The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications ranging from channel communication to identifying COVID-19-infected individuals efficiently. Despite significant research on group testing and its variants since the 1940s, testing strategies robust to deletion noise have yet to be studied. Many practical systems exhibit deletion errors, for instance, in wireless communication and data storage systems. Such deletions of test outcomes lead to asynchrony between the tests, which the current group testing strategies cannot handle. In this work, we initiate the study of non-adaptive group testing strategies resilient to deletion noise. We characterize the necessary and sufficient conditions to successfully identify the defective items even after the adversarial deletion of certain test outputs. We also provide constructions of testing matrices along with an efficient recovery algorithm.

This work focuses on non-adaptive group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of elements using the fewest possible number of tests. Non-adaptive combinatorial group testing often employs disjunctive codes and union-free codes. This paper discusses union-free codes with fast decoding (UFFD codes), a recently introduced class of union-free codes that combine the best of both worlds -- the linear complexity decoding of disjunctive codes and the fewest number of tests of union-free codes. In our study, we distinguish two subclasses of these codes -- one subclass, denoted as $(=d)$-UFFD codes, can be used when the number of defectives $d$ is a priori known, whereas $(\le d)$-UFFD codes works for any subset of at most$d$ defectives. Previous studies have established a lower bound on the rate of these codes for $d=2$. Our contribution lies in deriving new lower bounds on the rate for both $(=d)$- and $(\le d)$-UFFD codes for an arbitrary number $d \ge 2$ of defectives. Our results show that for $d\to\infty$, the rate of $(=d)$-UFFD codes is twice as large as the best-known lower bound on the rate of $d$-disjunctive codes. In addition, the rate of $(\le d)$-UFFD code is shown to be better than the known lower bound on the rate of $d$-disjunctive codes for small values of $d$.

Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites. In this paper, we will showcase a technique that will eliminate the first phase of the primality testing algorithms. The computational simulations show a reduction of the primality generation time by about 30% in the case of 1024-bit RSA key pairs. This can be particularly beneficial in the case of decentralized environments for shared RSA keys as the initial trial division part of the key generation algorithms can be avoided at no cost. This also significantly reduces the communication complexity. Another essential contribution of the paper is the introduction of a new one-way function that is computationally simpler than the existing ones used in public-key cryptography. This function can be used to create new random number generators, and it also could be potentially used for designing entirely new public-key encryption systems.

Following the design of more efficient blockchain consensus algorithms, the execution layer has emerged as the new performance bottleneck of blockchains, especially under high contention. Current parallel execution frameworks either rely on optimistic concurrency control (OCC) or on pessimistic concurrency control (PCC), both of which see their performance decrease when workloads are highly contended, albeit for different reasons. In this work, we present NEMO, a new blockchain execution engine that combines OCC with the object data model to address this challenge. NEMO introduces four core innovations: (i) a greedy commit rule for transactions using only owned objects; (ii) refined handling of dependencies to reduce re-executions; (iii) the use of incomplete but statically derivable read/write hints to guide execution; and (iv) a priority-based scheduler that favors transactions that unblock others. Through simulated execution experiments, we demonstrate that NEMO significantly reduces redundant computation and achieves higher throughput than representative approaches. For example, with 16 workers NEMO's throughput is up to 42% higher than the one of Block-STM, the state-of-the-art OCC approach, and 61% higher than the pessimistic concurrency control baseline used.

This paper investigates the issue of fairness in Distributed Ledger Technology (DLT), specifically focusing on the shortcomings observed in current blockchain systems due to Miner Extractable Value (MEV) phenomena and systemic centralization. We explore the potential of Directed Acyclic Graphs (DAGs) as a solution to address or mitigate these fairness concerns. Our objective is to gain a comprehensive understanding of fairness in DAG-based DLTs by examining its different aspects and measurement metrics. We aim to establish a shared knowledge base that facilitates accurate fairness assessment and allows for an evaluation of whether DAG-based DLTs offer a more equitable design. We describe the various dimensions of fairness and conduct a comparative analysis to examine how they relate to different components of DLTs. This analysis serves as a catalyst for further research, encouraging the development of cryptographic systems that promote fairness.

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.

