Physical unclonable function modeling method based on repetition information

Abstract

The invention belongs to the field of information security, and discloses a physical unclonable function modeling method based on repetition information, and the method comprises the steps: collecting multiple responses of a PUF to the same excitation, calculating repetition data, and constructing an excitation-repetition data pair; the value of the repetition degree data is converted into a limited category label by adopting a data binning strategy, so that the training complexity is reduced; and training a repetition degree model by using a multi-classification feedforward neural network, and finally obtaining a PUF response through model prediction label mapping. According to the method, response and stability information contained in the repetition degree is fully utilized, efficient modeling of the complex structure PUF is achieved, limitation of traditional reliability attacks is broken through, the method has the advantages of being wide in attack range, high in efficiency, free of knowing the internal structure of the PUF and the like, and the method is suitable for various strong PUF structures and suitable for evaluating the anti-modeling safety of the PUF.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of hardware security and cryptographic analysis, and in particular to a repeatability information-based physical unclonable function (PUF) modeling method, which is suitable for efficient modeling of various strong PUFs. BACKGROUND

[0002] As a hardware security mechanism based on integrated circuit manufacturing process deviation, the physical unclonable function (PUF) generates unpredictable responses using random process deviations introduced in the integrated circuit manufacturing process, and has been widely used in device authentication, key generation, copyright protection and other fields. Typical strong PUF structures include arbiter PUF (APUF), XOR PUF (XOR PUF), intervening PUF (iPUF), multiplexer PUF (MPUF), etc.

[0003] Although this technology has the potential to replace traditional security mechanisms, its own security is threatened by machine learning modeling attacks. Currently, attackers establish a model of the PUF based on a sufficient number of challenge response pairs (CRP) to simulate its challenge response behavior, thereby losing its security features.

[0004] Existing PUF modeling methods mainly include machine learning modeling and side channel modeling. The traditional method has the following disadvantages: the traditional machine learning attack relies on single response information and has insufficient modeling ability for high nonlinearity PUF; the existing reliability side channel attack only uses the stability information of the PUF response, but it does not use the response information, and its scope of application is limited. For example, the covariance matrix adaptive evolution strategy (CMA-ES) modeling attack analyzes the response instability to infer the internal parameters of the PUF through an equal heuristic algorithm, but has the problems of narrow application scope (only for specific structures), low success rate, and long training time.

[0005] Reliability is one of the important performance indicators of PUF, reflecting the consistency of PUF responses under different environmental conditions. Existing modeling methods do not fully utilize the response and stability information contained in repeated measurement data, resulting in insufficient security evaluation efficiency and universality. SUMMARY

[0006] To solve the problems of narrow application scope and low efficiency of existing PUF modeling methods, the present application proposes a repeatability information-based physical unclonable function modeling method, which directly utilizes the response and stability information in the repeatability data, combines data binning strategy and multi-classification machine learning algorithm, and realizes efficient modeling of complex structure PUF.

[0007] To achieve the above object, the present application adopts the following technical solutions: A physical unclonable function modeling method based on redundancy information, comprising: Step 1: Collecting stimulus-redundancy data; Step 2: Classifying the values of the redundancy data based on a data binning strategy, replacing the redundancy data with classification labels, and converting the stimulus-redundancy data into stimulus-label pairs; Step 3: Training a multi-class machine learning algorithm using the stimulus-label pairs to obtain a redundancy model of the physical unclonable function; Step 4: Based on the redundancy model and a given stimulus, obtaining a predicted classification label, and according to the data binning strategy used, obtaining a corresponding response prediction value from the predicted classification label.

[0008] Further, the step 1 comprises: Randomly selecting stimuli Obtaining redundancy data through m measurements under fixed operating conditions Combining the stimuli and the corresponding redundancy data to form stimulus-redundancy data pairs ).

[0009] Further, the redundancy data is the sum of m measurement responses obtained by repeatedly inputting the same stimulus into the physical unclonable function. Further, the redundancy data is the sum of m measurement responses obtained by repeatedly inputting the same stimulus into the physical unclonable function. Further, the redundancy data is the sum of m measurement responses obtained by repeatedly inputting the same stimulus into the physical unclonable function.

