With the growing need to comply with privacy regulations and respond to user data deletion requests, integrating machine unlearning into IoT-based federated learning has become imperative. Traditional unlearning methods, however, often lack verifiable mechanisms, leading to challenges in establishing trust. This paper delves into the innovative integration of blockchain technology with federated learning to surmount these obstacles. Blockchain fortifies the unlearning process through its inherent qualities of immutability, transparency, and robust security. It facilitates verifiable certification, harmonizes security with privacy, and sustains system efficiency. We introduce a framework that melds blockchain with federated learning, thereby ensuring an immutable record of unlearning requests and actions. This strategy not only bolsters the trustworthiness and integrity of the federated learning model but also adeptly addresses efficiency and security challenges typical in IoT environments. Our key contributions encompass a certification mechanism for the unlearning process, the enhancement of data security and privacy, and the optimization of data management to ensure system responsiveness in IoT scenarios.
In many smart contract architectures, every contract or object is mutably shared by default. The Sui smart contract platform bears the unique feature of distinguishing between shared and owned objects. While transactions operating on shared objects require consensus to sequence reads and writes, those involving only owned objects are independent and may bypass consensus; thus, the latter are less prone to this throughput bottleneck. However, it may not always be possible or desirable to avoid using shared objects. This article aims at identifying and investigating decentralized applications that require shared objects. Utilizing the Sui Rust SDK to query programmable transaction blocks, we analyze the frequency of transactions involving shared objects, shared resource contention levels, and most “popular” applications that contain shared objects. The presented results are reproducible and show the extensive usage of shared objects in Sui, low contention levels, and moderate dependency among shared objects in atomic transactions. This novel study of shared object use cases in a relatively new smart contract platform is important for improving the efficiency of such object-based architectures. This work is relevant for smart contract platform designers and smart contract developers.
The Internet of Things (IoT) necessitates robust access control mechanisms to secure a vast array of interconnected devices. Most of the existing IoT systems in practice use centralized solutions. We identify the problems in such solutions and adopt the blockchain based decentralized access control approach. Though there are works in the literature that use blockchain for access control, there are some gaps in these works. We develop a blockchain embedded access control (BEAC) framework to bridge the gaps. First, blockchain based solutions for access control require an enabling P2P network while existing P2P overlays do not support some required features. We develop a novel P2P infrastructure to seamlessly support our BEAC framework. Second, most of the works consider blockchain based access control for a single access control model, and we develop a generic blockchain mechanism and show that it can support the embedding of various access control models. Finally, existing works adopt existing blockchain mechanisms which may incur a high communication overhead. We develop a shortcut approach to improve the number of message rounds in the access protocol. Our experiments demonstrate the efficacy of our system, showing that the shortcut mechanism can reduces access time by approximately 43%.
Today, scientific research is increasingly becoming data-centric and compute-intensive, relying on data and models across distributed sources. However, challenges still exist in the traditional cooperation mode, given the high storage and computing costs, geolocation barriers, and local confidentiality regulations. The Jupyter environment has recently emerged and evolved into a vital virtual research environment for scientific computing, which researchers can use to scale computational analyses up to larger datasets and high-performance computing resources. Nevertheless, existing approaches lack robust support of a decentralized cooperation mode to unlock the full potential of decentralized collaborative scientific research, e.g., seamlessly secure data sharing. In this work, we change the basic structure and legacy norms of current research environments via the seamless integration of Jupyter with Ethereum blockchain capabilities. As such, it creates a Decentralized Virtual Research Environment (D-VRE) from private computational notebooks to a decentralized collaborative research ecosystem. We propose a novel architecture for the D-VRE and prototype some essential D-VRE elements for enabling secure data sharing with decentralized identity, user-centric agreement-making, membership, and research asset management. To validate our method, we conduct an experimental study to test all functionalities of D-VRE smart contracts and their gas consumption. In addition, we deploy the D-VRE prototype on a test net of the Ethereum blockchain for demonstration. The feedback from the studies showcases the current prototype's usability, ease of use, and potential, and suggests further improvements.
