Auditability enables tracking of all read operations performed on a register, allowing data owners to monitor access to their data. This paper explores formal models of single-writer auditable registers and examines their feasibility and synchronization requirements.A natural definition of auditable registers, atomic audit, requires that all write, read, and audit operations be linearized. We show that atomic auditing is a powerful synchronization primitive, as it can be used to solve consensus. The ability to solve consensus with atomic audit depends on the number of readers and auditors: if there is a single reader or a single auditor (the writer), consensus can be solved among two processes. If there are n readers and n auditors, consensus can be solved among n processes. This result highlights the strong synchronization needed to support atomic auditing.We present wait-free implementations of single-writer atomic registers with atomic audit. For multiple readers and a single auditor, our implementation relies on primitives with consensus number 2 (e.g., swap and test&set). When there are n readers and multiple auditors, we introduce an implementation based on (n+1)-sliding registers, which have consensus number n+1.Due to the inherent complexity of atomic auditing, we introduce a weaker definition: regular audit, where audit operations are not linearized with reads and writes. We prove that atomic registers with regular audit can be implemented using standard atomic registers, demonstrating that auditability can be achieved with lower synchronization costs in this weaker model.

In this paper, we propose a methodology to design and analyze the correctness and fairness of committee-based blockchains. We specify the problem that these blockchains implement, specifically, the Byzantine repeated consensus problem. Moreover, we define the problem of fair reward distribution among committee members and study the impact of synchronous assumptions on fairness. It is common knowledge that in permisionless blockchain systems, the main threat is the tragedy of commons that may yield the system to collapse if the rewarding mechanism is not adequate. At minimum, the reward mechanism must be fair, i.e., distribute the rewards in proportion to the merit of the participants. We prove, for the first time in blockchain systems, that in repeated-consensus based blockchains there exists an (eventual) fair rewarding mechanism if and only if the system is (eventual) synchronous.As a case study, we study Tendermint both from Byzantine Repeated Consensus perspective and its fairness with respect to the rewarding of committee members. We prove that in eventual synchronous systems, a modified version of Tendermint solves: (i) one-shot consensus for the validation of one single block with message complexity O(n3) where is the size of the validators set and (ii) a variant of the repeated consensus problem for multiple blocks. Our second contribution is related to the fairness of the Tendermint rewarding mechanism. We show that the rewarding in Tendermint is not fair, but a small modification of Tendermint is eventually fair.

Federated Learning requires secure aggregation to prevent gradient leakage, yet existing protocols suffer from key limitations: they assume synchrony, require heavy peer-to-peer coordination, and do not tolerate aggregators that halt or omit messages. These constraints make current secure aggregation schemes impractical in large-scale, unreliable distributed settings.To overcome these limitations, we introduce a new secure aggregation protocol that operates in fully asynchronous networks, where messages may be arbitrarily delayed, and tolerates fully Byzantine aggregators that are capable of arbitrary deviations including premature halting. Our design combines several key mechanisms: clustering clients under verifiable coordinators, lightweight LWE-based masking (with masking components distributed across aggregators), and differential privacy applied to both intermediary and final aggregated models. We further propose verifiable shuffling of clients across clusters, which prevents any client from being systematically excluded by a Byzantine coordinator, and a fair inclusion mechanism that ensures the inclusion of straggling clients whose messages are late. The protocol eliminates all client-to-client communication, and its communication overhead scales only with the number of aggregators. It also ensures equal representation of clients across rounds, avoiding bias and preventing unbalanced privacy risks among clients. Overall, our protocol provides the first secure aggregation primitive that is both privacy-preserving and robust to fully Byzantine behavior in asynchronous networks, closing the gap between prior secure aggregation assumptions and real-world distributed systems.

We present Ledgera, a distributed validation and traceability system that enables decentralized applications without relying on global consensus. We demonstrate its use through a collaborative fine-tuning workflow in which multiple stakeholders jointly construct training data and produce machine learning models while retaining control over their contributions. Ledgera provides verifiable execution, cryptographic proofs, and contentbased auditability, allowing all artifacts-from data edits to model checkpoints-to be independently verified. The demo illustrates how decentralized AI workflows can achieve strong guarantees of provenance, accountability, and reproducibility without the overhead of blockchain-based approaches.

Blockchain technology offers an immutable record of verified information, which enables its participants to exchange data in a trustless environment. However, providing at once the properties of integrity, verifiability, availability raises challenges in scenarios where data confidentiality must be preserved. While techniques such as data anchoring, zero-knowledge proofs, or homomorphic encryption have been proposed to address these challenges, formalizing their uses in the context of blockchains, into accessible design patterns for non-expert audiences remains underexplored. This paper proposes a comprehensive collection of blockchain patterns addressing confidentiality-related use cases. The patterns are organized into three families: (1) patterns for confidential data sharing; (2) patterns for claim management—including proof issuance and verification—originally introduced in a previous paper and revised herein; and (3) patterns for secure computation over private inputs. This collection provides a conceptual framework that structures and unifies emerging approaches in this fast-evolving area, laying the groundwork for future standardization and implementation efforts. It offers actionable insights for practitioners, combining best practices with architectural guidance for safeguarding data within blockchain systems.

