CRAug 18, 2023
Attesting Distributional Properties of Training Data for Machine LearningVasisht Duddu, Anudeep Das, Nora Khayata et al.
The success of machine learning (ML) has been accompanied by increased concerns about its trustworthiness. Several jurisdictions are preparing ML regulatory frameworks. One such concern is ensuring that model training data has desirable distributional properties for certain sensitive attributes. For example, draft regulations indicate that model trainers are required to show that training datasets have specific distributional properties, such as reflecting diversity of the population. We propose the notion of property attestation allowing a prover (e.g., model trainer) to demonstrate relevant distributional properties of training data to a verifier (e.g., a customer) without revealing the data. We present an effective hybrid property attestation combining property inference with cryptographic mechanisms.
CRAug 21, 2022
Inferring Sensitive Attributes from Model ExplanationsVasisht Duddu, Antoine Boutet
Model explanations provide transparency into a trained machine learning model's blackbox behavior to a model builder. They indicate the influence of different input attributes to its corresponding model prediction. The dependency of explanations on input raises privacy concerns for sensitive user data. However, current literature has limited discussion on privacy risks of model explanations. We focus on the specific privacy risk of attribute inference attack wherein an adversary infers sensitive attributes of an input (e.g., race and sex) given its model explanations. We design the first attribute inference attack against model explanations in two threat models where model builder either (a) includes the sensitive attributes in training data and input or (b) censors the sensitive attributes by not including them in the training data and input. We evaluate our proposed attack on four benchmark datasets and four state-of-the-art algorithms. We show that an adversary can successfully infer the value of sensitive attributes from explanations in both the threat models accurately. Moreover, the attack is successful even by exploiting only the explanations corresponding to sensitive attributes. These suggest that our attack is effective against explanations and poses a practical threat to data privacy. On combining the model predictions (an attack surface exploited by prior attacks) with explanations, we note that the attack success does not improve. Additionally, the attack success on exploiting model explanations is better compared to exploiting only model predictions. These suggest that model explanations are a strong attack surface to exploit for an adversary.
LGNov 18, 2022
On the Alignment of Group Fairness with Attribute PrivacyJan Aalmoes, Vasisht Duddu, Antoine Boutet
Group fairness and privacy are fundamental aspects in designing trustworthy machine learning models. Previous research has highlighted conflicts between group fairness and different privacy notions. We are the first to demonstrate the alignment of group fairness with the specific privacy notion of attribute privacy in a blackbox setting. Attribute privacy, quantified by the resistance to attribute inference attacks (AIAs), requires indistinguishability in the target model's output predictions. Group fairness guarantees this thereby mitigating AIAs and achieving attribute privacy. To demonstrate this, we first introduce AdaptAIA, an enhancement of existing AIAs, tailored for real-world datasets with class imbalances in sensitive attributes. Through theoretical and extensive empirical analyses, we demonstrate the efficacy of two standard group fairness algorithms (i.e., adversarial debiasing and exponentiated gradient descent) against AdaptAIA. Additionally, since using group fairness results in attribute privacy, it acts as a defense against AIAs, which is currently lacking. Overall, we show that group fairness aligns with attribute privacy at no additional cost other than the already existing trade-off with model utility.
CRApr 30
PAL*M: Property Attestation for Large Generative ModelsPrach Chantasantitam, Adam Ilyas Caulfield, Vasisht Duddu et al.
Machine learning property attestations allow provers (e.g., model providers or owners) to attest properties of their models/datasets to verifiers (e.g., regulators, customers), enabling accountability towards regulations and policies. But, current approaches do not support generative models or large datasets. We present PAL*M, a property attestation framework for large generative models, illustrated using large language models. PAL*M defines properties across training and inference, leverages confidential virtual machines with security-aware GPUs for coverage of CPU-GPU operations, and proposes using incremental multiset hashing over memory-mapped datasets to efficiently track their integrity. We implement PAL*M on Intel TDX+NVIDIA H100 and evaluate it using state-of-the-art models and datasets, showing PAL*M is efficient, incurring < 11% overhead for common operations. Finally, we use the Tamarin Prover symbolic verification tool to formally model PAL*M's property attestation protocol, confirming that its security guarantees are upheld under the defined threat model.
