Communication Efficient Byzantine Agreement with Predictions
Source: arXiv:2605.12935 · Published 2026-05-13 · By Muhammad Ayaz Dzulfikar, Seth Gilbert
TL;DR
This paper addresses Byzantine agreement protocols enhanced by classification predictions that indicate which processes are honest or faulty. Prior work showed that while such predictions can reduce rounds required for agreement, they induce cubic communication overhead (Ω(n^3) bits) because all processes must share predictions to reconcile classifications. This paper demonstrates that this high communication cost is not fundamental. The authors design unauthenticated algorithms achieving sub-cubic communication Õ(n^{2.5}) bits, and an authenticated algorithm achieving optimal O(n^2 κ) bits (κ is security parameter), while preserving the optimal round complexity O(min{B/n, f}) for any number of erroneous prediction bits B. The authenticated solution also improves resilience to near the theoretical maximum t < (1/2 - ϵ)n. They achieve these results by replacing global prediction reconciliation with group-based leader election protocols that limit communication and exploiting cryptographic signatures for authentication and message aggregation. Their work significantly improves the practicality of Byzantine agreement with unreliable classification predictions, reducing communication by orders of magnitude without sacrificing speed or fault tolerance.
Key findings
- Byzantine agreement with classification predictions can achieve round complexity O(min{B/n, f}) for any number of prediction errors B, improving upon the previous Ω(f) lower bound.
- Unauthenticated algorithm achieves resilience t < (1/3 - ϵ)n, Õ(n^2) messages, and O(n^3) bits of communication with optimal rounds (Theorem 1).
- Improved unauthenticated algorithm reduces bit communication to Õ(n^{2.5}) by a committee-based group leader election with resilience t < (1/6 - ϵ)n (Theorem 2).
- Authenticated algorithm achieves near-optimal resilience t < (1/2 - ϵ)n, O(n^2) messages, and optimal O(n^2 κ) bits of communication with threshold signatures (Theorem 3).
- Group leader election algorithms elect the same honest leader in good groups in O(1) rounds using O(n^2 |G|) bits, reducing the need for global prediction sharing.
- More than 2m/3 groups can be guaranteed good under respective resilience and misclassification assumptions, enabling reliable leader election.
- Communication complexity bottleneck shifts from prediction sharing to leader election, which is addressed by differentiating small and large groups with refined election protocols.
- Authenticated protocol uses threshold signature aggregation to limit communication and permit leader election with minimal exchanges, eliminating costly prediction reconciliation.
Threat model
An adaptive Byzantine adversary can control up to t < n/3 (unauthenticated) or t < n/2 (authenticated) processes that deviate arbitrarily, potentially colluding and sending arbitrary messages. The adversary has full knowledge of the protocol and prediction bits but cannot break cryptographic primitives or forge signatures in the authenticated setting. The communication network is synchronous and reliable.
Methodology — deep read
Threat model & assumptions: The system has n total processes, with up to t Byzantine corruptions. The adversary is adaptive and can deviate arbitrarily but cannot break cryptographic primitives. Two setting are considered: unauthenticated (no crypto) and authenticated (with PKI and threshold signatures). The protocol assumes synchronous reliable communication.
Data: Not a data-driven paper but theoretical. Inputs are binary values per process and each process receives an n-bit classification prediction string indicating which other processes are honest or faulty, potentially noisy with B incorrect bits.
Architecture / algorithm: Three key protocols:
- First, an unauthenticated Byzantine agreement protocol tolerating t<(1/3 -ϵ)n, uses guess-and-double approach from prior work dividing processes into m groups, electing leaders in each group by simple majority vote on predictions, then executing agreement on committee of leaders. Election shares all predictions to reconcile classifications, costing O(n^3) bits.
- Second, an improved unauthenticated protocol reduces communication to Õ(n^{2.5}) bits by refining group leader election: splitting groups into small and large; small groups perform direct vote among their members; large groups restrict communicated prediction bits to only c√n top candidates and perform committee conciliation rounds to agree leader, combining both approaches to reduce bit complexity.
- Third, an authenticated algorithm uses threshold signatures to authenticate leader election votes and aggregate approvals, removing the need for repeated communication. Leaders are chosen alternately by round-robin and group leader election results, following guess-and-double strategy for estimates of misclassifications. Uses existing validated Byzantine agreement primitives with cryptographic proofs, limiting communication to O(n^2 κ) bits.
Training regime: Not applicable.
