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**2024/637**

**Title:**

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

**Authors:**
Marshall Ball, Juan Garay, Peter Hall, Aggelos Kiayias, Giorgos Panagiotakos

**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 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−ε} for some constant ε > 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.

**ePrint:**
https://eprint.iacr.org/2024/637

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