LGApr 17, 2023
GrOVe: Ownership Verification of Graph Neural Networks using EmbeddingsAsim Waheed, Vasisht Duddu, N. Asokan
Graph neural networks (GNNs) have emerged as a state-of-the-art approach to model and draw inferences from large scale graph-structured data in various application settings such as social networking. The primary goal of a GNN is to learn an embedding for each graph node in a dataset that encodes both the node features and the local graph structure around the node. Embeddings generated by a GNN for a graph node are unique to that GNN. Prior work has shown that GNNs are prone to model extraction attacks. Model extraction attacks and defenses have been explored extensively in other non-graph settings. While detecting or preventing model extraction appears to be difficult, deterring them via effective ownership verification techniques offer a potential defense. In non-graph settings, fingerprinting models, or the data used to build them, have shown to be a promising approach toward ownership verification. We present GrOVe, a state-of-the-art GNN model fingerprinting scheme that, given a target model and a suspect model, can reliably determine if the suspect model was trained independently of the target model or if it is a surrogate of the target model obtained via model extraction. We show that GrOVe can distinguish between surrogate and independent models even when the independent model uses the same training dataset and architecture as the original target model. Using six benchmark datasets and three model architectures, we show that consistently achieves low false-positive and false-negative rates. We demonstrate that is robust against known fingerprint evasion techniques while remaining computationally efficient.
LGSep 5, 2024
Privacy Bias in Language Models: A Contextual Integrity-based Auditing MetricYan Shvartzshnaider, Vasisht Duddu
As large language models (LLMs) are integrated into sociotechnical systems, it is crucial to examine the privacy biases they exhibit. We define privacy bias as the appropriateness value of information flows in responses from LLMs. A deviation between privacy biases and expected values, referred to as privacy bias delta, may indicate privacy violations. As an auditing metric, privacy bias can help (a) model trainers evaluate the ethical and societal impact of LLMs, (b) service providers select context-appropriate LLMs, and (c) policymakers assess the appropriateness of privacy biases in deployed LLMs. We formulate and answer a novel research question: how can we reliably examine privacy biases in LLMs and the factors that influence them? We present a novel approach for assessing privacy biases using a contextual integrity-based methodology to evaluate the responses from various LLMs. Our approach accounts for the sensitivity of responses across prompt variations, which hinders the evaluation of privacy biases. Finally, we investigate how privacy biases are affected by model capacities and optimizations.
CVApr 30, 2024
Espresso: Robust Concept Filtering in Text-to-Image ModelsAnudeep Das, Vasisht Duddu, Rui Zhang et al.
Diffusion based text-to-image models are trained on large datasets scraped from the Internet, potentially containing unacceptable concepts (e.g., copyright-infringing or unsafe). We need concept removal techniques (CRTs) which are i) effective in preventing the generation of images with unacceptable concepts, ii) utility-preserving on acceptable concepts, and, iii) robust against evasion with adversarial prompts. No prior CRT satisfies all these requirements simultaneously. We introduce Espresso, the first robust concept filter based on Contrastive Language-Image Pre-Training (CLIP). We identify unacceptable concepts by using the distance between the embedding of a generated image to the text embeddings of both unacceptable and acceptable concepts. This lets us fine-tune for robustness by separating the text embeddings of unacceptable and acceptable concepts while preserving utility. We present a pipeline to evaluate various CRTs to show that Espresso is more effective and robust than prior CRTs, while retaining utility.
CRDec 7, 2023
SoK: Unintended Interactions among Machine Learning Defenses and RisksVasisht Duddu, Sebastian Szyller, N. Asokan
Machine learning (ML) models cannot neglect risks to security, privacy, and fairness. Several defenses have been proposed to mitigate such risks. When a defense is effective in mitigating one risk, it may correspond to increased or decreased susceptibility to other risks. Existing research lacks an effective framework to recognize and explain these unintended interactions. We present such a framework, based on the conjecture that overfitting and memorization underlie unintended interactions. We survey existing literature on unintended interactions, accommodating them within our framework. We use our framework to conjecture on two previously unexplored interactions, and empirically validate our conjectures.
CRSep 15, 2025
Amulet: a Python Library for Assessing Interactions Among ML Defenses and RisksAsim Waheed, Vasisht Duddu, Rui Zhang et al.