[0010] Further, the redundancy data is represented as: Wherein is the redundancy value corresponding to the i-th stimulus; is the i-th response corresponding to the i-th stimulus.

[0011] Further, the data binning strategy includes equal-width binning and equal-frequency binning.

[0012] Further, the multi-class machine learning algorithm includes a feedforward neural network and a random forest.

[0013] Further, in step 4, the response prediction value is calculated as follows: Wherein is the response prediction value, is the predicted classification label, is the number of classes.​​​​

[0014] Furthermore, q is an even number.

[0015] Furthermore, when modeling the 10-XOR APUF with 128-bit excitation, a feedforward neural network is used, and the number of neurons in the feedforward neural network from the input layer, the two hidden layers to the output layer are 129, 70, 70 and 8 respectively.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. Strong Modeling Capability: This invention utilizes both response and stability information from repetitive data, while previous modeling methods only utilized one type of information; machine learning modeling only used response information, and reliability side-channel modeling methods only used stability information. Therefore, this invention can model physically unclonable functions that are difficult to crack using traditional methods.

[0017] 2. Wide applicability: When using a feedforward neural network (FNN) as a multi-classification method, it does not rely on the internal structure information of the PUF and is applicable to various strong PUFs (such as XOR APUF, iPUF, MPUF, rMPUF, LPUF, SOI PUF, etc.).

[0018] 3. Higher efficiency: The training time is significantly shorter than that of traditional reliability side-channel modeling methods (such as CMA-ES).

[0019] 4. Good scalability: The number of sub-bins (q) and the number of measurements can be adjusted. Balancing modeling accuracy and efficiency; compatible with attacks on traditional machine learning models (when...) (At that time, the present invention degenerated into a traditional modeling method). Attached Figure Description

[0020] Figure 1 A flowchart illustrating a method for modeling physically unclonable functions based on repeatability information, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the FNN network structure provided in an embodiment of the present invention; Figure 3 A schematic diagram of a secure PUF circuit constructed for an embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments: like Figure 1 As shown, a method for modeling physically unclonable functions (PUFs) based on repetition information is proposed. This method involves collecting stimulus-repetition data pairs, preprocessing the data through binning, training a repetition model, and finally predicting the PUF response. The specific steps are as follows: 1) Data Collection Randomly select incentives Repeatability data are obtained through m measurements under fixed operating conditions. The stimulus and the corresponding reliability data (i.e., repeatability data) are combined to form a stimulus-repeatability data pair. ).

[0022] Repeatability (rep) is a measure of reliability, referring to the sum of responses obtained from multiple measurements of the same challenge. Repeatability data not only contains information about response stability but also implies information about the response itself.

[0023] Repeatability data is measured by repeatedly inputting the same stimulus to the PUF. Next, obtained The sum of the measured responses is shown in the formula.

[0024] in It is the repetition data corresponding to the i-th stimulus; It is the first Incentives The corresponding number Second response.

[0025] Repeatability data is combined with stimuli to form stimuli-repetition data pairs. The range of values ​​is When the repeatability value is 0 or When the repeatability value is close to a certain value, it indicates that the PUF has a stable response behavior to the stimulus; this means that when the stimulus is substituted into the noisy PUF mathematical model, the resulting total delay difference is much greater than the delay caused by the environmental noise. When the response is zero, it indicates that the PUF's response to the stimulus is extremely unstable, approximating a random value. This means that when the stimulus is substituted into the noisy PUF mathematical model, the resulting total delay difference is close to 0, and the PUF's response to the external environment depends almost entirely on the influence of environmental noise. Therefore, repeatability, as a statistical metric of the response, reflects the magnitude of the total delay difference and, to some extent, reveals the internal parameters of the PUF, thus it can be used to model the PUF.

[0026] Repeat the above steps until enough training data has been collected.

[0027] 2) Data binning Raw data collected ( Repeated data cannot be directly used as training data for modeling. An excessively wide range of values ​​will result in too many classifications, reducing modeling accuracy. Therefore, based on a data binning strategy, the values ​​of the repeated data are divided into q classes. Then, classification labels are used... to replace The value of . Ultimately, all the stimulus-repetition data pairs ( ) is converted into incentive-label pairs ( The transformation rules depend on the data binning strategy used.

