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Practical Provably Secure Flooding for Blockchains

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

Abstract

In recent years, permisionless blockchains have received a lot of attention both from industry and academia, where substantial effort has been spent to develop consensus protocols that are secure under the assumption that less than half (or a third) of a given resource (e.g., stake or computing power) is controlled by corrupted parties. The security proofs of these consensus protocols usually assume the availability of a network functionality guaranteeing that a block sent by an honest party is received by all honest parties within some bounded time. To obtain an overall protocol that is secure under the same corruption assumption, it is therefore necessary to combine the consensus protocol with a network protocol that achieves this property under that assumption. In practice, however, the underlying network is typically implemented by flooding protocols that are not proven to be secure in the setting where a fraction of the considered total weight can be corrupted. This has led to many so-called eclipse attacks on existing protocols and tailor-made fixes against specific attacks.

To close this apparent gap, we present the first practical flooding protocol that provably delivers sent messages to all honest parties after a logarithmic number of steps. We prove security in the setting where all parties are publicly assigned a positive weight and the adversary can corrupt parties accumulating up to a constant fraction of the total weight. This can directly be used in the proof-of-stake setting, but is not limited to it. To prove the security of our protocol, we combine known results about the diameter of Erdős–Rényi graphs with reductions between different types of random graphs. We further show that the efficiency of our protocol is asymptotically optimal.

The practicality of our protocol is supported by extensive simulations for different numbers of parties, weight distributions, and corruption strategies. The simulations confirm our theoretical results and show that messages are delivered quickly regardless of the weight distribution, whereas protocols that are oblivious of the parties’ weights completely fail if the weights are unevenly distributed. Furthermore, the average message complexity per party of our protocol is within a small constant factor of such a protocol.

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Notes

  1. 1.

    The probability to choose the unordered neighborhood set \(N = \{q_1 ,\dots , q_K\}\) is the sum over the probabilities of all permuted tuples.

  2. 2.

    An attack where an adversary tricks an honest party into talking only with adversarial parties. It is thereby possible for the adversary to manipulate the honest node in various ways.

  3. 3.

    For a discussion of the necessity of the zero-weight requirement see Sect. 4 and for methods to anyway achieve delivery to such zero-weight parties we refer to the full version of this work [26].

  4. 4.

    Note that for protocols with no secrecy (each event is leaked to the adversary), and for functionalities that give the adversary full control while respecting these properties a simulation-based security notion is directly implied by the property-based definition. For flooding networks, this technique is used in the proofs in [30].

  5. 5.

    For a function to be an emulation function, we require that all parties should emulate at least 1 node, which is why the codomain of the function is defined to be \(\mathbb {N}{\setminus }\left\{ { 0 }\right\} \).

  6. 6.

    This property was used in the proof of Lemma 2.

  7. 7.

    This set may be different from the actual set of nodes that will be emulated in an execution of the protocol as dishonest parties might choose to deviate from the protocol. However, it is still useful to define the set in order to define honest behavior.

  8. 8.

    All simulations were performed on the ETH Zurich Euler cluster, but there are no hindrances to running them on less powerful computers.

  9. 9.

    The maximum latency observed in any of our simulations is \(9\cdot \delta _\text {Channel}\) for any succeeding run.

  10. 10.

    The protocol \(\textsf {WOF} {:}{=}\pi _\text {Flood}(\textsf {WFS} (\texttt{E},k))\) for \(\texttt{E} (p) {:}{=}1\) corresponds to the protocol where each party simply selects \(k\) parties uniformly at random as their neighbors without taking weight into account.

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Acknowledgements

The work was in part done while Chen-Da Liu-Zhang was at Carnegie Mellon University and Søren Eller Thomsen was at Purdue University. Chen-Da Liu-Zhang was supported in part by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Authors and Affiliations

  1. NTT Research, Sunnyvale, USA

    Chen-Da Liu-Zhang

  2. Concordium, Zurich, Switzerland

    Christian Matt

  3. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Ueli Maurer & Guilherme Rito

  4. Concordium Blockchain Research Center, Aarhus University, Aarhus, Denmark

    Søren Eller Thomsen

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Correspondence to Søren Eller Thomsen .

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  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Liu-Zhang, CD., Matt, C., Maurer, U., Rito, G., Thomsen, S.E. (2022). Practical Provably Secure Flooding for Blockchains. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_26

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