Machine learning (ML) models are susceptible to various risks to security, privacy, and fairness. Most defenses are designed to protect against each risk individually (intended interactions) but can inadvertently affect susceptibility to other unrelated risks (unintended interactions). We introduce Amulet, the first Python library for evaluating both intended and unintended interactions among ML defenses and risks. Amulet is comprehensive by including representative attacks, defenses, and metrics; extensible to new modules due to its modular design; consistent with a user-friendly API template for inputs and outputs; and applicable for evaluating novel interactions. By satisfying all four properties, Amulet offers a unified foundation for studying how defenses interact, enabling the first systematic evaluation of unintended interactions across multiple risks.
CRNov 14, 2024
Combining Machine Learning Defenses without ConflictsVasisht Duddu, Rui Zhang, N. Asokan
Machine learning (ML) defenses protect against various risks to security, privacy, and fairness. Real-life models need simultaneous protection against multiple different risks which necessitates combining multiple defenses. But combining defenses with conflicting interactions in an ML model can be ineffective, incurring a significant drop in the effectiveness of one or more defenses being combined. Practitioners need a way to determine if a given combination can be effective. Experimentally identifying effective combinations can be time-consuming and expensive, particularly when multiple defenses need to be combined. We need an inexpensive, easy-to-use combination technique to identify effective combinations. Ideally, a combination technique should be (a) accurate (correctly identifies whether a combination is effective or not), (b) scalable (allows combining multiple defenses), (c) non-invasive (requires no change to the defenses being combined), and (d) general (is applicable to different types of defenses). Prior works have identified several ad-hoc techniques but none satisfy all the requirements above. We propose a principled combination technique, Def\Con, to identify effective defense combinations. Def\Con meets all requirements, achieving 90% accuracy on eight combinations explored in prior work and 81% in 30 previously unexplored combinations that we empirically evaluate in this paper.
CROct 14, 2025
Locket: Robust Feature-Locking Technique for Language ModelsLipeng He, Vasisht Duddu, N. Asokan
Chatbot providers (e.g., OpenAI) rely on tiered subscription schemes to generate revenue, offering basic models for free users, and advanced models for paying subscribers. However, a finer-grained pay-to-unlock scheme for premium features (e.g., math, coding) is thought to be more economically viable for the providers. Such a scheme requires a feature-locking technique (FLoTE) which is (i) effective in refusing locked features, (ii) utility-preserving for unlocked features, (iii) robust against evasion or unauthorized credential sharing, and (iv) scalable to multiple features and users. However, existing FLoTEs (e.g., password-locked models) are not robust or scalable. We present Locket, the first robust and scalable FLoTE to enable pay-to-unlock schemes. Locket uses a novel merging approach to attach adapters to an LLM for refusing unauthorized features. Our comprehensive evaluation shows that Locket is effective ($100$% refusal on locked features), utility-preserving ($\leq 7$% utility degradation in unlocked features), robust ($\leq 5$% attack success rate), and scales to multiple features and clients.
CROct 8, 2025
PATCH: Mitigating PII Leakage in Language Models with Privacy-Aware Targeted Circuit PatcHingAnthony Hughes, Vasisht Duddu, N. Asokan et al.
Language models (LMs) may memorize personally identifiable information (PII) from training data, enabling adversaries to extract it during inference. Existing defense mechanisms such as differential privacy (DP) reduce this leakage, but incur large drops in utility. Based on a comprehensive study using circuit discovery to identify the computational circuits responsible PII leakage in LMs, we hypothesize that specific PII leakage circuits in LMs should be responsible for this behavior. Therefore, we propose PATCH (Privacy-Aware Targeted Circuit PatcHing), a novel approach that first identifies and subsequently directly edits PII circuits to reduce leakage. PATCH achieves better privacy-utility trade-off than existing defenses, e.g., reducing recall of PII leakage from LMs by up to 65%. Finally, PATCH can be combined with DP to reduce recall of residual leakage of an LM to as low as 0.01%. Our analysis shows that PII leakage circuits persist even after the application of existing defense mechanisms. In contrast, PATCH can effectively mitigate their impact.
