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Ethereum has undergone a recent change called \textit{the Merge}, which made Ethereum a Proof-of-Stake blockchain shifting closer to BFT consensus. Ethereum, which wished to keep the best of the two protocols designs (BFT and Nakomoto-style), now has an involved consensus protocol as its core. The result is a blockchain being possibly produced in a tree-like form while participants try to finalize blocks. Several attacks jeopardizing liveness have been found in this new setting. The Ethereum community has responded by creating a patch. We discovered a new attack on the patched protocol. To support our analysis, we propose a new formalization of the properties of liveness and availability of the Ethereum blockchain, and we provide a pseudo-code. We believe this formalization to be helpful for other analyses as well. Our results yield that the Ethereum Proof-of-Stake has probabilistic liveness, influenced by the parameter describing the time frame allowed for validators to change their mind about the current main chain.

In a single secret leader election protocol (SSLE), one of the system participants is chosen and, unless it decides to reveal itself, no other participant can identify it. SSLE has a great potential in protecting blockchain consensus protocols against denial of service (DoS) attacks. However, all existing solutions either make strong synchrony assumptions or have expiring registration, meaning that they require elected processes to re-register themselves before they can be re-elected again. This, in turn, prohibits the use of these SSLE protocols to elect leaders in partially-synchronous consensus protocols as there may be long periods of network instability when no new blocks are decided and, thus, no new registrations (or re-registrations) are possible. In this paper, we propose Homomorphic Sortition -- the first asynchronous SSLE protocol with non-expiring registration, making it the first solution compatible with partially-synchronous leader-based consensus protocols. Homomorphic Sortition relies on Threshold Fully Homomorphic Encryption (ThFHE) and is tailored to proof-of-stake (PoS) blockchains, with several important optimizations with respect to prior proposals. In particular, unlike most existing SSLE protocols, it works with arbitrary stake distributions and does not require a user with multiple coins to be registered multiple times. Our protocol is highly parallelizable and can be run completely off-chain after setup. Some blockchains require a sequence of rounds to have non-repeating leaders. We define a generalization of SSLE, called Secret Leader Permutation (SLP) in which the application can choose how many non-repeating leaders should be output in a sequence of rounds and we show how Homomorphic Sortition also solves this problem.

In the industry, blockchains are increasingly used as the backbone of product and process traceability. Blockchain-based traceability participates in the demonstration of product and/or process compliance with existing safety standards or quality criteria. In this perspective, services and applications built on top of blockchains are business-critical applications, because an intended failure or corruption of the system can lead to an important reputation loss regarding the products or the processes involved. The development of a blockchain-based business-critical application must be then conducted carefully, requiring a thorough justification of its dependability and security. To this end, this paper encourages an engineering perspective rooted in well-understood tools and concepts borrowed from the engineering of safety-critical systems. Concretely, we use a justification framework, called CAE (Claim, Argument, Evidence), by following an approach based on assurance cases, in order to provide convincing arguments that a business-critical blockchain-based application is dependable and secure. The application of this approach is sketched with a case study based on the blockchain HYPERLEDGER FABRIC., 8 pages, 6 figures, The Third IEEE International Conference on Blockchain Computing and Applications (BCCA 2021)

The paper presents Pluralize a formal logical framework able to extend the execution of blockchain transactions to events coming from external oracles, like external time, sensor data, human-made declarations, etc. These events are by essence non-reliable, since transaction execution can be triggered by information whose veracity cannot be established by the blockchain. To overcome this problem, the language features a first-order logic and an authority algebra to allow formal reasoning and establish accountability of agents for blockchain-enabled transactions. We provide an accountability model that allows to formally prove the accountability of agents by a formal proof locally executable by each agent of the blockchain.

Since the invention of Bitcoin one decade ago, numerous cryptocurrencies have sprung into existence. Among these, proof-of-work is the most common mechanism for achieving consensus, whilst a number of coins have adopted "ASIC-resistance" as a desirable property, claiming to be more "egalitarian,"S where egalitarianism refers to the power of each coin to participate in the creation of new coins. While proof-of-work consensus dominates the space, several new cryptocurrencies employ alternative consensus, such as proof-of-stake in which block minting opportunities are based on monetary ownership. A core criticism of proof-of-stake revolves around it being less egalitarian by making the rich richer, as opposed to proof-of-work in which everyone can contribute equally according to their computational power. In this paper, we give the first quantitative definition of a cryptocurrency's \emph{egalitarianism}. Based on our definition, we measure the egalitarianism of popular cryptocurrencies that (may or may not) employ ASIC-resistance, among them Bitcoin, Ethereum, Litecoin, and Monero. Our simulations show, as expected, that ASIC-resistance increases a cryptocurrency's egalitarianism. We also measure the egalitarianism of a stake-based protocol, Ouroboros, and a hybrid proof-of-stake/proof-of-work cryptocurrency, Decred. We show that stake-based cryptocurrencies, under correctly selected parameters, can be perfectly egalitarian, perhaps contradicting folklore belief., Comment: 29 pages, 4 figures, Tokenomics 2019