watermarking attack
Watermarking techniques [Nagai2018, watermarking] embed information into the target model weights in order to mark its provenance. Since work in [watermarking] operated on the MNIST dataset, and provided detailed parameters, we implemented this watermarking technique on the same models (MLP, CNN, and IRNN). The watermark insertion proceeds by fine-tuning the model over adversarial examples to re-integrate them into their original class, in order to obtain specific classifications for specific input queries (thus constituting a watermark). This approach requires a parameter for the mark that we set to , consistently with remarks made in [watermarking] for maintaining the watermarked model accuracy.
4.2.5 Trojaning attack
We leverage the code provided in a GitHub repository, under the name of Stux-DNN, and that aims at trojaning a convolutional neural network for the MNIST dataset[stuxdnn]. We first train the provided original model, and obtain an accuracy of over the MNIST test set. The trojaning is also achieved with the provided code.
After applying those five attacks, the models accuracies changed; those are summarized on Table 2. Note that some attacks may surprisingly result in a slight accuracy improvement, as this is the case for MLP and quantization with the considered parameters.
|Original model accuracy||0.9849||0.9932 (0.9397†)||0.9919|
|Trojaning L0 [stuxdnn]||-||(0.9340†)||-|
|Trojaning mask [stuxdnn]||-||(0.9369†)||-|
4.3 Settings of algorithms
4.3.1 Settings for Sm
The SM uses a sample of images from the original MNIST test set, selected at random.
4.3.2 Settings for Grid
We use the python Numpy uniform random generator for populating markers, that are images of 28x28 pixels.
4.3.3 Settings for Wght
All the weights in the model are perturbed by adding to each of them a random float within , or for the MLP, CNN and IRNN architectures respectively. These operations must keep the accuracy loss with a small percentage, while making it possible to cause enough classification changes for populating (those values allowed to identify just over inputs).
4.3.4 Settings for Badv
For generating adversarial examples that are part of the key, we leverage the Cleverhans python library777https://github.com/tensorflow/cleverhans. The FGSM algorithm used in BADV, requires the parameter for the perturbation of inputs to be small enough but as well to allows for the generation at least around adversarial examples out of files in the test set. is set to , and for the MLP, CNN and IRNN networks respectively.
4.4 Experimental results
Results are presented on Figure 5, for all the attacks (excluding the trojaning attack), the three models and the four algorithms. We set key size ; each experiment is executed times.
SM generates markers that trigger with a probability below 0.02 for all attacks and all models; this means that some attacks such as for instance quantization over the MLP or IRNN models remain largely undetected after query challenges.
All three proposed algorithms significantly beat that strawman approach; the most efficient algorithm, on average and in relative top-performances is BADV. Most notably, the IRNN model manages to trigger a ratio of up to 0.791 of markers, that is around of them, for the flooring attack. This validates the intuition that creating sensitive markers from adversarial examples by the boundary (i.e., with limited values) is possible.
The third observation is that GRID arrives in second position for general performances: this simple algorithm, that operates solely within the data input space for generating markers, manages to be sensitive to boundary movements.
The WGHT algorithm has high performance peaks for the MLP model, with up to half of triggered markers for the fine-tuning attack, and a ratio of for flooring (i.e., more than one third of markers are triggered); it has the lowest performances of the three proposed algorithms, specifically for the IRNN model. This may come from the functioning of its recurrent architecture that makes it more robust to direct perturbations of weights: the model is more stable during learning (it requires around 900 epochs to be trained, while the two other model need only 10 epochs to reach their peak accuracy).
The watermark attack is very well detected on the IRNN model with the BADV algorithm (ratio of ), on an equivalent rate on three models by GRID, while SM still shows trace amounts of markers triggered for MLP and CNN, and none for IRNN.
Considering the relatively low degradation of the models reported on Table 2 (i.e., within around maximum)888Trojaning attacks in [trojannn] reports degradation over the original models of (VGG Face recognition), (speech recognition) or (speech altitude recognition)., we conclude that all three proposed algorithms capture efficiently the effects of even small attacks on the models to be defended, while SM would only be valuable in cases of large degradation of models. We illustrate in the subsection 4.6 the degradation-detectability trade-off.
4.5 Validation on a trojaning attack on MNIST
The modification of accuracy made to the neural network model proposed by [stuxdnn] is reported on Table 2 for two trojaning modes (L0 and mask). We now question the ability of one of our algorithms to also be outperforming the strawman approach SM; we experiment with GRID. Results are that SM manages to trigger a ratio of and of markers, for L0 and mask modes respectively (please refer to their original paper for details on these techniques). GRID reaches the level of and , that are 8.7x and 8.5x increases in efficiency. This suggest that for practical usage of this algorithm for tampering detection, a small key of will detect the attack, while SM is likely to raise a false negative.