Evaluation protocol: Theoretical complexity analysis with proofs. Metrics are round complexity, message complexity, bit communication complexity, and resilience thresholds. Protocols compared against prior work [3] baselines that required Ω(n^3) bits and had more limited resilience or higher communication. The authors prove lemmas guaranteeing existence of many "good groups" for leader election under assumptions on B and t.
Reproducibility: No code or empirical evaluation released; results are analytical. Some algorithms described with pseudocode (e.g., Algorithm 1). New leader election protocols and cryptographic threshold signature usage detailed to enable reproduction in theory.
Example (end-to-end): Consider guess-and-double phases estimating misclassified processes ˆk. The processes are partitioned into m=Θ(ˆk) groups. Each group runs leader election protocols (simple or committee-based depending on group size and ˆk). The elected group leaders form a committee that performs Byzantine agreement rapidly in O(min{B/n, f}) rounds. As estimates ˆk and f double, the protocol refines leader sets and eventually all honest processes agree on output. The authenticated variant uses threshold signatures to authenticate and compress signatures for leader proofs, drastically reducing exchanged bits in leader election.
Overall, the paper combines combinatorial arguments about groupings, classification error bounds, cryptographic signature techniques, and guess-and-double iterative protocol design to optimize communication and rounds in Byzantine agreement with unreliable classification predictions.
Technical innovations
- Demonstrating that the Ω(n^3) communication barrier in prior Byzantine agreement with predictions is avoidable, by replacing global prediction reconciliation with local group leader election.
- A new committee-based group leader election protocol that handles large and small groups differently to reduce overall bit complexity to Õ(n^{2.5}) in unauthenticated settings.
- Use of threshold signature aggregation and authentication to further reduce communication to O(n^2 κ) bits while achieving near-optimal resilience t < (1/2 - ϵ)n.
- Combining guess-and-double estimate refinement with group partitioning and leader election to achieve optimal O(min{B/n, f}) rounds independent of prediction error magnitude.
Baselines vs proposed
- [3] unauthenticated: bit complexity = O(n^3) vs this paper (unauthenticated): bit complexity = Õ(n^{2.5})
- [3] authenticated (threshold signatures): bit complexity = Õ(n^{4 κ}) vs this paper (authenticated): bit complexity = O(n^{2} κ)
- [3] round complexity: O(min{B/n, f}) vs this paper: same round complexity but improved communication
- [3] resilience unauthenticated: t < n/3 vs this paper unauthenticated second result: t < (1/6 - ϵ)n
- [3] resilience authenticated: t < (1/2 - ϵ)n same as this paper with improved communication
Limitations
- Unauthenticated algorithms with reduced communication sacrifice resilience (t < (1/6 - ϵ)n) compared to classical n/3 bound.
- Protocols assume synchrony and reliable message delivery; asynchronous settings not addressed.
- Authentication-dependent protocol requires trusted PKI and secure threshold signature schemes, adding cryptographic assumptions and setup complexity.
- No empirical validation or simulation to evaluate practical performance; results are purely theoretical.
- The guess-and-double strategy may incur overhead in practice due to estimation phases.
- The quality and distribution of classification predictions beyond worst-case B-bit error bounds are not extensively explored.
Open questions / follow-ons
- Can the unauthenticated group-leader election approach be improved to achieve resilience closer to the n/3 bound while maintaining sub-cubic communication?
- How do these algorithms perform under more realistic prediction error models, such as correlated or probabilistic misclassification rather than worst-case B-bit errors?
- Can these techniques be adapted to partially synchronous or asynchronous network models?
- Is it possible to design more efficient authenticated Byzantine agreement protocols that use lighter cryptography while retaining communication optimality?
Why it matters for bot defense
For bot-defense and CAPTCHA engineers, this paper provides a foundational advancement in reducing communication overhead in distributed consensus protocols that leverage imperfect machine learning predictions about node honesty. The group-based leader election approach shows how unreliable predictions, common in bot detection pipelines, can be used to speed up consensus or decision protocols without prohibitive message overhead. This principle could inform the design of challenge-response or consensus-based bot detection systems that integrate heuristic or AI-based node reputation signals. The authenticated protocol demonstrates how cryptographic proofs can compress communication when trusting external signatures, suggesting avenues to combine ML-based predictions with cryptographic attestations for more scalable bot mitigation in high-load distributed environments.
Cite
@article{arxiv2605_12935,
title={ Communication Efficient Byzantine Agreement with Predictions },
author={ Muhammad Ayaz Dzulfikar and Seth Gilbert },
journal={arXiv preprint arXiv:2605.12935},
year={ 2026 },
url={https://arxiv.org/abs/2605.12935}
}