Sensor hardware Trojan horse detection method and system based on image processing

Abstract

The invention discloses a sensor hardware Trojan horse detection method and system based on image processing, and belongs to the field of sensor anomaly detection. The method comprises the following steps: acquiring sensor circuit images containing different types and manufacturing processes and containing implanted and non-implanted Trojan horses and corresponding original design files, and introducing quality defects into part of the images; registering images and files, marking Trojan horse areas to construct a first training sample set, and cutting different types of interested areas to construct a second training sample set; the two sample sets are used for training a target recognition model for recognizing a Trojan horse area and a detection model for judging whether the interested area contains image quality defects or not, and finally, the two models are combined, an image restoration technology is introduced, and whether Trojan horses exist in a circuit image of a to-be-detected sensor sample or not is judged. The method can accurately identify the malicious circuit of the sensor, reduces the false alarm through image evaluation and feature extraction, improves the efficiency through automatic detection, guarantees the safety of the sensor, and is suitable for various circuit Trojan horses.

Description

Technical Field

[0001] The present invention relates to the field of sensor anomaly detection, and in particular to a sensor hardware Trojan detection method and system based on image processing. Background Art

[0002] Sensors are crucial in cyber-physical systems (CPS), supporting a wide range of applications from infrastructure management to everyday convenience. Reliable sensor measurements are crucial to ensuring the secure operation of applications supported by CPS. Sensors primarily consist of four key components: transducers, amplifiers, filtering circuits, and ADCs. Sensor Trojans may reside in any or all of these components. Sensor Trojans primarily exploit specific characteristics in transmitted electrical signals as triggers. Potential consequences of sensor Trojans include denial-of-service (DoS) attacks on sensors, manipulation of sensor outputs by attackers, and damage to the attacked sensor.

[0003] Modern sensors are becoming increasingly advanced, integrating complex integrated circuits and intelligent processing capabilities. Similar to integrated circuit manufacturing, the sensor production process involves a globally distributed supply chain. Designers and manufacturers must collaborate with numerous third-party suppliers, each of which may have access to sensor designs, production processes, or testing procedures. This makes it possible to embed sensor Trojans at multiple stages. The threat model of sensor Trojans aligns with that of hardware Trojans: attackers with supply chain access can modify the sensor's hardware components or embedded software. Such modifications may be designed to activate under specific analog input signals, potentially compromising the integrity of the sensor without being detected during standard testing. Unlike existing detection methods, sensor Trojans are primarily composed of analog circuits, making mainstream digital circuit-based detection methods unsuitable.

[0004] In summary, there is an urgent need to address the huge threat of sensor backdoors and improve the detection mechanism of sensor backdoors. Summary of the Invention

[0005] To address the above issues, the present invention proposes a sensor hardware Trojan detection method and system based on image processing, which can accurately identify malicious circuits in sensors, reduce false alarms through image evaluation and feature extraction, automate the detection process, and improve efficiency. It is applicable to various types of sensors to ensure their safety and functionality, and is applicable to both printed circuit board and integrated circuit Trojans.

[0006] The technical solutions proposed by the present invention are as follows:

[0007] In a first aspect, the present invention proposes a sensor hardware Trojan detection method based on image processing, comprising the following steps:

[0008] (1) obtaining sensor circuit images of different types and different manufacturing processes and their corresponding original design files; the sensor circuit images include those with and without Trojans; and introducing image quality defects into some of the sensor circuit images;

[0009] (2) aligning the sensor circuit image and the original design file, marking the area where the Trojan is implanted, and constructing a first training sample set; and cropping the area of interest containing image quality defects, the area of interest not containing image quality defects but containing the Trojan, and the area of interest containing neither image quality defects nor the Trojan in the sensor circuit image, and constructing a second training sample set;

[0010] (3) using the first training sample set to train an object recognition model for identifying the Trojan region in the registered image pair, and using the second training sample set to train a region of interest detection model for determining whether the region of interest image contains image quality defects;

[0011] (4) The target recognition model and the region of interest detection model are combined, and image restoration technology targeting image quality defects is introduced to determine whether there is a Trojan in the sensor circuit image of the sensor sample to be tested.