4.6 Undetectable attacks and indistinguishably: illustrations
We now present examples that illustrate the inherent limits of a black-box interaction setup, as defined in subsection 2.1.
Let’s consider the MLP model, along its best performing algorithm for tamper detection, WGHT. Assume that the model is tampered with using compression (flooring), and that we observe successive attacks: from an attack value starting at 0, its reaches a value of by increments of (i.e., at each attack, weights under are floored). We observe the results after every attack; we plot on Figure 6 the loss in accuracy of the attacked model (top-Figure), and the Euclidean distance between both model weights (bottom-Figure). For instance, we observe accuracy loss at a distance of 40. Since the loss is noticeable from around , we zoom in for plotting the corresponding ratio of markers triggered on Figure 7.
Those two figures convey two different observations, presented in the next two subsections.
4.6.1 Limits of the algorithms and of the black-box setup
The following cases may happen for attacks that have a very small impact on the model weights.
Case 1: Accuracy changed after the attack, but the algorithm failed in finding at least one input that has changed class (i.e., no marker from has shown a classification change).
Case 2: We did not manage to find such inputs despite the attack.
Case 1 for instance occurs with , as seen on Figure 7. This means that both algorithms have failed, for the chosen key length , to provide markers that were present in the zones where boundary moved due to the attack. (Please remind that, if the accuracy post attack has been modified, this means that some inputs from the test set have changed their label, then indicating that boundaries have de facto moved).
Case 2 is particularly interesting as it permits to illustrate Definition 3 in its restricted form: an attack occurred on (as witness by a positive Euclidean distance between the two models on Figure 6), but it does not results in a measurable accuracy change. It is -set indistinguishable, with here being the MNIST test set. We measure this case for , where pre and post accuracies are both 0.9849.
Case 1 motivates the proposal of new algorithms for the problem. We nevertheless highlight that the trojan attack [trojannn] degrades the model on a basis of around , while our algorithm is here unable to detect a tampering that is of two order of magnitude smaller (delta in accuracy of of the attacked model). This indicate extreme cases for all future tampering detection approaches. Case 2 questions the black-box interaction setup. This setup enables tampering detection in a lightweight and stealthy fashion, but may cause indecision due to the inability to conclude on tampering due to the lack of test data that can assess accuracy changes.
4.6.2 Wght outperforms Sm by nearly two orders of magnitude for small attacks
As observed on Figure 7, the SM markers triggered ratio ranges from to around , while for WGHT it ranges from to , in this extreme case for attack detection with very low model degradation.
Figure 8 concludes this experiment by presenting the key size that is to be chosen, depending on the algorithm and on the tolerance to attack intensity. This is in direct relation with the efficiency gap observed on previous Figure: the more efficient the algorithm for finding sensitive markers, the smaller the query key for satisfying the according detection confidence. For an equivalent confidence, the key size to leverage for SM is times longer than for the WGHT algorithm, confirming the efficiency of the techniques we proposed in this paper.
4.7 Validation on five large classifier models
We conducted extensive experiments on the standard MNIST dataset for it allows computations to run in a reasonable amount of time, due to the limited sizes of both its datasets and of the models for learning it. In order to validate the general claim of this paper, we now perform experiments on five large and recent models for image classification, using a state of the art dataset. This validation is interested in checking the consistency with the observation from the MNIST experiments, that have shown that our algorithms significantly outperform the strawman approach.
We leverage five open-sourced and pre-trained models: VGG16[VGG16] (containing 138,357,544 parameters 999For comparison, MNIST models contain 669,706 (MLP), 710,218 (CNN) and 199,434 (IRNN) parameters.), VGG19[VGG16] (143,667,240 parameters), ResNet50[ResNet] (25,636,712 parameters), MobileNet[MobileNet] (4,253,864 parameters) and DenseNet121[DenseNet] (8,062,504 parameters). Except for the two VGG variants VGG16 and VGG19, all four architectures are broadly different models, that each were proposed as independent improvements for those image classification tasks101010Please refer to https://keras.io/applications for each their own characteristics..
The VGGFace2 dataset has been made public recently [Cao18]; it consists of a split of training (8631 labels) and test (500 labels) sets. The labels in the two sets are disjoint. We consider a random sample of images of the VGGFace2 test dataset, for serving as inputs to the SM and WGHT algorithms. We note that despite that labels in the test set are different from the one learnt in the models, this is a classic procedure (used e.g., for experiments in work by Liu et al. [trojannn]): a neural network with good performances will output stable features for new images, and thus in our case predict consistently the same class for each new given input. Those images are imported as 224x224 pixel images to query the tested models (versus 28x28 for MNIST). As for previous experiment (Figure 7), we experiment with the SM and WGHT algorithms and , with the flooring attack. We perform the computations on four Nvidia TESLAs V100 with 32 Gb of RAM each; each setup is run three times and results are averaged (standard deviations are presented).