Sharding is a promising technique for addressing the scalability issues of blockchain, and this technique is especially important for IoT, edge, or mobile computing. It divides the $n$ participating nodes into $s$ disjoint groups called shards, where each shard processes transactions in parallel. We examine batch scheduling problems on the shard graph $G_s$, where we find efficient schedules for a set of transactions. First, we present a centralized scheduler where one of the shards is considered as a leader, who receives the transaction information from all of the other shards and determines the schedule to process the transactions. For general graphs, where a transaction and its accessing objects are arbitrarily far from each other with a maximum distance $d$, the centralized scheduler provides $O(kd)$ approximation to the optimal schedule, where $k$ is the maximum number of shards each transaction accesses. Next, we provide a centralized scheduler with a bucketing approach that offers improved bounds for the case where $G_s$ is a line graph, or the $k$ objects are randomly selected. Finally, we provide a distributed scheduler where shards do not require global transaction information. We achieve this by using a hierarchical clustering of the shards and using the centralized scheduler in each cluster. We show that the distributed scheduler has a competitive ratio of $O(A_{CS} \cdot \log d \cdot \log s)$, where $A_{CS}$ is the approximation ratio of the centralized scheduler. To our knowledge, we are the first to give provably fast transaction scheduling algorithms for blockchain sharding systems. We also present simulation results for our schedulers and compare their performance with a lock-based approach. The results show that our schedulers are generally better with up to 3x lower latency and 2x higher throughput.
Distributed ledger technology such as blockchain is considered essential for supporting large numbers of micro-transactions in the Machine Economy, which is envisioned to involve billions of connected heterogeneous and decentralized cyber-physical systems. This stresses the need for performance and scalability of distributed ledger technologies. Addressing this, sharding techniques that divide the blockchain network into multiple committees are a common approach to improve scalability. However, with current sharding approaches, costly cross-shard verification is needed to prevent double-spending. This article proposes a novel and more scalable distributed ledger method named ScaleGraph that implements dynamic sharding by using routing and logical proximity concepts from distributed hash tables. ScaleGraph addresses cybersecurity in terms of integrity and availability to support frequent micro-transactions between autonomous devices. Benefits of ScaleGraph include a total storage space complexity of \(O(t)\) , where \( t \) is the global number of transactions (assuming a constant replication degree). This space is sharded over \( N \) nodes so that each node needs \(O(t/N)\) storage in expectation, which provides a high level of concurrency and data localization as compared to other delegated consensus proposals. ScaleGraph allows for a dynamic grouping of validators that are selected based on a distance metric. We analyze the consensus requirements in such a dynamic setting and show that a synchronous consensus protocol allows shards to be smaller than an asynchronous one, and likely yields better performance. Moreover, we provide an experimental analysis of security aspects regarding the required size of the consensus groups with ScaleGraph. Our analysis shows that dynamic sharding based on proximity concepts brings attractive scalability properties in general, especially when the fraction of corrupt nodes is small.
Leon Witt, Armando Teles Fortes, Kentaroh Toyoda, Wojciech Samek · 5 authors
Blockchain technology and Artificial Intelligence (AI) have emerged as transformative forces in their respective domains. This paper explores synergies and challenges between these two technologies. Our research analyses the biggest projects combining blockchain and AI, based on market capitalization, and derives a novel framework to categorize contemporary and future use cases. Despite the theoretical compatibility, current real-world applications combining blockchain and AI remain in their infancy.
This paper presents a framework for securing blockchain-based IoT systems by integrating Physical Unclonable Functions (PUFs) and Zero-Knowledge Proofs (ZKPs) within a Hyperledger Fabric environment. Our approach leverages PUFs for robust device authentication and ZKPs for privacy-preserving transaction processing, addressing key challenges of security, privacy, and scalability in IoT systems. The framework’s architecture utilizes Hyperledger Fabric’s modular design and private channels to enhance scalability. Off-chain experimental results demonstrate the framework’s feasibility, with compact proof sizes (median 805 bytes) and efficient processing times (average 2,800 ms end-to-end). A comprehensive security analysis shows the framework’s resilience against various attacks, including device impersonation and data tampering. This work provides a foundation for secure and scalable blockchain-based IoT systems, with directions for future on-chain implementation and optimization for resource-constrained devices.