[0012] Furthermore, the step (4) is specifically as follows:

[0013] A sensor circuit image of the sensor sample to be tested is obtained and aligned with the original design file; the aligned image pair is input into the target recognition model to identify the Trojan area as a suspected abnormal area; if a suspected abnormal area exists, an image of a region of interest containing a separate suspected abnormal area is captured, and each region of interest image is judged by the region of interest detection model to determine whether it is an image quality defect; if so, the region of interest of the sensor circuit image is repaired and the suspected abnormal area is re-identified until the suspected abnormal area marked by the target recognition model does not belong to an image quality problem. At this time, the suspected abnormal area is judged to be implanted with a Trojan; if the suspected abnormal area is not marked after repair, it is judged to be a false alarm caused by image quality defects, and the sensor does not have a Trojan.

[0014] Furthermore, the image restoration technology adopts a gated convolution image restoration algorithm.

[0015] Furthermore, the sensor circuit image is a scanning electron microscope image of a sensor with an integrated circuit structure, or a visible light image of a sensor with a circuit printed plate structure.

[0016] Furthermore, the image quality defects include dust, dirt, excessive contrast, and blur.

[0017] Furthermore, each sample in the first training sample set is an image pair obtained by registering a sensor circuit image and an original design file. If a Trojan is implanted in the sensor circuit image in the image pair, the area where the Trojan is implanted is marked; otherwise, no marking is required.

[0018] Furthermore, the target recognition model adopts a ResNet network.

[0019] Furthermore, each sample in the second training sample set is a local region of interest of the sensor circuit image. If the region of interest contains image quality defects, the label is 1, otherwise the labels are all 0.

[0020] Furthermore, the region of interest detection model adopts the VGG model.

[0021] In a second aspect, the present invention provides a sensor hardware Trojan detection system based on image processing, which is used to implement the above-mentioned sensor hardware Trojan detection method based on image processing.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] (1) The present invention obtains sensor circuit images and original design files of different types and manufacturing processes, including those with and without Trojans implanted. It also introduces image quality defects and constructs a sample set covering multiple features, providing sufficient and diverse data for model training and improving model adaptability.

[0024] (2) The present invention uses different sample sets to train the target recognition model and the region of interest detection model respectively. One model focuses on identifying the Trojan area, and the other model judges the image quality defects. The functions are clear and the detection accuracy is improved.

[0025] (3) The present invention combines two models and introduces image restoration technology, which can more accurately determine whether there is a Trojan in the image of the sensor circuit to be tested. The automated detection process improves the detection efficiency.

[0026] The present invention provides an efficient and accurate method for detecting hardware Trojans in sensors. This method can not only accurately identify potential hardware Trojans, but also effectively reduce the false alarm rate by means of image quality assessment and feature extraction, ensuring the reliability of the detection results. At the same time, the automated process significantly reduces manual intervention and improves the detection efficiency. It is applicable to various types of sensor products, ensuring their safety and functionality in different application scenarios, greatly enhancing the level of sensor security detection, and providing a strong guarantee for preventing malicious tampering. In the case of untrusted producers, this method can effectively reduce threats, enhance sensor security, prevent malicious Trojans from causing the sensor to get out of control or even be damaged, and avoid incorrect operations of intelligent devices such as cars and drones. The present invention is applicable to Trojan detection at the circuit printed board level of the sensor layer and also to integrated circuit Trojan detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 FIG. is a schematic flow chart of a method for detecting hardware Trojans in sensors based on image processing proposed by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] The present invention will be further described and explained below in conjunction with the specific embodiments. The described embodiments are only illustrative of the present disclosure and do not delimit the scope of limitation. The technical features of each embodiment of the present invention can be combined correspondingly without conflict.

[0029] The drawings are only schematic illustrations of the present invention and are not necessarily drawn to scale. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0030] The flow charts shown in the drawings are only illustrative and do not necessarily include all the steps. For example, some steps can be further decomposed, while some steps can be combined or partially combined. Therefore, the actual execution order may be changed according to the actual situation.