Figure 9 presents the results. The -axis of each figure represents the flooring intensity, with the same values for all models, except for DenseNet because of its noticeable sensitivity to attacks. VGG16 corresponds to the neural network architecture of trojaned in paper [trojannn] and that we use as an illustration in Section 1.1. For all models, we observe that an attack of is bellow what both SM and WGHT can detect (situation presented in Section 4.6). For the second smaller considered attack values on the -axis, only WGHT manages to trigger markers; this constitutes another evidence that crafted markers are more sensitive and will trigger first for the smallest detectable attacks. For all the remaining flooring parameters, SM triggers markers, but always significantly less than WGHT (up a factor of 15 times less, at on VGG19). All the models exhibit a very similar trend for both curves. The triggering ratio in the case of ResNet is lower for both WGHT and SM, while gap between the two approaches remains similar. Finally, in the DenseNet case, we note a higher triggering ratio for SM than for other models on the last three flooring values; the results are still largely in favor of the WGHT algorithm.
5 Related Work
Research works in the context of the security of embedded devices such as IoT devices, suggest that traditional security mechanisms must be reconsidered. Main problems for traditional security tools is the difficulty to fix software flaws on those devices, the frequency to which those flows are reported, and finally their limited resources for the implementation of efficient protections.
Anti-tampering techniques for traditional software applications may be applied directly on the host machine in some defense scenarios. This is the case for the direct examination of the suspected piece of software . Remote attestation techniques [Coker2011] allows for the distant checking of potential illegitimate modifications of software or hardware components; this is nevertheless requiring the deployment of a specific challenge/response framework (often using cryptographic schemes), that both parties should comply with. Program result checking (or black-box testing) is an old technique that inspects the compliance of a software by observing outputs on some inputs with expected results [10.1007/3-540-54967-6_57]
; it has been applied in conventional software applications, but not on the particular case of deep learning models, where the actions are driven by an interpretation of a model (its weights in particular) at runtime. In that light, the work we proposed in this paper is a form of result checking for neural model integrity attestation. Since it is intractable to iterate over all possible inputs of a neural network model to fully characterize it (like for reverse engineering finite state machines for instance), due to the practical dimensionality of inputs in current applications, the challenger is bound to create some algorithms to find some specific inputs that will carry the desired observations.
After a fast improvement of the results provided by neural network-based learning techniques in the past years, models found practical deployments into user devices [Lane:2016:DSA:2959355.2959378]. The domain of security for those models is a nascent field [DBLP:journals/corr/PapernotMSW16], following the discovery of several types of attacks. The first one is the intriguing properties of adversarial attacks [BIGGIO2018317, Kurakin2016AdversarialEI, Goodfellow:2015, DBLP:journals/corr/SzegedyZSBEGF13] for fooling the classifications of models; a wide range of proposals are attempting to circumvent those attacks [7546524, Meng:2017:MTD:3133956.3134057, DBLP:journals/corr/XuEQ17]. Counter measures for preventing the stealing of machine learning models such as neural networks thought prediction APIs are discussed in stealing; it includes the recommendation for the service provider not to send probability vectors along with labels in online classification services. Some attacks are willing to leak information about individual data records that were used during the training of a model [Song:2017:MLM:3133956.3134077, 7958568]; countermeasures are to restrict the precision of probability vectors returned by the queries, or to limit those vectors solely to top- classes . The possibility to embed information within the models themselves with watermarking techniques [Nagai2018, watermarking] is being discussed on the watermark removal side by approaches like [wat-removal]. Trojaning attacks [trojannn, stuxdnn] are yet not addressed, except by this paper.
Neural network-based models enable applications to reach new levels of quality of service for the end-user. Those outstanding performances are in balance, facing the risks that are highlighted by new attacks issued by researchers and practitioners. This paper introduced the problem of tampering detection for remotely executed models, by the use of their standard API for classification. We proposed algorithms that craft markers to query the model with; the challenger assesses an attack on the remote model by checking prediction changes on those markers. We have shown a high level of performance as compared to a strawman approach that would use inputs from classic test sets for that purpose; the challenger can then expect to detect a tampering with very few queries to the remote model, avoiding false negatives. We believe that this application-level security checks, that operate at the model level and then at the granularity of the input data itself, is raising interesting futureworks for the community.
While we experimented those algorithms facing small modifications made to the model by attacks, we also shown that below a certain level of modification, the black-box setup may not permit to detect tampering attacks. In other situations, where the attack is observed in practice through accuracy change in the model, our algorithms can fail in the detection task. Some even more sensitive approaches might be proposed in the future. We believe this is an interesting futurework direction, that is to be linked with the growing understanding of the inner functioning of neural networks, and on their resilience facing attacks.