Federated Learning (FL) enables collaborative model training across distributed devices while preserving data privacy. However, its reliance on a centralized aggregator introduces single points of failure and trust concerns. This tutorial explores how decentralization, specifically through blockchain technology, can enhance the reliability and trustworthiness of FL. We will discuss architectural choices for integrating blockchain into FL while minimizing its impact on learning efficiency. In particular, we will examine how to leverage the Cosmos blockchain and its Application Blockchain Interface (ABCI) to achieve decentralized and efficient aggregation, ensuring scalability and security in federated learning systems.

Auditability allows to track all the read operations performed on a register. It abstracts the need of data owners to control access to their data, tracking who read which information. This work considers possible formalizations of auditing and their ramification for the possibility of providing it. The natural definition is to require a linearization of all write, read and audit operations together (atomic auditing). The paper shows that atomic auditing is a powerful tool, as it can be used to solve consensus. The number of processes that can solve consensus using atomic audit depends on the number of processes that can read or audit the register. If there is a single reader or a single auditor (the writer), then consensus can be solved among two processes. If multiple readers and auditors are possible, then consensus can be solved among the same number of processes. This means that strong synchronization primitives are needed to support atomic auditing. We give implementations of atomic audit when there are either multiple readers or multiple auditors (but not both) using primitives with consensus number 2 (swap and fetch add). When there are multiple readers and multiple auditors, the implementation uses compare swap. These findings motivate a weaker definition, in which audit operations are not linearized together with the write and read operations (regular auditing). We prove that regular auditing can be implemented from ordinary reads and writes on atomic registers.

Federated Learning is a decentralized framework that enables multiple clients to collaboratively train a machine learning model under the orchestration of a central server without sharing their local data. The centrality of this framework represents a point of failure which is addressed in literature by blockchain-based federated learning approaches. While ensuring a fully-decentralized solution with traceability, such approaches still face several challenges about integrity, confidentiality and scalability to be practically deployed. In this paper we propose Fantastyc, a solution designed to address these challenges that have been never met together in the state of the art.

An auditable register extends the classical register with an audit operation that returns information on the read operations performed on the register. In this paper, we study Byzantine resilient auditable register implementations in an asynchronous message-passing system. Existing solutions implement the auditable register on top of at least 4f+1 servers, where at most $f$ can be Byzantine. We show that 4f+1 servers are necessary to implement auditability without communication between servers, or implement does not implement strong auditability when relaxing the constraint on the servers' communication, letting them interact with each other. In this setting, it exists a solution using 3f+1 servers to implement a simple auditable atomic register. In this work, we implement strong auditable register using 3f+1 servers with server to server communication, this result reinforced that with communication between servers, auditability (event strong auditability) does not come with an additional cost in terms of the number of servers.

This paper proposes the first implementation of a self-stabilizing regular register emulated by n servers that is tolerant to both Mobile Byzantine Agents and transient failures in a round-free synchronous model. Differently from existing Mobile Byzantine Tolerant register implementations, this paper considers a weaker model where: (i) the computation of the servers is decoupled from the movements of the Byzantine agents, i.e., movements may happen before, concurrently, or after the generation or the delivery of a message, and (ii) servers are not aware of their failure state i.e., they do not know if and when they have been corrupted by a Mobile Byzantine agent. The proposed protocol tolerates (i) any finite number of transient failures, and (ii) up to f Mobile Byzantine agents. In addition, our implementation uses bounded timestamps from the Z13 domain and it is optimal with respect to the number of servers needed to tolerate f Mobile Byzantine agents in the given model (i.e., n>6f when Δ=2δ, and n>8f when Δ=δ, where Δ represents the period at which the Byzantine agents move and δ is the upper bound on the communication latency).

Tendermint, as HotStuff, Diem (ex Libra), Algorand, etc., is a committee-based blockchain where subsets of processes, called committees, use an agreement procedure tolerant to Byzantine behaviors to decide on the next block to add to the blockchain. Tendermint has been the first blockchain proposing such a committee-based approach, where committees are selected on the basis of the participants' stake. Tendermint agreement procedure takes inspiration from classical Byzantine fault-tolerant (BFT) consensus distributed algorithms, which allows to formalize and prove its safety and liveness following distributed computing theory's tools and methodology. In this chapter, we present the Tendermint platform and architecture, alongside a deep analysis of Tendermint core distributed algorithms. In this respect, we show the differences between the first implemented algorithm which contained a very subtle design bug-hindering liveness and the current, correct algorithm where the bug has been solved.

An auditable register extends the classical register with an audit operation that returns information on the read operations performed on the register. In this paper, we study Byzantine resilient auditable registers implementations in an asynchronous message-passing system. Existing solutions implement the auditable register on top of at least $4\mathrm{f}+1$ servers, where at most $f$ can be Byzantine. We show that $4\mathrm{f}+1$ servers are necessary to implement auditability without communication between servers. Then, we pursue the study by relaxing the constraint on the servers' communication, letting them interact with each other. In this setting, we prove that $3\mathrm{f}+1$ servers are sufficient. This result establishes that with communication between servers, auditability does not come with an additional cost in terms of the number of servers.