[0031] The present invention proposes a method for detecting hardware Trojans in sensors based on image processing. The present invention uses high-resolution scanning electron microscope (SEM) images / visible light images and advanced image registration techniques to accurately correspond the physical device images with the original design files. With the help of the ResNet model, the subtle differences between the two are automatically identified and marked, and the suspected abnormal areas of potential hardware Trojans are accurately located. In addition, a post-processing module is introduced to evaluate the image quality of the suspected abnormal areas and repair the abnormalities caused by non-Trojans, effectively reducing the false alarm rate and improving the detection reliability.

[0032] As Figure 1As shown in the figure, a method for detecting hardware Trojans in sensors based on image processing proposed by the present invention mainly includes the following steps:

[0033] S1. Data preparation work.

[0034] Obtain a batch of sensor samples and their original design files. Among them, the sensor contains one or more of integrated circuits and printed circuits, and the original design file should be considered a clean version without malicious backdoors. Ensure that these data cover sensor circuits of different types and different manufacturing processes to improve the generalization ability of the model. In this embodiment, different types of sensor circuits can be thermistor-type temperature sensor circuits, thermocouple-type temperature sensor circuits, piezoresistive pressure sensor circuits, capacitive pressure sensor circuits, inductive displacement sensor circuits, optoelectronic displacement sensor circuits, etc.; sensor circuits with different manufacturing processes can be semiconductor process (integrated circuit structure) sensor circuits, thick film and thin film process (circuit printed board structure) sensor circuits, etc.

[0035] For sensors with an integrated circuit structure, their original design files are usually provided in the GDSII format, which is the blueprint for manufacturing semiconductor devices. For sensors with a circuit printed board structure, their original design files are usually provided in the pcb format, which is also the necessary material for producing subsequent circuit boards.

[0036] The sensor samples and their original design files are used for subsequent analysis to determine whether there are any unauthorized modifications or hardware Trojans in the sensor circuit.

[0037] S2. Obtain the sensor circuit image.

[0038] For sensors with an integrated circuit structure, it is necessary to preprocess the integrated circuit chip, including removing the top encapsulation material and exposing the underlying circuit structure for subsequent imaging; for sensors with a circuit printed board structure, directly take a visible light image of the circuit part.

[0039] In a specific implementation of the present invention, for an integrated circuit chip, due to its high integration degree, it is necessary to use a scanning electron microscope (SEM) to obtain a high-resolution image of the internal structure of the chip. In order to cover the entire chip area, multiple SEM images need to be collected and stitched into a complete image. For the circuit printed board, a clear and readable visible light image can be obtained through a high-resolution camera.

[0040] This step needs to include a large number of normal circuit images of known harmless hardware trojans and images corresponding to the trojans, and it is necessary to know the location where the trojans are implanted for the following image annotation. To improve the model performance, defects of the image itself such as local dust, dirt, excessive contrast, and blurring can be introduced into the normal circuit images and / or the images corresponding to the trojans, and there is no need to annotate them in the following.

[0041] S3, preprocessing of the sensor circuit images and the original design files to construct a training dataset.

[0042] The sensor circuit images may be affected by factors such as uneven illumination and noise interference, resulting in a decrease in image quality. For example, SEM images may have electronic noise, and visible light images may have inconsistent brightness due to uneven ambient light. The present invention improves the clarity and contrast of the sensor circuit images through preprocessing, making the features in the images easier to identify.

[0043] In addition, SEM images and visible light images obtained by different devices may have different formats, resolutions, and sizes. Preprocessing can convert the images into a unified format and appropriate size, facilitating subsequent registration operations and processing, and ensuring the consistency of the images during feature extraction and matching.

[0044] In this embodiment, image processing tools are used to preprocess the collected images, such as adjusting the contrast (linear contrast stretching, histogram equalization), removing noise (mean filtering, median filtering), etc., to improve the image quality for subsequent analysis.

[0045] The original design file specifies information such as the standard layout, size, and circuit path of the circuit board. By registering the SEM image or visible light image with it, the differences between the actual circuit board and the design can be accurately compared, which helps to automatically identify and label the subtle differences between the two. In this embodiment, the image registration method can be implemented using existing registration algorithms in the art, such as feature-based registration, template-based registration, or registration combining scale-invariant feature transform (SIFT) and random sample consensus algorithm (RANSAC). The SEM image or visible light image is accurately registered with the original design file to ensure that the registered image is accurately aligned with the design file in terms of spatial position.