Open access
3 source records
Blockchain Technology Applications and Security
Physical Unclonable Functions (PUFs) and Hardware Security
Advanced Steganography and Watermarking Techniques
This study proposes a framework to enhance privacy in Blockchain-based Internet of Things (BIoT) systems used in the healthcare sector. The framework addresses the challenge of leveraging health data for analytics while protecting patient privacy. To achieve this, the study integrates Differential Privacy (DP) with Federated Learning (FL) to protect sensitive health data collected by IoT nodes. The proposed framework utilizes dynamic personalization and adaptive noise distribution strategies to balance privacy and data utility. Additionally, blockchain technology ensures secure and transparent aggregation and storage of model updates. Experimental results on the SVHN dataset demonstrate that the proposed framework achieves strong privacy guarantees against various attack scenarios while maintaining high accuracy in health analytics tasks. For 15 rounds of federated learning with an epsilon value of 8.0, the model obtains an accuracy of 64.50%. The blockchain integration, utilizing Ethereum, Ganache, Web3.py, and IPFS, exhibits an average transaction latency of around 6 seconds and consistent gas consumption across rounds, validating the practicality and feasibility of the proposed approach.
We have designed an innovative portfolio rebalancing mechanism termed the Cascading Waterfall Round Robin Mechanism. This algorithmic approach recommends an ideal size and number of trades for each asset during the periodic rebalancing process, factoring in the gas fee and slippage. The essence of the model we have created gives indications regarding whether trades should be made on individual assets depending on the uncertainty in the micro - asset level characteristics - and macro - aggregate market factors - environments. In the hyper-volatile crypto market, our approach to daily rebalancing will benefit from volatility. Price movements will cause our algorithm to buy assets that drop in prices and sell as they soar. In fact, the buying and selling happen only when certain boundaries are crossed in order to weed out any market noise and ensure sound trade execution. We have provided several numerical examples to illustrate the steps - including the calculation of several intermediate variables - of our rebalancing mechanism. The Algorithm we have developed can be easily applied outside blockchain to investment funds across all asset classes at any trading frequency and rebalancing duration. Shakespeare As A Crypto Trader: To Trade Or Not To Trade, that is the Question, Whether an Optimizer can Yield the Answer, Against the Spikes and Crashes of Markets Gone Wild, To Quench One's Thirst before Liquidity Runs Dry, Or Wait till the Tide of Momentum turns Mild.
Peiyao Sheng, Chenyuan Wu, Dahlia Malkhi, Michael K. Reiter · 7 authors
This paper introduces and develops the concept of ``ticketing'', through which atomic broadcasts are orchestrated by nodes in a distributed system. The paper studies different ticketing regimes that allow parallelism, yet prevent slow nodes from hampering overall progress. It introduces a hybrid scheme which combines managed and unmanaged ticketing regimes, striking a balance between adaptivity and resilience. The performance evaluation demonstrates how managed and unmanaged ticketing regimes benefit throughput in systems with heterogeneous resources both in static and dynamic scenarios, with the managed ticketing regime performing better among the two as it adapts better. Finally, it demonstrates how using the hybrid ticketing regime performance can enjoy both the adaptivity of the managed regime and the liveness guarantees of the unmanaged regime.
This paper outlines a method aiming to increase the efficiency of proof-of-work based blockchains using a ticket-based approach. To avoid the limitation of serially adding one block at a time to a blockchain, multiple semi-independent chains are used such that several valid blocks can be added in parallel, when they are added to separate chains. Blocks are added to different chains, the chain index being determined by a ``ticket'' that the miner must produce before creating a new block. This allows increasing the transaction rate by several orders of magnitude while the system is still fully decentralized and permissionless, and maintaining security in the sense that a successful attack would require the attacker to control a significant portion of the whole network.