Topos is an open interoperability protocol designed to reduce as much as possible trust assumptions by replacing them with cryptographic constructions and decentralization while exhibiting massive scalability. The protocol does not make use of a central blockchain, nor uses consensus to ensure consistent delivery of messages across a heterogeneous ecosystem of public and private blockchains, named subnets, but instead relies on a weak causal reliable broadcast implemented by a distributed network which we call $\textit{Transmission Control Engine}$ (TCE). The validity of cross-subnet messages is ensured by the $\textit{Universal Certificate Interface}$ (UCI) and stems from zkSTARK proofs asserting the validity of subnets' state transitions executed by the Topos zkVM. Such proofs of computational integrity are publicly verifiable by any other participants in and out the protocol such as other subnets or audit companies. The interface between the TCE and subnets leverages the ICE-FROST protocol, an innovative threshold signature scheme, whose static public key allows for uniquely identifying subnets after they register in the protocol. The Topos protocol is designed to provide $\textit{uniform security}$ to the ecosystem and to handle any type of subnets (e.g., permissioned, permissionless) in order to fit any business use cases and pave the way for global adoption and a new standard for the Internet base layer.

This work investigates the Fork Accountability problem in the BFT-Consensus-based Blockchain context. When there are more attackers than the tolerated ones, BFT-Consensus may fail in delivering safety. When this occurs, Fork Accountability aims to account for the responsible processes for that safety violation. As a case study, we consider Tenderbake when the assumption on the maximum number of Byzantine validators – participants involved in creating the next block – does not hold anymore. When a fork occurs, there are more than one-third of Byzantine validators, and we aim to account for the responsible validators to remove them from the system. In this work, we compare three different approaches to implementing accountability in the case of a fork. In particular, we show that in the case of a fork, if we do not modify Tenderbake or we enrich it with a reliable broadcast communication abstraction, then we can account Byzantine processes only in particular scenarios. Contrarily, if we change Tenderbake such that the exchanged messages also carry extra information (which size is proportional to the duration of the current consensus computation), then we can account for Byzantine processes in all kinds of scenarios; however, at the cost of unbounded message size and unbounded local memory.

This paper revisits the ubiquitous problem of achieving state machine replication in blockchains based on repeated consensus, like Tendermint. To achieve state machine replication in blockchains built on top of consensus, one needs to guarantee fairness of user transactions. A huge body of work has been carried out on the relation between state machine replication and consensus in the past years, in a variety of system models and with respect to varied problem specifications. We systematize this work by proposing novel and rigorous abstractions for state machine replication and repeated consensus in a system model that accounts for realistic blockchains in which blocks may contain several transactions issued by one or more users, and where validity and order of transactions within a block is determined by an external application-dependent function that can capture various approaches for order-fairness in the literature. Based on these abstractions, we propose a reduction from state machine replication to repeated consensus, such that user fairness is achieved using the consensus module as a black box. This approach allows to achieve fairness as an add-on on top of preexisting consensus modules in blockchains based on repeated consensus.

First-generation blockchains provide probabilistic finality: a block can be revoked, albeit the probability decreases as the block sinks deeper into the chain. Recent proposals revisited committee-based BFT consensus to provide deterministic finality: as soon as a block is validated, it is never revoked. A distinguishing characteristic of these second-generation blockchains over classical BFT protocols is that committees change over time as the participation and the blockchain state evolve. In this paper, we push forward in this direction by proposing a formalization of the Dynamic Repeated Consensus problem and by providing generic procedures to solve it in the context of blockchains. Our approach is modular in that one can plug in different synchronizers and single-shot consensus instances. To offer a complete solution, we provide a concrete instantiation, called Tenderbake, and present a blockchain synchronizer and a single-shot consensus algorithm, working in a Byzantine and partially synchronous system model with eventually synchronous clocks. In contrast to recent proposals, our methodology is driven by the need to bound the message buffers. This is essential in preventing spamming and run-time memory errors. Moreover, Tenderbake processes can synchronize with each other without exchanging messages, leveraging instead the information stored in the blockchain.

In this paper we analyze Tendermint proposed in [10], one of the most popular blockchains based on PBFT Consensus. Our methodology consists in identifying the algorithmic principles of Tendermint necessary for a specific communication model. The current paper dissects Tendermint under two system communication models: synchronous and eventually synchronous communication models. This methodology allowed to identify bugs [6] in preliminary versions of the protocol ([21], [10]) and to prove its correctness under the most adversarial conditions: an eventually synchronous communication model and Byzantine faults.

The presented work continues the line of recent distributed computing communityefforts dedicated to the theoretical aspects of blockchains. This paper is the rst tospecify blockchains as a composition of abstract data types all together with a hierarchyof consistency criteria that formally characterizes the histories admissible for distributedprograms that use them. Our work is based on an original oracle-based constructionthat, along with new consistency deffnitions, captures the eventual convergence processin blockchain systems. The paper presents as well some results on implementability ofthe presented abstractions and a mapping of representative existing blockchains fromboth academia and industry in our framework.