[0046] For the areas where Trojans are known to be implanted, mark them as the areas of difference from the original design document on the SEM image or visible light image; for clean sensors, their corresponding SEM images or visible light images do not need to be marked. It should be noted that only the implanted areas of the Trojan circuit need to be marked, and local dust, dirt, excessive contrast, blurring, etc. do not need to be marked. Preprocess the registered image pairs, including but not limited to operations such as resizing the images and normalizing the pixel values, so that the image data has a unified format and range. For the marked data, corresponding conversions should also be performed to facilitate the input and processing of the model, and finally obtain the first training dataset for the following object recognition model.

[0047] In addition, for the local dust, dirt, excessive contrast, and blurred parts on the SEM image or visible light image, intercept the local regions of interest and mix them into the normal local regions and the Trojan implantation regions, where the image labels of the local regions of interest for local dust, dirt, excessive contrast, blurring, etc. are 1; the labels of the normal local regions and the Trojan implantation regions are 0, and finally obtain the second training dataset for the following region of interest detection model.

[0048] S4. Construct and train an object recognition model for annotating suspected abnormal regions.

[0049] Use the first training dataset prepared above to train a convolutional neural network CNN. In this embodiment, a network with a ResNet architecture is adopted. ResNet has significant advantages in the task of annotating differences in circuit board images. Its residual connections effectively solve the problem of gradient disappearance, enabling the deep network to learn complex and subtle features to accurately identify differences. Its powerful feature extraction ability enables it to grasp various image features to judge differences. This model is trained to identify and annotate the subtle differences between two input images, and the output includes the specific positions of the differences, which may be the positions of potential hardware Trojans.

[0050] In a specific implementation of the present invention, the process of training the model is as follows:

[0051] Divide the preprocessed dataset into a 70% training set, a 15% validation set, and a 15% test set.

[0052] Set the parameters during the training process, including the learning rate, the number of training epochs, the batch size, etc. The learning rate determines the step size of parameter update during the training of the model, the number of training epochs controls the number of times the model is trained, and the batch size represents the amount of data input into the model each time. Reasonably setting these parameters is crucial for the training effect of the model.

[0053] The ResNet model is trained using the training set data. During the training process, the model calculates the loss function (such as the cross-entropy loss function) between the predicted result and the true annotation based on the input image pairs and annotation information, and updates the model's parameters through the backpropagation algorithm to minimize the loss function. At the same time, the validation set data is used to monitor the model's performance, and the hyperparameters are adjusted according to the validation results to prevent the model from overfitting.

[0054] The trained ResNet model is evaluated using the test set data. The registered image pairs are input into the model, and the model will output the predicted annotation results of the difference regions. The model is evaluated based on the results until the model meets the requirements.

[0055] The trained ResNet model can compare the differences between the registered image pairs and annotate the difference regions, and this difference is very likely caused by the suspicious Trojan circuit. Using this model can automatically identify and annotate the subtle differences in the input registered images, and accurately locate the suspected abnormal regions of potential hardware Trojans.

[0056] S5. Build and train a region of interest detection model for verifying suspected abnormal regions.

[0057] Use the second training data set prepared above to train a convolutional neural network CNN. In this embodiment, the VGG model is adopted, and this model consists of a stack of multiple convolutional layers and pooling layers. This enables it to automatically learn different levels of features in the image, gradually extracting high-level semantic features from simple features such as edges and textures at the bottom layer. For local dust, dirt, excessive contrast, blurring, etc. on the image, it can accurately capture their subtle textures, shapes, etc. features and identify them through its deep feature extraction ability.

[0058] The training process of the VGG model is similar to that of the ResNet model. The difference is that the data set used to train the VGG model is the second training data set, and it is trained as a binary classifier to identify images with dust, dirt, excessive contrast, and blurring. The training process will not be elaborated here. Before training, data augmentation techniques including rotation, scaling, and flipping can also be adopted to improve the generalization ability of the model.