In the Internet of Things (IoT) domain, devices need a platform to transact seamlessly without a trusted intermediary. Although Distributed Ledger Technologies (DLTs) could provide such a platform, blockchains, such as Bitcoin, were not designed with IoT networks in mind, hence are often unsuitable for such applications: they offer poor transaction throughput and confirmation times, put stress on constrained computing and storage resources, and require high transaction fees. In this work, we consider a class of IoT-friendly DLTs based on directed acyclic graphs, rather than a blockchain, and with a reputation system in the place of Proof of Work (PoW). However, without PoW, implementation of these DLTs requires an access control algorithm to manage the rate at which nodes can add new transactions to the ledger. We model the access control problem and present an algorithm that is fair, efficient and secure. Our algorithm represents a new design paradigm for DLTs in which concepts from networking are applied to the DLT setting for the first time. For example, our algorithm uses distributed rate setting which is similar in nature to transmission control used in the Internet. However, our solution features novel adaptations to cope with the adversarial environment of DLTs in which no individual agent can be trusted. Our algorithm guarantees utilisation of resources, consistency, fairness, and resilience against attackers. All of this is achieved efficiently and with regard for the limitations of IoT devices. We perform extensive simulations to validate these claims.

Distributed Ledger Technologies (DLTs) promise decentralization, transparency, and security, yet the reality often falls short due to fundamental governance flaws. Poorly designed governance frameworks leave these systems vulnerable to coercion, vote-buying, centralization of power, and malicious protocol exploits: threats that undermine the very principles of fairness and equity these technologies seek to uphold. This paper surveys the state of DLT governance, identifies critical vulnerabilities, and highlights the absence of universally accepted best practices for good governance. By bridging insights from cryptography, social choice theory, and e-voting systems, we not only present a comprehensive taxonomy of governance properties essential for safeguarding DLTs but also point to technical solutions that can deliver these properties in practice. This work underscores the urgent need for robust, transparent, and enforceable governance mechanisms. Ensuring good governance is not merely a technical necessity but a societal imperative to protect the public interest, maintain trust, and realize the transformative potential of DLTs for social good.

This paper introduces Slipstream, a Byzantine Fault Tolerance (BFT) protocol where nodes concurrently propose blocks to be added to a Directed Acyclic Graph (DAG) and aim to agree on block ordering. Slipstream offers two types of block orderings: an optimistic ordering, which is live and secure in a sleepy model under up to 50% Byzantine nodes, and a final ordering, which is a prefix of the optimistic ordering and ensures safety and liveness in an eventual lock-step synchronous model under up to 33% Byzantine nodes. Additionally, Slipstream integrates a payment system that allows for fast UTXO transaction confirmation independently of block ordering. Transactions are confirmed in three rounds during synchrony, and unconfirmed double spends are resolved in a novel way using the DAG structure.

This paper is a Systematization of Knowledge (SoK) on Directed Acyclic Graph (DAG)-based consensus protocols, analyzing their performance and trade-offs within the framework of consistency, availability, and partition tolerance inspired by the CAP theorem. We classify DAG-based consensus protocols into availability-focused and consistency-focused categories, exploring their design principles, core functionalities, and associated trade-offs. Furthermore, we examine key properties, attack vectors, and recent developments, providing insights into security, scalability, and fairness challenges. Finally, we identify research gaps and outline directions for advancing DAG-based consensus mechanisms.

An $n$-vertex graph $G$ is weakly $F$-saturated if $G$ contains no copy of $F$ and there exists an ordering of all edges in $E(K_n) \setminus E(G)$ such that, when added one at a time, each edge creates a new copy of $F$. The minimum size of a weakly $F$-saturated graph $G$ is called the weak saturation number $\mathrm{wsat}(n, F)$. We obtain exact values and new bounds for $\mathrm{wsat}(n, K_{s,t})$ in the previously unaddressed range s+t < n < 3t-3, where $3\leq s\leq t$. To prove lower bounds, we introduce a new method that takes into account connectivity properties of subgraphs of a complement $G'$ to a weakly saturated graph $G$. We construct an auxiliary hypergraph and show that a linear combination of its parameters always increases in the process of the deletion of edges of $G'$. This gives a lower bound which is tight, up to an additive constant.