CRFeb 4, 2022
Dikaios: Privacy Auditing of Algorithmic Fairness via Attribute Inference AttacksJan Aalmoes, Vasisht Duddu, Antoine Boutet
Machine learning (ML) models have been deployed for high-stakes applications. Due to class imbalance in the sensitive attribute observed in the datasets, ML models are unfair on minority subgroups identified by a sensitive attribute, such as race and sex. In-processing fairness algorithms ensure model predictions are independent of sensitive attribute. Furthermore, ML models are vulnerable to attribute inference attacks where an adversary can identify the values of sensitive attribute by exploiting their distinguishable model predictions. Despite privacy and fairness being important pillars of trustworthy ML, the privacy risk introduced by fairness algorithms with respect to attribute leakage has not been studied. We identify attribute inference attacks as an effective measure for auditing blackbox fairness algorithms to enable model builder to account for privacy and fairness in the model design. We proposed Dikaios, a privacy auditing tool for fairness algorithms for model builders which leveraged a new effective attribute inference attack that account for the class imbalance in sensitive attributes through an adaptive prediction threshold. We evaluated Dikaios to perform a privacy audit of two in-processing fairness algorithms over five datasets. We show that our attribute inference attacks with adaptive prediction threshold significantly outperform prior attacks. We highlighted the limitations of in-processing fairness algorithms to ensure indistinguishable predictions across different values of sensitive attributes. Indeed, the attribute privacy risk of these in-processing fairness schemes is highly variable according to the proportion of the sensitive attributes in the dataset. This unpredictable effect of fairness mechanisms on the attribute privacy risk is an important limitation on their utilization which has to be accounted by the model builder.
CRDec 4, 2021
SHAPr: An Efficient and Versatile Membership Privacy Risk Metric for Machine LearningVasisht Duddu, Sebastian Szyller, N. Asokan
Data used to train machine learning (ML) models can be sensitive. Membership inference attacks (MIAs), attempting to determine whether a particular data record was used to train an ML model, risk violating membership privacy. ML model builders need a principled definition of a metric to quantify the membership privacy risk of (a) individual training data records, (b) computed independently of specific MIAs, (c) which assesses susceptibility to different MIAs, (d) can be used for different applications, and (e) efficiently. None of the prior membership privacy risk metrics simultaneously meet all these requirements. We present SHAPr, a membership privacy metric based on Shapley values which is a leave-one-out (LOO) technique, originally intended to measure the contribution of a training data record on model utility. We conjecture that contribution to model utility can act as a proxy for memorization, and hence represent membership privacy risk. Using ten benchmark datasets, we show that SHAPr is indeed effective in estimating susceptibility of training data records to MIAs. We also show that, unlike prior work, SHAPr is significantly better in estimating susceptibility to newer, and more effective MIA. We apply SHAPr to evaluate the efficacy of several defenses against MIAs: using regularization and removing high risk training data records. Moreover, SHAPr is versatile: it can be used for estimating vulnerability of different subgroups to MIAs, and inherits applications of Shapley values (e.g., data valuation). We show that SHAPr has an acceptable computational cost (compared to naive LOO), varying from a few minutes for the smallest dataset to ~92 minutes for the largest dataset.
LGApr 26, 2021
Good Artists Copy, Great Artists Steal: Model Extraction Attacks Against Image Translation ModelsSebastian Szyller, Vasisht Duddu, Tommi Gröndahl et al.
Machine learning models are typically made available to potential client users via inference APIs. Model extraction attacks occur when a malicious client uses information gleaned from queries to the inference API of a victim model $F_V$ to build a surrogate model $F_A$ with comparable functionality. Recent research has shown successful model extraction of image classification, and natural language processing models. In this paper, we show the first model extraction attack against real-world generative adversarial network (GAN) image translation models. We present a framework for conducting such attacks, and show that an adversary can successfully extract functional surrogate models by querying $F_V$ using data from the same domain as the training data for $F_V$. The adversary need not know $F_V$'s architecture or any other information about it beyond its intended task. We evaluate the effectiveness of our attacks using three different instances of two popular categories of image translation: (1) Selfie-to-Anime and (2) Monet-to-Photo (image style transfer), and (3) Super-Resolution (super resolution). Using standard performance metrics for GANs, we show that our attacks are effective. Furthermore, we conducted a large scale (125 participants) user study on Selfie-to-Anime and Monet-to-Photo to show that human perception of the images produced by $F_V$ and $F_A$ can be considered equivalent, within an equivalence bound of Cohen's d = 0.3. Finally, we show that existing defenses against model extraction attacks (watermarking, adversarial examples, poisoning) do not extend to image translation models.
