Luca Zanolini

Luca Zanolini

Researcher at the Ethereum Foundation. PhD in Computer Science.

Evolution of the Ethereum Proof-of-Stake Consensus Protocol

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Curious to know how the Ethereum proof-of-stake protocol, Gasper, evolved over the years?

In order to better understand the currently implemented proof-of-stake consensus protocol of Ethereum, we start by presenting the original protocol, Gasper, by Buterin et al. In particular, in the first part, we highlight its underlying components and we formally present its properties. In the second part we analyze some of the most important problems faced by Gasper, and we present the current solutions that have been devised to cope with them.

Part 1

Part 2

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Quorum systems in permissionless networks

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Fail-prone systems, and their quorum systems, are useful tools for the design of distributed algorithms. However, fail-prone systems as studied so far require every process to know the full system membership in order to guarantee safety through globally intersecting quorums. Thus, they are of little help in an open, permissionless setting, where such knowledge may not be available. We propose to generalize the theory of fail-prone systems to make it applicable to permissionless systems. We do so by enabling processes not only to make assumptions about failures, but also to make assumptions about the assumptions of other processes. Thus, by transitivity, processes that do not even know of any common process may nevertheless have intersecting quorums and solve, for example, reliable broadcast. Our model generalizes existing models such as the classic fail-prone system model [Malkhi and Reiter, 1998] and the asymmetric fail-prone system model [Cachin and Tackmann, OPODIS 2019]. Moreover, it gives a characterization with standard formalism of the model used by the Stellar blockchain.

Quick Fair Order

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Leader-based protocols for consensus, i.e., atomic broadcast, allow some processes to unilaterally affect the final order of transactions. This has become a problem for blockchain networks and decentralized finance because it facilitates front-running and other attacks. To address this, order fairness for payload messages has be en introduced recently as a new safety property for atomic broadcast complementing traditional agreement and liveness. We relate order fairness to the standard validity notions for consensus protocols and highlight some limitations with the existing formalization. Based on this, we introduce a new differential order fairness property that fixes these issues. We also present the quick order-fair atomic broadcast protocol that guarantees payload message delivery in a differentially fair order and is much more efficient than existing order-fair consensus protocols. It works for asynchronous and for eventually synchronous networks with optimal resilience, tolerating corruptions of up to one third of the processes. Previous solutions required there to be less than one fourth of faults. Furthermore, our protocol incurs only quadratic cost, in terms of amortized message complexity per delivered payload.

How to Trust Strangers

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Trust is the basis of any distributed, fault-tolerant, or secure system. A trust assumption specifies the failures that a system, such as a blockchain network, can tolerate and determines the conditions under which it operates correctly. In systems subject to Byzantine faults, the trust assumption is usually specified through sets of processes that may fail together. Trust has traditionally been symmetric, such that all processes in the system adhere to the same, global assumption about potential faults. Recently, asymmetric trust models have also been considered, especially in the context of blockchains, where every participant is free to choose who to trust. In both cases, it is an open question how to compose trust assumptions. Consider two or more systems, run by different and possibly disjoint sets of participants, with different assumptions about faults: how can they work together? This work answers this question for the first time and offers composition rules for symmetric and for asymmetric quorum systems. These rules are static and do not require interaction or agreement on the new trust assumption among the participants. Moreover, they ensure that if the original systems allow for running a particular protocol (guaranteeing consistency and availability), then so will the joint system. At the same time, the composed system tolerates as many faults as possible, subject to the underlying consistency and availability properties. Reaching consensus with asymmetric trust in the model of personal Byzantine quorum systems (Losa et al., DISC 2019) was shown to be impossible, if the trust assumptions of the processes diverge from each other. With asymmetric quorum systems, and by applying our composition rule, we show how consensus is actually possible, even with the combination of disjoint sets of processes.

Revisiting signature-free asynchronous Byzantine consensus

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Among asynchronous, randomized, and signature-free implementations of consensus, the protocols of Mostéfaoui et al. (PODC 2014 and JACM 2015) represent a landmark result, which has been extended later and taken up in practical systems. The protocols achieve optimal resilience and take, in expectation, only a constant expected number of rounds and have quadratic message complexity. Randomization is provided through a common-coin primitive. However, the first version of this simple and appealing protocol suffers from a little-known liveness issue due to asynchrony. The JACM 2015 version avoids the problem, but is considerably more complex.