This paper introduces a novel caching analysis that, contrary to prior work, makes no modeling assumptions for the file request sequence. We cast the caching problem in the framework of Online Linear Optimization (OLO), and introduce a class of minimum regret caching policies, which minimize the losses with respect to the best static configuration in hindsight when the request model is unknown. These policies are very important since they are robust to popularity deviations in the sense that they learn to adjust their caching decisions when the popularity model changes. We first prove a novel lower bound for the regret of any caching policy, improving existing OLO bounds for our setting. Then we show that the Online Gradient Ascent (OGA) policy guarantees a regret that matches the lower bound, hence it is universally optimal. Finally, we shift our attention to a network of caches arranged to form a bipartite graph, and show that the Bipartite Subgradient Algorithm (BSA) has no regret

This paper presents a novel leaderless protocol (FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures) with a low communicational complexity and which allows a set of nodes to come to a consensus on a value of a single bit. The paper makes the assumption that part of the nodes are Byzantine, and are thus controlled by an adversary who intends to either delay the consensus, or break it (this defines that at least a couple of honest nodes come to different conclusions). We prove that, nevertheless, the protocol works with high probability when its parameters are suitably chosen. Along this the paper also provides explicit estimates on the probability that the protocol finalizes in the consensus state in a given time. This protocol could be applied to reaching consensus in decentralized cryptocurrency systems. A special feature of it is that it makes use of a sequence of random numbers which are either provided by a trusted source or generated by the nodes themselves using some decentralized random number generating protocol. This increases the overall trustworthiness of the infrastructure. A core contribution of the paper is that it uses a very weak consensus to obtain a strong consensus on the value of a bit, and which can relate to the validity of a transaction.

Consensus plays a crucial role in distributed ledger systems, impacting both scalability and decentralization. Many blockchain systems use a weighted lottery based on a scarce resource such as a stake, storage, memory, or computing power to select a committee whose members drive the consensus and are responsible for adding new information to the ledger. Therefore, ensuring a robust and fair committee selection process is essential for maintaining security, efficiency, and decentralization. There are two main approaches to randomized committee selection. In one approach, each validator candidate locally checks whether they are elected to the committee and reveals their proof during the consensus phase. In contrast, in the second approach, a sortition algorithm decides a fixed-sized committee that is globally verified. This paper focuses on the latter approach, with cryptographic sortition as a method for fair committee selection that guarantees a constant committee size. Our goal is to develop deterministic guarantees that strengthen decentralization. We introduce novel methods that provide deterministic bounds on the influence of adversaries within the committee, as evidenced by numerical experiments. This approach overcomes the limitations of existing protocols that only offer probabilistic guarantees, often providing large committees that are impractical for many quorum-based applications like atomic broadcast and randomness beacon protocols.

Rapidly growing distributed ledger technologies (DLTs) have recently received attention among researchers in both industry and academia. While a lot of existing analysis (mainly) of the Bitcoin and Ethereum networks is available, the lack of measurements for other crypto projects is observed. This article addresses questions about tokenomics and wealth distributions in cryptocurrencies. We analyze the time-dependent statistical properties of top cryptocurrency holders for 14 different distributed ledger projects. The provided metrics include approximated Zipf coefficient, Shannon entropy, Gini coefficient, and Nakamoto coefficient. We show that there are quantitative differences between the coins (cryptocurrencies operating on their own independent network) and tokens (which operate on top of a smart contract platform). Presented results show that coins and tokens have different values of approximated Zipf coefficient and centralization levels. This work is relevant for DLTs as it might be useful in modeling and improving the committee selection process, especially in decentralized autonomous organizations (DAOs) and delegated proof of stake (DPoS) blockchains.

DAG-based DLTs allow for parallel, asynchronous writing access to a ledger. Consequently, the perception of the most recent blocks may differ considerably between nodes, and the underlying network properties of the P2P layer have a direct impact on the performance of the protocol. Moreover, the stronger inter-dependencies of several core components demand a more complex and complete approach to studying such DLTs. This paper presents an agent-based, open-sourced simulator for large-scale networks that implement the leaderless Tangle 2.0 consensus protocol. Its scope includes modelling the underlying peer-to-peer communication with network topology, package loss, heterogeneous latency, the gossip protocol with reliable broadcast qualities, the underlying DAG-based data structure, and the consensus protocol. The simulator allows us to explore the performance of the protocol in different network environments, as well as different attack scenarios.

A significant portion of research on distributed ledgers has focused on circumventing the limitations of leader-based blockchains mainly in terms of scalability, decentralization and power consumption. Leaderless architectures based on directed acyclic graphs (DAGs) avoid many of these limitations altogether, but their increased flexibility and performance comes at the cost of increased design complexity, so their potential has remained largely unexplored. Management of write access to these ledgers presents a major challenge because ledger updates may be made in parallel, hence transactions cannot simply be serialised and prioritised according to token fees paid to validators. In this work, we propose an access control scheme for leaderless DAG-based ledgers which is based on consuming credits rather than paying fees in the base token. We outline a general model for this new approach and provide some simulation results showing promising performance boosts.