[0028] Data binning strategies can use any of the following: equal-width binning, equal-frequency binning, etc. Considering the uniqueness of PUF, it is recommended to set the parameter q to an even number regardless of the binning strategy used, so as to facilitate the extraction of response from the predicted label during the prediction phase.

[0029] 3) Model Training Incentive-label pairs ( The data is used as training data for a multi-class machine learning algorithm, and after training, a PUF repetition rate model is obtained. Methods such as Feedforward Neural Networks (FNNs) and Random Forests can all achieve multi-class classification, and any one of them can be selected during the selection process.

[0030] 4) Response Prediction The trained model outputs a label for a given stimulus. Based on the data binning strategy adopted, the response can be obtained from the predicted labels through simple mapping. The response extraction rules for equal-width binning and equal-frequency binning are the same, as shown in the formula.

[0031] in In response to the predicted value, For the predicted category label, This refers to the number of boxes.

[0032] The modeling algorithm is described as follows: Modeling principles Not only does the excitation response of a PUF contain useful information, but the reliability of the response also reveals information related to the PUF's internal parameters. The following explanation uses an APUF as an example. An ideal APUF mathematical model does not consider environmental noise, and its response remains stable at all times. However, PUFs do not operate in an ideal environment. During operation, environmental noise can affect the electrical characteristics of the PUF circuit, such as propagation delay, thereby altering the PUF's excitation response behavior and causing the PUF's response to the same excitation to exhibit an unstable state.

[0033] Typically, ambient noise can be considered as Gaussian white noise, so the APUF transmission delay difference introduced by ambient noise... It also follows a normal distribution N( ). At this time, the excitation response behavior of APUF can also be represented by a linear cumulative model.

[0034] Since the transmission delay introduced by environmental noise is not a stable value, if the response of APUF to a certain excitation is unstable under the influence of noise, it means , the operation value of and the delay difference value formed by noise are of the same order of magnitude, at this time the response is mainly determined by noise, and therefore presents instability. On the contrary, if , the delay introduced by noise can always affect the final response, and the response of APUF presents a stable state.

[0035] If the delay difference corresponding to an excitation is less than a certain small threshold, under the influence of environmental noise, the delay difference superimposed by the delay effect of noise causes the response to be unstable. In other words, the more unstable the response is under the influence of noise, the closer the delay difference corresponding to the excitation is to 0. The fact that the reliability-based side channel modeling method successfully models APUF proves that the reliability data leaks the delay difference information of APUF.

[0036] As an implementable way, FNN is used as a modeling tool, as shown in Figure 2 . FNN consists of 1 input layer, 2 hidden layers and 1 output layer. Information only propagates forward in FNN, passing through input layer, hidden layer and finally reaching output layer. ReLU function is used as the activation function of input layer and hidden layer in FNN to avoid gradient disappearance; softmax function is used as the activation function of output layer to realize multi-classification. Table 1 gives the FNN hyperparameters used for modeling the degree of repetition under the multi-classification framework, where the number of hidden layers and the number of nodes per layer should change with the target size. When modeling 10-XOR APUF with 128-bit excitation, the number of neurons from input layer, hidden layer (two), to output layer is 129, 70, 70, and 8, respectively.

[0037] Table 1 FNN hyperparameter values used in the degree of repetition modeling rMPUF Modeling 10-XOR APUF makes CRP generated by pypuf, the noiseness parameter is selected as 0.1, the collection number m is set to 100, and the bin number q is set to 8. The collection CRPs were used in modeling experiments, achieving a modeling accuracy of 96.91%. In contrast, using the same number of CRPs and a neural network with the same structure (the output layer was changed to a single neuron suitable for binary classification, with a sigmoid activation function), the modeling accuracy was 50.03%. This comparison demonstrates that the PUF modeling method based on repetition information has a performance advantage over traditional modeling methods.

[0038] As one possible implementation, the PUF modeling method (RMA) based on repetition information was compared with three modeling attacks, including the reliability-based CMA-ES attack, the gradient-based reliability attack (GRA), and the FNN attack.

