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The Unique Chain Rule and Its Applications

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Financial Cryptography and Data Security (FC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13950))

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Abstract

Most existing Byzantine fault-tolerant State Machine Replication (SMR) protocols rely explicitly on either equivocation detection or quorum certificate formations to ensure protocol safety. These mechanisms inherently require \(O(n^2)\) communication overhead among n participating servers. This work proposes the Unique Chain Rule (UCR), a simple rule for hash chains where extending a block by including its hash in the next block, is treated as a vote for the proposed block and its ancestors. When a block obtains a vote from at least one correct server, we can commit the block and its ancestors. While this idea was used implicitly earlier in conjunction with equivocation detection or quorum certificate generation, this work employs it explicitly to show safety.

We present three applications of UCR. We design Apollo, and Artemis: two novel synchronous SMR protocols with linear best-case communication complexity using round-robin, and stable leaders, respectively as the first two applications. Next, we employ UCR in a black-box fashion toward making any SMR commits publicly verifiable, where clients will no longer have to wait for \(2t+1\) confirmations on every block, where t is the number of Byzantine faults tolerated by the protocol, but can instead collect a UCR proof consisting of \(\min (\kappa , t) +1\) extensions on a block, where \(\kappa \) is a security parameter. This results in faster syncing times for clients as the publicly verifiable proofs can also be gossiped with every new block extension confirming a new block.

An extended version is available at https://eprint.iacr.org/2021/180.

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Notes

  1. 1.

    It is possible for SMR protocols to tolerate more than 1/2 faults. However, these SMR protocols cannot safely convince any external observer of statements regarding the latest state of the system due to the dishonest majority [30].

  2. 2.

    Many related works claim constant latency [1, 3]. The correct term should be \((\min (\kappa ,t) +1) \) as leader randomization is inherently assumed and for small t round-robin protocols are sufficient.

  3. 3.

    This list is not exhaustive.

  4. 4.

    Our protocol is adaptively secure, but a different randomization protocol will be needed. There is a trade-off between constant latency and increased signature complexity using [11], or \(O(f\delta )\) latency and constant signature complexity using round-robin.

  5. 5.

    In practice, \(\delta \) varies between pairs of servers, instances of time, and size of the message. However, the analysis here assumes that a single \(\delta \) value is the optimistic delay time, a violation of which implies that we are not in the optimistic scenario.

  6. 6.

    We use the notation from Python.

  7. 7.

    Non-synchronous includes partial synchrony, asynchronous networks, etc. that are not standard synchrony.

  8. 8.

    This assumption can be removed by slightly changing the blaming mechanism to not blame if the local transaction buffer is empty and attempting to send transactions to \(L _v\) on timeout first, and then blaming. An example of this implementation can be found in Concord-BFT [22].

  9. 9.

    In Proof-of-Stake protocols, the stake is defined by the chain, and thus the leaders are publicly verifiable. However, the public verifiability of the chain depends on the underlying SMR used in the protocol.

  10. 10.

    We cannot discuss it in terms of block heights because any number of blocks might be successfully committed within \(\varDelta \) because of the responsiveness of our protocols. For partially synchronous systems it is not possible to guarantee any form of the latest state before GST.

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Acknowledgements

We thank Ling Ren and Ittai Abraham for helpful feedback on the applications of UCR, Kartik Nayak for discussions regarding good-case latency, Nibesh Shrestha for feedback on the draft, and Manish Nagaraj for early discussions. This work was supported in part by NIFA award number 2021-67021-34252, the National Science Foundation (NSF) under grant CNS1846316, the United States Department of Agriculture, and the Army Research Lab Contract number W911NF-2020-221.

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Authors and Affiliations

  1. Purdue University, West Lafayette, IN, 47906, USA

    Adithya Bhat, Akhil Bandarupalli, Saurabh Bagchi & Aniket Kate

  2. Duke University, Durham, NC, 27708, USA

    Michael K. Reiter

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  1. Adithya Bhat
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  2. Akhil Bandarupalli
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Correspondence to Adithya Bhat .

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  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

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Bhat, A., Bandarupalli, A., Bagchi, S., Kate, A., K. Reiter, M. (2024). The Unique Chain Rule and Its Applications. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_3

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  • DOI: https://doi.org/10.1007/978-3-031-47754-6_3

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