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Simplex Consensus: A Simple and Fast Consensus Protocol

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14372))

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Abstract

We present a theoretical framework for analyzing the efficiency of consensus protocols, and apply it to analyze the optimistic and pessimistic confirmation times of state-of-the-art partially-synchronous protocols in the so-called “rotating leader/random leader” model of consensus (recently popularized in the blockchain setting).

We next present a new and simple consensus protocol in the partially synchronous setting, tolerating \(f < n/3\) byzantine faults; in our eyes, this protocol is essentially as simple to describe as the simplest known protocols, but it also enjoys an even simpler security proof, while matching and, even improving, the efficiency of the state-of-the-art (according to our theoretical framework).

As with the state-of-the-art protocols, our protocol assumes a (bare) PKI, a digital signature scheme, collision-resistant hash functions, and a random leader election oracle, which may be instantiated with a random oracle (or a CRS).

B. Y. Chan—Supported in part by NSF CNS-2128519, NSF Award RI-1703846 and AFOSR Award FA9550-18-1-0267.

R. Pass—Supported in part by NSF Award RI-1703846, AFOSR Award FA9550-18-1-0267, a JP Morgan Faculty Award and an award from the Algorand Foundation.

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Notes

  1. 1.

    As usual, the model can also be extended a more general model where liveness hold during “periods of synchrony”; for simplicity, we ignore this distinction.

  2. 2.

    See the related notion of chain quality [32], which (informally) requires that any sufficiently long chain contain a large fraction of blocks that are mined by honest parties.

  3. 3.

    We may also consider an expected worst-case confirmation time, where, for any transaction arrival time t after \(\textsf {GST}\), both fixed ahead of time, a transaction must be finalized soon after t in expectation over the coins of the execution. Such a bound may be useful to capture real-world liveness, but is typically difficult to analyze in a setting where the adversary can control the scheduling of messages.

  4. 4.

    While the version of Algorand agreement in [28] is not optimistically responsive, it can be easily made so if every period has a unique leader known ahead of time (provided by a leader election oracle in lieu of using a VRF). Then, players can simply ‘soft-vote’ immediately on seeing a proposal from the leader, and ‘cert-vote’ immediately on seeing 2n/3 soft-votes, much like in PBFT.

  5. 5.

    We do not consider optimizations of the variety made in Parametrized FaB Paxos [49] and SBFT [36], where if \(f < (n+2)/5\), a proposal confirmation time of \(2\delta \) is possible without affecting worst-case fault tolerance. We are particularly interested in the case when leaders are honest, but 1/3 of voters are not.

  6. 6.

    Here, Chained Hotstuff is analyzed using a timeout-based pacemaker from LibraBFT [11] and a timeout of \(3\varDelta \), since they don’t instantiate their own pacemaker. PaLa is analyzed with a less conservative timeout of 1min=\(5\varDelta \), and 1sec=\(2\varDelta \) than the ones presented in their paper.

  7. 7.

    An alternative is to have a single leader be in power for k iterations in a row, before switching to the next leader; this sacrifices fairness, since we would like to rotate leaders more frequently, and the latency is still not ideal, since a faulty leader can delay the execution for k iterations.

  8. 8.

    To recover a streamlined protocol, it is possible to “piggyback” the finalize message onto the first vote message of the next block; this would only make liveness a little slower, and consistency would still hold.

  9. 9.

    Note that this is referred to as a Bare PKI [10] since malicious parties may pick their own, potentially malformed, public keys.

  10. 10.

    In addition, we could optimistically fire the timer when the leader “equivocates”; we omit the rule for brevity.

  11. 11.

    Doing this composably has been visited in-depth in works such as [9, 12, 21, 40, 41, 44]. However, here we ignore the question of composability and use an simple stand-alone model for convenience.

  12. 12.

    Sometimes, this is referred to as the ‘hidden lock problem’.

  13. 13.

    Another reason we use a different variable is to make clear that it is possible to elect leaders from an entirely different set of processes than the main set of protocol processes; indeed, our protocol supports a setting where most leaders are corrupt (i.e. \(\gamma > 3/2\)) even when the number of faulty voters is required to be small (\(f < n/3\)).

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Authors and Affiliations

  1. Cornell Tech, New York, USA

    Benjamin Y. Chan

  2. Tel-Aviv University & Cornell Tech, Tel Aviv, Israel

    Rafael Pass

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  1. Benjamin Y. Chan
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Correspondence to Benjamin Y. Chan .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Chan, B.Y., Pass, R. (2023). Simplex Consensus: A Simple and Fast Consensus Protocol. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14372. Springer, Cham. https://doi.org/10.1007/978-3-031-48624-1_17

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