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arxiv: 1907.10308 · v2 · pith:KQI6QI74new · submitted 2019-07-24 · 💻 cs.DC · cs.DS

Scalable and Secure Computation Among Strangers: Resource-Competitive Byzantine Protocols

John Augustine , Valerie King , Anisur R. Molla , Gopal Pandurangan , Jared Saia This is my paper

Pith reviewed 2026-05-24 16:46 UTC · model grok-4.3

classification 💻 cs.DC cs.DS
keywords Byzantine agreementresource-competitive protocolspermissionless systemsscalable consensusleader electioncommittee electionByzantine faults
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0 comments X

The pith

Byzantine agreement among unknown nodes can be solved with honest nodes sending expected O((T+n) log n) bits total.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends Byzantine agreement to a model where nodes start without knowing each other's identities and can only contact random nodes or reply to incoming messages. It focuses on resource-competitive protocols, in which the total bits sent by honest nodes stay comparable to those sent by Byzantine nodes rather than growing much larger. The main construction is a randomized algorithm that solves Byzantine agreement along with leader election and committee election under these constraints. A sympathetic reader would care because this bound holds even when the network size is large and the fraction of Byzantine nodes is close to one quarter. The authors also give matching lower bounds showing that some dependence on the adversary's communication cost is unavoidable in general.

Core claim

Our randomized scalable algorithm solves Byzantine agreement, leader election, and committee election by sending an expected O((T+n)log n) bits with O(polylog(n)) latency, where T is the minimum of n² and the number of bits sent by adversarially controlled nodes. The algorithm is resilient to (1/4−ε)n Byzantine nodes for any fixed ε>0 and succeeds with high probability in a synchronous fully-connected network under a static full-information adversary where each node initially knows no other identities.

What carries the argument

A randomized algorithm that achieves resource-competitive Byzantine agreement by sending messages only to random destinations or nodes from which messages have already been received.

If this is right

  • Honest nodes incur communication cost comparable to the Byzantine nodes' cost even as n grows.
  • The same bounds apply simultaneously to Byzantine agreement, leader election, and committee election.
  • Latency stays polylogarithmic in n independent of the adversary's actions.
  • Any protocol must incur communication cost at least roughly proportional to the adversary's cost in the worst case.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The model captures the essential communication restrictions of permissionless systems, so the bounds may carry over to dynamic participation settings.
  • The lower bound implies that resource-competitive design is required rather than optional for this class of problems.
  • The polylog latency suggests the protocol remains practical when n is very large.

Load-bearing premise

The network is synchronous and fully connected with a static adversary.

What would settle it

An execution in which the protocol succeeds against (1/4−ε)n Byzantine nodes yet honest nodes send asymptotically more than O((T+n) log n) bits in total.

Figures

Figures reproduced from arXiv: 1907.10308 by Anisur R. Molla, Gopal Pandurangan, Jared Saia, John Augustine, Valerie King.

Figure 1
Figure 1. Figure 1: This figure illustrates possible outcomes of L [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
read the original abstract

Motivated, in part, by the rise of permissionless systems such as Bitcoin where arbitrary nodes (whose identities are not known apriori) can join and leave at will, we extend established research in scalable Byzantine agreement to a more practical model where each node (initially) does not know the identity of other nodes. A node can send to new destinations only by sending to random (or arbitrary) nodes, or responding (if it chooses) to messages received from those destinations. We assume a synchronous and fully-connected network, with a full-information, but static Byzantine adversary. A general drawback of existing Byzantine protocols is that the communication cost incurred by the honest nodes may not be proportional to those incurred by the Byzantine nodes; in fact, they can be significantly higher. Our goal is to design Byzantine protocols for fundamental problems which are {\em resource competitive}, i.e., the number of bits sent by honest nodes is not much more than those sent by Byzantine nodes. We describe a randomized scalable algorithm to solve Byzantine agreement, leader election, and committee election in this model. Our algorithm sends an expected $O((T+n)\log n)$ bits and has latency $O(polylog(n))$, where $n$ is the number of nodes, and $T$ is the minimum of $n^2$ and the number of bits sent by adversarially controlled nodes. The algorithm is resilient to $(1/4-\epsilon)n$ Byzantine nodes for any fixed $\epsilon > 0$, and succeeds with high probability. Our work can be considered as a first application of resource-competitive analysis to fundamental Byzantine problems. To complement our algorithm we also show lower bounds for resource-competitive Byzantine agreement. We prove that, in general, one cannot hope to design Byzantine protocols that have communication cost that is significantly smaller than the cost of the Byzantine adversary.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a randomized algorithm for Byzantine agreement, leader election, and committee election in a synchronous fully-connected network where nodes initially lack knowledge of others' identities and communicate only via random/arbitrary sends or responses. The algorithm is resource-competitive, achieving expected O((T + n) log n) bits of communication and O(polylog n) latency, where T is the minimum of n² and the bits sent by the adversary; it tolerates (1/4 − ε)n static full-information Byzantine faults for any fixed ε > 0 and succeeds with high probability. Complementary lower bounds show that communication cannot be asymptotically smaller than the adversary's cost.