Abstract. The purpose of a consensus protocol is to keep a distributed network of nodes “in sync,” even in the presence of an unpredictable communication network and adversarial behavior by some of the participating nodes. In the permissionless setting relevant to modern blockchain protocols, these nodes may be operated by a large number of unknown players, with each player free to use multiple identifiers and to start or stop running the protocol at any time. Establishing that a permissionless consensus protocol is “secure” thus requires both a distributed computing argument (that the protocol guarantees consistency and liveness unless the fraction of adversarial participation is sufficiently large) and an economic argument (that carrying out an attack would be prohibitively expensive for a potential attacker). There is a mature toolbox for assembling arguments of the former type; the goal of this paper is to lay the foundations for arguments of the latter type. For example, the Ethereum protocol is oft-claimed to be “more economically secure” after “the merge,” meaning in its current proof-of-stake incarnation relative to the (proof-of-work) original. What, formally, does this assertion mean? Is it true? Could there be alternative protocols that are “still more economically secure” than Ethereum? How do the answers depend on the assumptions imposed on, for example, the reliability of message delivery or the active participation of non-malicious players? An ideal permissionless consensus protocol would, in addition to satisfying standard consistency and liveness guarantees, render consistency violations prohibitively expensive for the attacker without collateral damage to honest participants—for example, by programatically confiscating an attacker’s resources without reducing the value of honest participants’ resources, as is the intention for slashing in a proof-of-stake protocol. We make this idea precise with our notion of the EAAC (expensive to attack in the absence of collapse) property and prove the following results: (1) In the synchronous and dynamically available setting (in which the communication network is reliable but nonmalicious players may be periodically inactive), with an adversary that controls at least one-half of the overall resources, no protocol can be EAAC. In particular, this result rules out EAAC for all typical longest-chain protocols (be they proof-of-work or proof-of-stake). (2) In the partially synchronous and quasi-permissionless setting (in which resource-controlling non-malicious players are always active but the communication network may suffer periods of unreliability), with an adversary that controls at least one-third of the overall resources, no protocol can be EAAC. In particular, slashing in a proof-of-stake protocol cannot achieve its intended purpose if message delays cannot be bounded a priori. (3) In the synchronous and quasi-permissionless setting, there is a proof-of-stake protocol with slashing that, provided the adversary controls less than two-thirds of the overall stake, satisfies the EAAC property. Thus, while only “classical security” is possible in the dynamically available or partially synchronous settings, proof-of-stake protocols with slashing can obtain additional “economic security” in the quasi-permissionless and synchronous settings. All three results are optimal with respect to the size of the adversary. With respect to Ethereum, our work formalizes the potential security benefits of proof-of-stake sybil-resistance coupled with slashing and the common belief that the merge has increased Ethereum’s economic security. Our work also provides mathematical justifications for several key design decisions behind the post-merge Ethereum protocol, ranging from long cooldown periods for unstaking to economic penalties for inactivity.
This article introduces a new asynchronous Byzantine-tolerant asset transfer system (cryptocurrency) with three noteworthy properties: quasi-anonymity, lightness, and consensus-freedom. Quasi-anonymity means no information is leaked regarding the receivers and amounts of the asset transfers. Lightness means that the underlying cryptographic schemes are \textit{succinct}, and each process only stores data polylogarithmic in the number of its own transfers.Consensus-freedom means the system does not rely on a total order of asset transfers. The proposed algorithm is the first asset transfer system that simultaneously fulfills all these properties in the presence of asynchrony and Byzantine processes. To obtain them, the paper adopts a modular approach combining a new distributed object called agreement proofs and well-known techniques such as vector commitments, universal accumulators, and zero-knowledge proofs. The paper also presents a new non-trivial universal accumulator implementation that does not need knowledge of the underlying accumulated set to generate (non-)membership proofs, which could benefit other crypto-based applications.
We present a formal specification for the implementation of Solana virtual machine (SVM) rollups deployed on top of the Solana Layer 1 (L1) blockchain. We further discuss our motivation, implementation, design decisions, limitations, and preliminary results. Overall, this paper is intended to serve as an initial introduction to building such system(s) on top of the Solana L1 blockchain, but does not represent an absolute. Lastly, we comment discuss on extensions of this specification to support SVM rollups on other well-established L1 blockchains systems such as Ethereum.
This paper introduces a novel blockchain-enabled authentication and communications network for scalable Internet of Vehicles, which aims to bolster security and confidentiality, diminish communications latency, and reduce dependence on centralised infrastructures like Certificate Authorities and Public Key Infrastructures by leveraging Blockchain-enabled Domain Name Services and Blockchain-enabled Mutual Authentication. The proposed network is structured into a primary layer, consisting of Road Side Units and edge servers as servers of Blockchain-enabled Domain Name Services for managing inter-vehicle communications identities, and a sub-layer within each vehicle for intra-vehicle communications via the Blockchain-enabled Mutual Authentication Protocol. This design facilitates secure connections across vehicles by coordinating between the layers, significantly improving communications security and efficiency. This study also evaluates Road Side Unit availability against the random distribution of Road Side Units along the route of different vehicles. The proposed model presents a novel pathway towards a decentralised, secure, and efficient Internet of Vehicles ecosystem, contributing to the advancement of autonomous and trustworthy vehicular networks.