CROct 2, 2020
GECKO: Reconciling Privacy, Accuracy and Efficiency in Embedded Deep LearningVasisht Duddu, Antoine Boutet, Virat Shejwalkar
Embedded systems demand on-device processing of data using Neural Networks (NNs) while conforming to the memory, power and computation constraints, leading to an efficiency and accuracy tradeoff. To bring NNs to edge devices, several optimizations such as model compression through pruning, quantization, and off-the-shelf architectures with efficient design have been extensively adopted. These algorithms when deployed to real world sensitive applications, requires to resist inference attacks to protect privacy of users training data. However, resistance against inference attacks is not accounted for designing NN models for IoT. In this work, we analyse the three-dimensional privacy-accuracy-efficiency tradeoff in NNs for IoT devices and propose Gecko training methodology where we explicitly add resistance to private inferences as a design objective. We optimize the inference-time memory, computation, and power constraints of embedded devices as a criterion for designing NN architecture while also preserving privacy. We choose quantization as design choice for highly efficient and private models. This choice is driven by the observation that compressed models leak more information compared to baseline models while off-the-shelf efficient architectures indicate poor efficiency and privacy tradeoff. We show that models trained using Gecko methodology are comparable to prior defences against black-box membership attacks in terms of accuracy and privacy while providing efficiency.
CROct 2, 2020
Quantifying Privacy Leakage in Graph EmbeddingVasisht Duddu, Antoine Boutet, Virat Shejwalkar
Graph embeddings have been proposed to map graph data to low dimensional space for downstream processing (e.g., node classification or link prediction). With the increasing collection of personal data, graph embeddings can be trained on private and sensitive data. For the first time, we quantify the privacy leakage in graph embeddings through three inference attacks targeting Graph Neural Networks. We propose a membership inference attack to infer whether a graph node corresponding to individual user's data was member of the model's training or not. We consider a blackbox setting where the adversary exploits the output prediction scores, and a whitebox setting where the adversary has also access to the released node embeddings. This attack provides an accuracy up to 28% (blackbox) 36% (whitebox) beyond random guess by exploiting the distinguishable footprint between train and test data records left by the graph embedding. We propose a Graph Reconstruction attack where the adversary aims to reconstruct the target graph given the corresponding graph embeddings. Here, the adversary can reconstruct the graph with more than 80% of accuracy and link inference between two nodes around 30% more confidence than a random guess. We then propose an attribute inference attack where the adversary aims to infer a sensitive attribute. We show that graph embeddings are strongly correlated to node attributes letting the adversary inferring sensitive information (e.g., gender or location).
CROct 31, 2019
Quantifying (Hyper) Parameter Leakage in Machine LearningVasisht Duddu, D. Vijay Rao
Machine Learning models, extensively used for various multimedia applications, are offered to users as a blackbox service on the Cloud on a pay-per-query basis. Such blackbox models are commercially valuable to adversaries, making them vulnerable to extraction attacks to reverse engineer the proprietary model thereby violating the model privacy and Intellectual Property. Here, the adversary first extracts the model architecture or hyperparameters through side channel leakage, followed by stealing the functionality of the target model by training the reconstructed architecture on a synthetic dataset. While the attacks proposed in literature are empirical, there is a need for a theoretical framework to measure the information leaked under such extraction attacks. To this extent, in this work, we propose a novel probabilistic framework, Airavata, to estimate the information leakage in such model extraction attacks. This framework captures the fact that extracting the exact target model is difficult due to experimental uncertainty while inferring model hyperparameters and stochastic nature of training to steal the target model functionality. Specifically, we use Bayesian Networks to capture uncertainty in estimating the target model under various extraction attacks based on the subjective notion of probability. We validate the proposed framework under different adversary assumptions commonly adopted in literature to reason about the attack efficacy. This provides a practical tool to infer actionable details about extracting blackbox models and help identify the best attack combination which maximises the knowledge extracted (or information leaked) from the target model.
CROct 30, 2019
Fault Tolerance of Neural Networks in Adversarial SettingsVasisht Duddu, N. Rajesh Pillai, D. Vijay Rao et al.
