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Towards Permissionless Consensus in the Standard Model via Fine-Grained Complexity

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Advances in Cryptology – CRYPTO 2024 (CRYPTO 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14921))

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Abstract

We investigate the feasibility of permissionless consensus (aka Byzantine agreement) under standard assumptions. A number of protocols have been proposed to achieve permissionless consensus, most notably based on the Bitcoin protocol; however, to date no protocol is known that can be provably instantiated outside of the random oracle model.

In this work, we take the first steps towards achieving permissionless consensus in the standard model. In particular, we demonstrate that worst-case conjectures in fine-grained complexity, in particular the orthogonal vectors conjecture (implied by the Strong Exponential Time Hypothesis), imply permissionless consensus in the random beacon model—a setting where a fresh random value is delivered to all parties at regular intervals. This gives a remarkable win-win result: either permissionless consensus exists relative to a random beacon, or there are non-trivial worst-case algorithmic speed-ups for a host of natural algorithmic problems (including \(\textsf{SAT}\)).

Our protocol achieves resilience against adversaries that control an inverse-polynomial fraction of the honest computational power, i.e., adversarial power \(A=T^{1-\epsilon }\) for some constant \(\epsilon >0\), where T denotes the honest computational power. This relatively low threshold is a byproduct of the slack in the fine-grained complexity conjectures.

One technical highlight is the construction of a Seeded Proof of Work: a Proof of Work where many (correlated) challenges can be derived from a single short public seed, and yet still no non-trivial amortization is possible.

The full version of this paper appears in the Cryptology ePrint Archive [3].

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Notes

  1. 1.

    And in some cases, such as randomized protocols in the information-theoretic setting, also private.

  2. 2.

    The reader may wonder why the PoW scheme presented in [5] doesn’t directly give a permissionless consensus protocol. The reason is that in Nakamoto’s protocol the PoW proving time must follow a geometric distribution, and it is not clear how to get this property from the scheme in [5] without an RO while retaining hardness. On the other hand, our (classical) approach to consensus directly benefits from deterministic-time PoW provers, as all parties are expected to produce a PoW by the end of the round deadline.

  3. 3.

    In contrast to a RO, a beacon has a feasibly short description.

  4. 4.

    Dwork and Naor themselves gave some candidates, for example assuming that existing attacks on the Ong-Schnorr-Shamir signature scheme could not be improved.

  5. 5.

    They additionally observed that this technique applies to a variety of problems in fine-grained complexity. Later, others [8, 30, 31] extended this method to show that the problem of counting k-cliques is itself hard on average.

  6. 6.

    A proof system is said to be doubly-efficient if the prover runs in polynomial time and the verifier runs in quasilinear time. We require the stronger property that the prover runs in the same time as performing the computation in the clear, up to subpolynomial factors.

  7. 7.

    More generally, a non-interactive proof system where the \(\textsf{Prover}\) runs in time \(\tilde{O}(n^k)\) and \(\textsf{Verifier}\) runs in time \(\tilde{O}(n^{k/2})\) is possible.

  8. 8.

    We note that other methods are possible, however we believe our robust direct sum theorem to be interesting in its own right.

  9. 9.

    Looking ahead, the simulator will be used in the reduction from an attacker against the consensus protocol to an attacker against PoW hardness in order to simulate the work of honest parties. Thus, an efficient simulator is important to prove our protocol secure.

  10. 10.

    Furthermore, in this approach digital signatures are also used, and thus the existence of one-way functions must be assumed, an assumption that as we show is not necessary.

  11. 11.

    d is a function n such that \(d=\omega (\log n)\) (for hardness) and \(d=\tilde{O}(1)\) (for efficiency). Typically we fix the choice of \(d=\log ^2 n\) for concreteness.

  12. 12.

    Note that this distribution is not pseudorandom in the traditional cryptographic sense: it is easy to distinguish from uniform (and moveover the adversary is given the seed describing a sample); it is only pseudorandom for the purposes of proving a Threshold Direct Sum theorem for \(f{\textsf{OV}}^k\).

  13. 13.

    If it is not the case that \(t(n)>>m(n)\), imagine that A outputs \((i,\hat{y}_i)_{i\in S}\) for some \(S\subseteq [n]\).

  14. 14.

    This choice is made in [2] to avoid deniable-of-service (DoS) attacks that may deplete the round-bounded computational power of the honest parties. We remark that handling DoS attacks this way is not the only option. For instance, one could block invalid PoW dissemination at the \(\mathcal {F}_{\textsc {diff}} \) level, but this is a strictly weaker option, as it actually allows verifying PoWs for free! On the other hand, one could opt for assuming even less about \(\mathcal {F}_{\textsc {diff}} \) and instead relying entirely on computational constraints/modeling to handle DoS. In such a setting it would be advantageous to have a PoW where the time to verify a “proof” scales directly with the work invested in producing the “proof.” We note that such PoW can be built from standard PoWs by simply generating parallel proofs for exponential tower of security parameters \((1,2,...,2^{\log \lambda })\) and verifying them in ascending order, yielding relative-cost verification. We believe our presentation in the simpler setting is more instructive.

  15. 15.

    We overload the term “round” here, and assume that in a round of duration x each party can take up to \(x\cdot c\) computational steps.

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Author information

Authors and Affiliations

  1. NYU, New York, USA

    Marshall Ball & Peter Hall

  2. Texas A&M University, College Station, USA

    Juan Garay

  3. University of Edinburgh, Edinburgh, UK

    Aggelos Kiayias

  4. Input Output, London, UK

    Aggelos Kiayias

  5. Input Output, Piraeus, Greece

    Giorgos Panagiotakos

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  1. Marshall Ball
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  4. Aggelos Kiayias
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Correspondence to Marshall Ball .

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Editors and Affiliations

  1. Boston University, Boston, MA, USA

    Leonid Reyzin

  2. University of Waterloo, Waterloo, ON, Canada

    Douglas Stebila

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Ball, M., Garay, J., Hall, P., Kiayias, A., Panagiotakos, G. (2024). Towards Permissionless Consensus in the Standard Model via Fine-Grained Complexity. In: Reyzin, L., Stebila, D. (eds) Advances in Cryptology – CRYPTO 2024. CRYPTO 2024. Lecture Notes in Computer Science, vol 14921. Springer, Cham. https://doi.org/10.1007/978-3-031-68379-4_4

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