The closed architecture of prevailing blockchain systems renders the usage of this technology mostly infeasible for a wide range of real-world problems. Most blockchains trap users and applications in their isolated space without the possibility of cooperating or switching to other blockchains. Therefore, blockchains need additional mechanisms for seamless communication and arbitrary data exchange between each other and external systems. Unfortunately, current approaches for cross-blockchain communication are resource-intensive or require additional blockchains or tailored solutions depending on the applied consensus mechanisms of the connected blockchains. Therefore, we propose an oracle with an off-chain aggregation mechanism based on Zero-Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) to facilitate cross-blockchain communication. The oracle queries data from another blockchain and applies a rollup-like mechanism to move state and computation off-chain. The zkOracle contract only expects the transferred data, an updated state root, and proof of the correct execution of the aggregation mechanism. The proposed solution only requires constant 378 kgas to submit data on the Ethereum blockchain and is primarily independent of the underlying technology of the queried blockchains.
Distributed consensus protocols reach agreement among $n$ players in the presence of $f$ adversaries; different protocols support different values of $f$. Existing works study this problem for different adversary types (captured by threat models). There are three primary threat models: (i) Crash fault tolerance (CFT), (ii) Byzantine fault tolerance (BFT), and (iii) Rational fault tolerance (RFT), each more general than the previous. Agreement in repeated rounds on both (1) the proposed value in each round and (2) the ordering among agreed-upon values across multiple rounds is called Atomic BroadCast (ABC). ABC is more generalized than consensus and is employed in blockchains. This work studies ABC under the RFT threat model. We consider $t$ byzantine and $k$ rational adversaries among $n$ players. We also study different types of rational players based on their utility towards (1) liveness attack, (2) censorship or (3) disagreement (forking attack). We study the problem of ABC under this general threat model in partially-synchronous networks. We show (1) ABC is impossible for $n/3< (t+k) <n/2$ if rational players prefer liveness or censorship attacks and (2) the consensus protocol proposed by Ranchal-Pedrosa and Gramoli cannot be generalized to solve ABC due to insecure Nash equilibrium (resulting in disagreement). For ABC in partially synchronous network settings, we propose a novel protocol \textsf{pRFT}(practical Rational Fault Tolerance). We show \textsf{pRFT} achieves ABC if (a) rational players prefer only disagreement attacks and (b) $t < \frac{n}{4}$ and $(t + k) < \frac{n}{2}$. In \textsf{pRFT}, we incorporate accountability (capturing deviating players) within the protocol by leveraging honest players. We also show that the message complexity of \textsf{pRFT} is at par with the best consensus protocols that guarantee accountability.
May 12, 2024·Proc of the 12th International Conference on Cloud Computing, GRIDs, and Virtualization (Cloud Computing 2021), Porto Portugal, April 2021, pp. 13-17, ISSN 2308-4294
We propose a decentralized authentication system for networks of unmanned aerial vehicles. A blockchain-based public key infrastructure allows the usage of public key cryptography and public key based authentication protocols. The blockchain provides a common storage of the public keys and their relations and can provide the required information for the authentication process. Furthermore, the unmanned aerial vehicles store selected parts of the blockchain in order to operate independently in areas where they might not have access to the Internet. This allows unmanned aerial vehicles to authenticate entities of the network, like other unmanned aerial vehicles, cloud services, cars, and any computer.
Synthetic data generation is increasingly recognized as a crucial solution to address data related challenges such as scarcity, bias, and privacy concerns. As synthetic data proliferates, the need for a robust evaluation framework to select a synthetic data generator becomes more pressing given the variety of options available. In this research study, we investigate two primary questions: 1) How can we select the most suitable synthetic data generator from a set of options for a specific purpose? 2) How can we make the selection process more transparent, accountable, and auditable? To address these questions, we introduce a novel approach in which the proposed ranking algorithm is implemented as a smart contract within a permissioned blockchain framework called Sawtooth. Through comprehensive experiments and comparisons with state-of-the-art baseline ranking solutions, our framework demonstrates its effectiveness in providing nuanced rankings that consider both desirable and undesirable properties. Furthermore, our framework serves as a valuable tool for selecting the optimal synthetic data generators for specific needs while ensuring compliance with data protection principles.