Significance. If the analysis and proofs hold, the result is significant as the first application of resource-competitive analysis to core Byzantine problems in a permissionless-style model with unknown identities. The bounds tie honest-node cost directly to adversary effort (rather than allowing it to be much higher), and the lower bounds provide a matching guarantee; this is a meaningful extension of prior Byzantine agreement work under the stated model assumptions.

major comments (2)
  1. [Abstract / Model description] The resilience threshold of (1/4 − ε)n is explicitly weaker than the classic 1/3 bound; while the abstract notes this is consistent with the restricted communication model, the manuscript should include a concrete argument (e.g., in the model or algorithm section) showing why 1/3 is not achievable under random/arbitrary-send communication.
  2. [Algorithm description / Analysis] The definition of T as min(n², adversary bits sent) is used to bound the honest communication; the manuscript must show explicitly (via the algorithm pseudocode or analysis) that the honest nodes' total bits remain O((T + n) log n) even when the adversary sends up to n² bits, without circular dependence on the honest nodes' own communication.
minor comments (2)
  1. [Abstract] The abstract states the latency is O(polylog(n)) but does not specify the base of the logarithm or the precise polylog degree; clarify this in the theorem statement.
  2. [Lower bounds] The lower-bound section should explicitly state the model parameters under which the impossibility holds (e.g., whether it applies only to the random-send model or more generally).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and the recommendation of minor revision. The comments are constructive, and we address each major point below. We will incorporate clarifications and additions as described.

read point-by-point responses

  1. Referee: [Abstract / Model description] The resilience threshold of (1/4 − ε)n is explicitly weaker than the classic 1/3 bound; while the abstract notes this is consistent with the restricted communication model, the manuscript should include a concrete argument (e.g., in the model or algorithm section) showing why 1/3 is not achievable under random/arbitrary-send communication.

    Authors: We agree that an explicit argument would strengthen the presentation. The abstract already notes consistency with the model, but we will add a dedicated paragraph in the model section of the revised manuscript that concretely explains why 1/3 resilience cannot be achieved under random/arbitrary-send communication (due to the inability to reliably target or flood specific nodes without prior identity knowledge, which prevents standard techniques for tolerating up to 1/3 faults). revision: yes

  2. Referee: [Algorithm description / Analysis] The definition of T as min(n², adversary bits sent) is used to bound the honest communication; the manuscript must show explicitly (via the algorithm pseudocode or analysis) that the honest nodes' total bits remain O((T + n) log n) even when the adversary sends up to n² bits, without circular dependence on the honest nodes' own communication.

    Authors: We will strengthen the analysis section to make this explicit. T is defined solely from the adversary's bit count (capped at n²), and the algorithm pseudocode ensures that honest nodes only respond to received messages or send a bounded number of random probes per phase; the total honest communication is therefore charged directly against the adversary's sends without depending on honest output volume. We will add a short lemma and proof sketch clarifying the independence from honest communication volume. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives an algorithm for Byzantine agreement, leader election, and committee election under a synchronous fully-connected model with static full-information adversary and unknown node identities. The central bound O((T + n) log n) communication with O(polylog n) latency is obtained directly from the protocol construction (random/arbitrary sends and responses), where T is defined as an external adversary cost (min(n², bits sent by Byzantines)). A matching lower bound is shown separately. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear; the (1/4 − ε) resilience is explicitly weaker than the classic 1/3 threshold and consistent with the model. The derivation is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The result rests on standard distributed-computing model assumptions rather than new free parameters or invented entities.

axioms (2)
  • domain assumption Network is synchronous and fully connected.
    Explicitly stated as part of the model in the abstract.
  • domain assumption Adversary is full-information but static.
    Explicitly stated as part of the model in the abstract.

pith-pipeline@v0.9.0 · 5889 in / 1196 out tokens · 19767 ms · 2026-05-24T16:46:24.736846+00:00 · methodology

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