[0059] Through the VGG model, it can be identified whether there are problems such as common variations, dust, dirt, excessive contrast, and blurring in the input suspicious images, which may cause false alarms in the target recognition model. This process is mainly to improve the detection quality and reduce the false alarm rate.

[0060] S6. Obtain the registered images of the sensor circuit images of the to-be-detected batch of sensor samples and the original design files, and identify whether there are sensor hardware Trojans.

[0061] Specifically: Obtain the sensor circuit image of the sensor sample and register it with the original design file;

[0062] The registered image pair is input into the ResNet model to identify suspected abnormal regions; if there are suspected abnormal regions, the region of interest (ROI) image containing one suspected abnormal region is intercepted. Each ROI image is used by the VGG model to determine whether it belongs to image quality problems such as local dust, dirt, excessive contrast, blur, etc. If so, the Gated Convolution method is used to repair the image. This algorithm allows the network to adaptively select the information to be filtered. The repair process aims to make the image as close as possible to the original lossless state while retaining the important details of the image. Through this method, the image quality can be effectively improved. Each ROI image belonging to the image quality problem needs to be repaired. After the repair is completed, it is re-identified by the ResNet model until the suspected abnormal region marked by the ResNet model does not belong to the image quality problem. At this time, the suspected abnormal region is determined to be implanted with a Trojan. If no suspected abnormal region is marked after the repaired image is re-input into the ResNet model, it is considered that the initial detection may be a false alarm due to image quality problems.

[0063] By evaluating the image quality of the suspected abnormal region and repairing the abnormalities not caused by the Trojan, it is ensured that even in the presence of image quality problems, the false alarm rate can be significantly reduced and the overall detection reliability can be improved through effective repair and re-detection processes.

[0064] Based on the same inventive concept, in this embodiment, a sensor hardware Trojan detection system based on image processing is also provided, which is used to implement the above embodiment. The following terms such as "module" and "unit" can be a combination of software and / or hardware that can achieve a predetermined function. Although the system described in the following embodiments is preferably implemented in software, implementation in hardware, or a combination of software and hardware is also possible.

[0065] In this embodiment, a sensor hardware Trojan detection system based on image processing includes:

[0066] A data acquisition module, which is used to acquire sensor circuit images of different types and different manufacturing processes and their corresponding original design files; the sensor circuit images include two cases of being implanted with a Trojan and not being implanted with a Trojan; image quality defects are introduced into some sensor circuit images.

[0067] a training sample set construction module for aligning the sensor circuit image and the original design file, marking the region where the Trojan is implanted, and constructing a first training sample set; and cropping the region of interest in the sensor circuit image that contains image quality defects, the region of interest that does not contain image quality defects but contains the Trojan, and the region of interest that contains neither image quality defects nor the Trojan, and constructing a second training sample set;

[0068] A target recognition model training module, configured to train a target recognition model for identifying a Trojan area in a registered image pair using a first training sample set;

[0069] A region of interest detection model training module, which is used to train a region of interest detection model for determining whether an image of the region of interest contains image quality defects using the second training sample set;

[0070] The Trojan joint detection module is used to combine the target recognition model and the region of interest detection model, and introduces image restoration technology for image quality defects to determine whether there is a Trojan in the sensor circuit image of the sensor sample to be tested.

[0071] As for the system embodiment, since it basically corresponds to the method embodiment, the relevant parts can be referred to the partial description of the method embodiment, and the implementation methods of the remaining modules will not be repeated here. The system embodiment described above is only illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present invention. Ordinary technicians in this field can understand and implement it without paying any creative work.

[0072] Embodiments of the system of the present invention can be applied to any device with data processing capabilities, such as a computer or other device. System embodiments can be implemented through software, hardware, or a combination of software and hardware. For example, a software implementation, as a logical device, is implemented by a processor of any device with data processing capabilities, reading corresponding computer program instructions from non-volatile memory into internal memory and executing them.

[0073] The above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above examples, and many variations are possible. All variations that can be directly derived or imagined by a person skilled in the art from the disclosure of the present invention should be considered to be within the scope of protection of the present invention.