Artificial Intelligence systems require a through assessment of different pillars of trust, namely, fairness, interpretability, data and model privacy, reliability (safety) and robustness against against adversarial attacks. While these research problems have been extensively studied in isolation, an understanding of the trade-off between different pillars of trust is lacking. To this extent, the trade-off between fault tolerance, privacy and adversarial robustness is evaluated for the specific case of Deep Neural Networks, by considering two adversarial settings under a security and a privacy threat model. Specifically, this work studies the impact of the fault tolerance of the Neural Network on training the model by adding noise to the input (Adversarial Robustness) and noise to the gradients (Differential Privacy). While training models with noise to inputs, gradients or weights enhances fault tolerance, it is observed that adversarial robustness and fault tolerance are at odds with each other. On the other hand, ($ε,δ$)-Differentially Private models enhance the fault tolerance, measured using generalisation error, theoretically has an upper bound of $e^ε - 1 + δ$. This novel study of the trade-off between different elements of trust is pivotal for training a model which satisfies the requirements for different pillars of trust simultaneously.
LGJul 6, 2019
Towards Enhancing Fault Tolerance in Neural NetworksVasisht Duddu, D. Vijay Rao, Valentina E. Balas
Deep Learning Accelerators are prone to faults which manifest in the form of errors in Neural Networks. Fault Tolerance in Neural Networks is crucial in real-time safety critical applications requiring computation for long durations. Neural Networks with high regularisation exhibit superior fault tolerance, however, at the cost of classification accuracy. In the view of difference in functionality, a Neural Network is modelled as two separate networks, i.e, the Feature Extractor with unsupervised learning objective and the Classifier with a supervised learning objective. Traditional approaches of training the entire network using a single supervised learning objective is insufficient to achieve the objectives of the individual components optimally. In this work, a novel multi-criteria objective function, combining unsupervised training of the Feature Extractor followed by supervised tuning with Classifier Network is proposed. The unsupervised training solves two games simultaneously in the presence of adversary neural networks with conflicting objectives to the Feature Extractor. The first game minimises the loss in reconstructing the input image for indistinguishability given the features from the Extractor, in the presence of a generative decoder. The second game solves a minimax constraint optimisation for distributional smoothening of feature space to match a prior distribution, in the presence of a Discriminator network. The resultant strongly regularised Feature Extractor is combined with the Classifier Network for supervised fine-tuning. The proposed Adversarial Fault Tolerant Neural Network Training is scalable to large networks and is independent of the architecture. The evaluation on benchmarking datasets: FashionMNIST and CIFAR10, indicates that the resultant networks have high accuracy with superior tolerance to stuck at "0" faults compared to widely used regularisers.
CRDec 31, 2018
Stealing Neural Networks via Timing Side ChannelsVasisht Duddu, Debasis Samanta, D Vijay Rao et al.
Deep learning is gaining importance in many applications. However, Neural Networks face several security and privacy threats. This is particularly significant in the scenario where Cloud infrastructures deploy a service with Neural Network model at the back end. Here, an adversary can extract the Neural Network parameters, infer the regularization hyperparameter, identify if a data point was part of the training data, and generate effective transferable adversarial examples to evade classifiers. This paper shows how a Neural Network model is susceptible to timing side channel attack. In this paper, a black box Neural Network extraction attack is proposed by exploiting the timing side channels to infer the depth of the network. Although, constructing an equivalent architecture is a complex search problem, it is shown how Reinforcement Learning with knowledge distillation can effectively reduce the search space to infer a target model. The proposed approach has been tested with VGG architectures on CIFAR10 data set. It is observed that it is possible to reconstruct substitute models with test accuracy close to the target models and the proposed approach is scalable and independent of type of Neural Network architectures.
CRMar 30, 2018
Fuzzy Graph Modelling of Anonymous NetworksVasisht Duddu, Debasis Samanta, D Vijay Rao
Anonymous networks have enabled secure and anonymous communication between the users and service providers while maintaining their anonymity and privacy. The hidden services in the networks are dynamic and continuously change their domains and service features to maintain anonymity and prevent fingerprinting. This makes modelling of such networks a challenging task. Further, modelling with crisp graphs is not suitable as they cannot capture the dynamic nature of the anonymous networks. In this work, we model the anonymous networks using fuzzy graphs and provide a methodology to simulate and analyze an anonymous network. We consider the case studies of two popular anonymous communication networks: Tor and Freenet, and show how the two networks can be analyzed using our proposed fuzzy representation.