Mitch Jacovetty, Joseph Oglio, Mikhail Nesterenko, Gokarna Sharma
We present TRAIL: an algorithm that uses a novel consensus procedure to tolerate failed or malicious shards within a blockchain-based cryptocurrency. Our algorithm takes a new approach of selecting validator shards for each transaction from those that previously held the assets being transferred. This approach ensures the algorithm's robustness and efficiency. TRAIL is presented using PBFT for internal shard transaction processing and a modified version of PBFT for external cross-shard validation. We describe TRAIL, prove it correct, analyze its message complexity, and evaluate its performance. We propose various TRAIL optimizations: we describe how it can be adapted to other Byzantine-tolerant consensus algorithms, how a complete system may be built on the basis of it, and how TRAIL can be applied to existing and future sharded blockchains.
Sergio Demian Lerner, Ramon Amela, Shreemoy Mishra, Martin Jonáš · 5 authors
BitVMX is a new design for a virtual CPU to optimistically execute arbitrary programs on Bitcoin based on a challenge response game introduced in BitVM. Similar to BitVM1 we create a general-purpose CPU to be verified in Bitcoin script. Our design supports common architectures, such as RISC-V or MIPS. Our main contribution to the state of the art is a design that uses hash chains of program traces, memory mapped registers, and a new challenge-response protocol. We present a new message linking protocol as a means to allow authenticated communication between the participants. This protocol emulates stateful smart contracts by sharing state between transactions. This provides a basis for our verification game which uses a graph of pre-signed transactions to support challenge-response interactions. In case of a dispute, the hash chain of program trace is used with selective pre-signed transactions to locate (via $n$-ary search) and then recover the precise nature of errors in the computation. Unlike BitVM1, our approach does not require the creation of Merkle trees for CPU instructions or memory words. Additionally, it does not rely on signature equivocations. These differences help avoid complexities associated with BitVM1 and make BitVMX a compelling alternative to BitVM2. Our approach is quite flexible, BitVMX can be instantiated to balance transaction cost vs round complexity, prover cost vs verifier cost, and precomputations vs round complexity.
May 9, 2024·Rehak, Rainer (2019) A Trustless Society. A political look at the blockchain vision, BZH Beitraege zur Hochschulforschung, Issue 3/2019, pp. 60-65
A lot of business and research effort currently deals with the so called decentralised ledger technology blockchain. Putting it to use carries the tempting promise to make the intermediaries of social interactions superfluous and furthermore keep secure track of all interactions. Currently intermediaries such as banks and notaries are necessary and must be trusted, which creates great dependencies, as the financial crisis of 2008 painfully demonstrated. Especially banks and notaries are said to become dispensable as a result of using the blockchain. But in real-world applications of the blockchain, the power of central actors does not dissolve, it only shifts to new, democratically illegitimate, uncontrolled or even uncontrollable power centers. As interesting as the blockchain technically is, it doesn't efficiently solve any real-world problem and is no substitute for traditional political processes or democratic regulation of power. Research efforts investigating the blockchain should be halted.
Consensus stands as a fundamental building block for constructing reliable and fault-tolerant distributed services. The increasing demand for high-performance and scalable blockchain protocols has brought attention to solving consensus in scenarios where each participant joins the system knowing only a subset of participants. In such scenarios, the participants' initial knowledge about the existence of other participants can collectively be represented by a directed graph known as knowledge connectivity graph. The Byzantine Fault Tolerant Consensus with Unknown Participants (BFT-CUP) problem aims to solve consensus in those scenarios by identifying the necessary and sufficient conditions that the knowledge connectivity graphs must satisfy when a fault threshold is provided to all participants. This work extends BFT-CUP by eliminating the requirement to provide the fault threshold to the participants. We indeed address the problem of solving BFT consensus in settings where each participant initially knows a subset of participants, and although a fault threshold exists, no participant is provided with this information -- referred to as BFT Consensus with Unknown Participants and Fault Threshold (BFT-CUPFT). With this aim, we first demonstrate that the conditions for knowledge connectivity graphs identified by BFT-CUP are insufficient to solve BFT-CUPFT. Accordingly, we introduce a new type of knowledge connectivity graphs by determining the necessary and sufficient conditions they must satisfy to solve BFT-CUPFT. Furthermore, we design a protocol for solving BFT-CUPFT.