[0039] Table 2 compares the performance of the aforementioned attacks. RMA can model all the PUFs listed in Table 2 and achieves better performance than FNN attacks, namely, a wider range of applicability, higher time efficiency, and more accurate prediction accuracy. With sufficient CRP, RMA successfully modeled the 128-bit 10-XOR PUF and (6,6)-iPUF; and the 64-bit (8,8)-iPUF, while attacks such as FNN and GRA could not model these targets.

[0040] Table 2 Comparison of Modeling Accuracy As one possible implementation, to study the impact of the number of classifications on modeling performance, seven values ​​(2, 4, 8, 16, 32, 64, and 101) were selected as the number of categories after binning for five target PUFs in experimental testing. The experimental results are as follows: Figure 3 As shown, the accuracy of RMA modeling varies with the number of categories. When the number of categories is 2, RMA degenerates into a traditional FNN modeling attack. Experimental results show that for all tested PUFs, RMA outperforms FNN attacks. This means that if a PUF design cannot resist traditional machine learning modeling attacks, it certainly cannot resist RMA attacks. Furthermore, experimental results show that, except for binary classification, RMA also performs poorly when the number of categories is 4. It can be inferred that this phenomenon is due to the loss of useful information caused by coarse-grained classification. As the number of categories increases, detailed information about the response is preserved, leading to more accurate predictions. When the number of categories is 101, corresponding to the case without data binning, the modeling accuracy of RMA also decreases to some extent due to the excessive number of categories.

[0041] Modeling performance corresponding to different numbers of classifications. Note: The training set size is used for modeling (5,5)-iPUF. CRPs, modeling (6,6)-iPUF using CRPs, modeling 8-XOR APUF uses CRPs, modeling 10-XOR APUF uses CRPs, modeling (128, 5)-rMPUF uses CRPs.

[0042] The experimental results show that the category number after data binning has a certain influence on the performance of RMA, especially when the category number is close to the minimum or maximum value. Therefore, when implementing RMA, it is not recommended to choose individual extreme values, such as 2, 4 and values close to the number of measurements m.

[0043] The above only shows the preferred embodiments of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for modeling physically unclonable functions based on repeatability information, characterized in that, include: Step 1: Collect stimulus-repetition data; Step 2: Based on the data binning strategy, classify the values ​​of the repetition data, replace the repetition data with classification labels, and convert the stimulus-repetition data into stimulus-label pairs; Step 3: Train a multi-class machine learning algorithm using the stimulus-label pair to obtain a repeatability model for the physically unclonable function; Step 4: Based on the repetition model and the given stimulus, obtain the predicted classification label, and according to the adopted data binning strategy, obtain the corresponding predicted response value through the predicted classification label.

2. The method for modeling physically unclonable functions based on repeatability information according to claim 1, characterized in that, Step 1 includes: Randomly select incentives Repeatability data are obtained through m measurements under fixed operating conditions. The incentive and the corresponding repetition data are combined to form an incentive-repetition data pair. ).

3. A method for modeling physically unclonable functions based on repeatability information according to claim 1 or 2, characterized in that, The repeatability data refers to the repeated input of the same excitation to a physically non-clonable function. Next, obtained The sum of the measured responses.

4. The method for modeling physically unclonable functions based on repeatability information according to claim 2, characterized in that, The Represented as: in It is the repetition data corresponding to the i-th stimulus; It is the first Incentives The corresponding number Second response.

5. The method for modeling physically unclonable functions based on repeatability information according to claim 1, characterized in that, The data binning strategy includes equal-width binning and equal-frequency binning.

6. The method for modeling physically unclonable functions based on repeatability information according to claim 1, characterized in that, The multi-class machine learning algorithms include feedforward neural networks and random forests.

7. The method for modeling physically unclonable functions based on repeatability information according to claim 1, characterized in that, In step 4, the predicted response value is calculated as follows: in In response to the predicted value, For the predicted category label, This refers to the number of boxes.

8. The method for modeling physically unclonable functions based on repeatability information according to claim 7, characterized in that, The q is an even number.

9. A method for modeling physically unclonable functions based on repeatability information according to claim 1, characterized in that, When modeling a 10-XOR APUF with 128-bit excitation, a feedforward neural network is used, and the number of neurons in the feedforward neural network from the input layer, the two hidden layers to the output layer are 129, 70, 70 and 8 respectively.

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