Claims

1. A method for detecting sensor hardware Trojans based on image processing, characterized in that, The following steps are involved: (1) obtaining sensor circuit images of different types and different manufacturing processes and their corresponding original design files; the sensor circuit images include those with and without Trojans; and introducing image quality defects into some of the sensor circuit images; (2) aligning the sensor circuit image and the original design file, marking the area where the Trojan is implanted, and constructing a first training sample set; and cropping the area of interest containing image quality defects, the area of interest not containing image quality defects but containing the Trojan, and the area of interest containing neither image quality defects nor the Trojan in the sensor circuit image, and constructing a second training sample set; (3) using the first training sample set to train an object recognition model for identifying the Trojan region in the registered image pair, and using the second training sample set to train a region of interest detection model for determining whether the region of interest image contains image quality defects; (4) The target recognition model and the region of interest detection model are combined, and image restoration technology targeting image quality defects is introduced to determine whether there is a Trojan in the sensor circuit image of the sensor sample to be tested.

2. The method for detecting sensor hardware Trojans based on image processing according to claim 1, characterized in that, The step (4) is specifically as follows: Obtaining a sensor circuit image of the sensor sample to be tested and registering it with the original design file; inputting the registered image pair into the target recognition model to identify the Trojan area as a suspected abnormal area; If there is a suspected abnormal area, the image of the region of interest containing the individual suspected abnormal area is intercepted. Each region of interest image is judged by the region of interest detection model to determine whether it is an image quality defect. If it is, the region of interest of the sensor circuit image is repaired and the suspected abnormal area is re-identified until the suspected abnormal area marked by the target recognition model does not belong to the image quality problem. At this time, the suspected abnormal area is judged to be implanted with a Trojan horse; If no suspected abnormal area is marked after repair, it is determined that the false alarm is caused by image quality defects and the sensor does not contain a Trojan.

3. The method for detecting sensor hardware Trojans based on image processing according to claim 1, wherein The image restoration technology adopts a gated convolution image restoration algorithm.

4. The method for detecting sensor hardware Trojans based on image processing according to claim 1, wherein The sensor circuit image is a scanning electron microscope image of a sensor with an integrated circuit structure, or a visible light image of a sensor with a circuit printed plate structure.

5. The method for detecting sensor hardware Trojans based on image processing according to claim 4, wherein, The image quality defects mentioned include dust, dirt, excessive contrast, and blur.

6. The method for detecting sensor hardware Trojans based on image processing according to claim 1, wherein Each sample in the first training sample set is an image pair obtained by registering a sensor circuit image with an original design file. If a Trojan is implanted in the sensor circuit image in the image pair, the region where the Trojan is implanted is marked. Otherwise no marking is required.

7. The method for detecting sensor hardware Trojans based on image processing according to claim 1 or 6, characterized in that The target recognition model adopts the ResNet network.

8. The method for detecting sensor hardware Trojans based on image processing according to claim 1, characterized in that Each sample in the second training sample set is a local region of interest of the sensor circuit image. If the region of interest contains image quality defects, the label is 1, otherwise the label is 0.

9. The method for detecting sensor hardware Trojans based on image processing according to claim 1, wherein The region of interest detection model adopts the VGG model.

10. A sensor hardware Trojan detection system based on image processing for implementing the method described in claim 1; characterized in that, The system comprises: A data acquisition module is used to acquire sensor circuit images of different types and manufacturing processes and their corresponding original design files; the sensor circuit images include those with and without Trojans; and image quality defects are introduced into some sensor circuit images; a training sample set construction module for aligning the sensor circuit image and the original design file, marking the region where the Trojan is implanted, and constructing a first training sample set; and cropping the region of interest in the sensor circuit image that contains image quality defects, the region of interest that does not contain image quality defects but contains the Trojan, and the region of interest that contains neither image quality defects nor the Trojan, and constructing a second training sample set; A target recognition model training module, configured to train a target recognition model for identifying a Trojan area in a registered image pair using a first training sample set; A region of interest detection model training module, which is used to train a region of interest detection model for determining whether an image of the region of interest contains image quality defects using the second training sample set; The Trojan joint detection module is used to combine the target recognition model and the region of interest detection model, and introduces image restoration technology for image quality defects to determine whether there is a Trojan in the sensor circuit image of the sensor sample to be tested.

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