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 ( n 3 ) 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.

Ethereum has undergone a recent change called the Merge , which made Ethereum a Proof-of-Stake blockchain shifting closer to BFT consensus. Ethereum, which wishes to keep the best of the two protocol designs (BFT and Nakomoto-style), now has a convoluted consensus protocol as its core. The result is a blockchain possibly being produced in a tree-like form while participants try to finalize blocks. We categorize different attacks jeopardizing the liveness of the protocol. The Ethereum community has responded by creating patches against some of them. We discovered a new attack on the patched protocol. To support our analysis, we propose a new high-level formalization of the properties of liveness and availability of the Ethereum blockchain, and we provide pseudo-code. We believe this formalization to be useful for other analyses as well. Our results yield that the Ethereum Proof-of-Stake has safety but only probabilistic liveness. The probability of the liveness is influenced by the parameter describing the time frame allowed for validators to change their mind about the current main chain.

In May 2023, the Ethereum blockchain experienced its first inactivity leak, a mechanism designed to reinstate chain finalization amid persistent network disruptions. This mechanism aims to reduce the voting power of validators who are unreachable within the network, reallocating this power to active validators. This paper investigates the implications of the inactivity leak on safety within the Ethereum blockchain. Our theoretical analysis reveals scenarios where actions by Byzantine validators expedite the finalization of two conflicting branches, and instances where Byzantine validators reach a voting power exceeding the critical safety threshold of one-third. Additionally, we revisit the probabilistic bouncing attack, illustrating how the inactivity leak can result in a probabilistic breach of safety, potentially allowing Byzantine validators to exceed the one-third safety threshold. Our findings uncover how penalizing inactive nodes can compromise blockchain properties, particularly in the presence of Byzantine validators capable of coordinating actions.

This paper investigates whether following the fork-choice rule in the Ethereum PoS consensus protocol constitutes a Nash equilibrium - i.e., whether the protocol that maintains the canonical chain in Ethereum is incentive-compatible. Specifically, we explore whether selfish participants may attempt to manipulate the fork-choice rule by forking out previous blocks and capturing the rewards associated with those blocks. Our analysis considers two strategies for participants: the obedient strategy, which adheres to the prescribed protocol, and the cunning strategy, which attempts to manipulate the fork-choice rule to gain more rewards. We evaluate the conditions under which selfish participants might deviate from the obedient strategy. We found that, in a synchronous system, following the prescribed fork-choice rule is incentive-compatible. However, in an eventually synchronous system, the protocol is eventually incentive-compatible - that is, only a limited number of proposers will find it profitable to fork the chain during the synchronous period. After this sequence of cunning proposers, subsequent proposers will find it more profitable to follow the protocol.

International audience

Committee-based blockchains are among the most popular alternatives of proof-of-work based blockchains, such as Bitcoin. They provide strong consistency (no fork) under classical assumptions, and avoid using energy-consuming mechanisms to add new blocks in the blockchain. For each block, these blockchains use a committee that executes Byzantine-fault tolerant distributed consensus to decide the next block they will add in the blockchain. Unlike Bitcoin, where there is only one creator per block, in committee-based blockchain any block is cooperatively created. In order to incentivize committee members to participate in the creation of new blocks, rewarding schemes have to be designed. In this paper, we study the fairness of rewarding in committee-based blockchains and we provide necessary and sufficient conditions on the system communication under which it is possible to have a fair reward mechanism.