# Quadratic worst-case message complexity for State Machine Replication in the partial synchrony model

@article{LewisPye2022QuadraticWM, title={Quadratic worst-case message complexity for State Machine Replication in the partial synchrony model}, author={Andrew Lewis-Pye}, journal={ArXiv}, year={2022}, volume={abs/2201.01107} }

We consider the message complexity of State Machine Replication protocols dealing with Byzantine failures in the partial synchrony model. A result of Dolev and Reischuk gives a quadratic lower bound for the message complexity, but it was unknown whether this lower bound is tight, with the most efficient known protocols giving worst-case message complexity $O(n^3)$. We describe a protocol which meets Dolev and Reischuk's quadratic lower bound, while also satisfying other desirable properties. To…

## 7 Citations

### Fever: Optimal Responsive View Synchronisation

- Computer ScienceArXiv
- 2023

A new view synchronisation protocol for partial synchrony assuming minimal clock synchronisation is affirmatively introduced, called Fever, which has worst-case word complexity $O(fn+n)$ and worst- case latency $O(\Delta f + \delta)$.

### Byzantine Consensus is Θ(n^2): The Dolev-Reischuk Bound is Tight even in Partial Synchrony! [Extended Version]

- Mathematics, Computer ScienceArXiv
- 2022

This paper introduces SQuad, a partially synchronous Byzantine consensus protocol with quadratic worst-case communication complexity, which is optimally-resilient and achieves linear worst- case latency complexity.

### Byzantine Consensus Is Θ(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!

- Computer Science, MathematicsDISC
- 2022

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic communication complexity in the worst case. While it has been shown that the bound is tight…

### On the Validity of Consensus

- MathematicsArXiv
- 2023

The Byzantine consensus problem involves $n$ processes, out of which t<n could be faulty and behave arbitrarily. Three properties characterize consensus: (1) termination, requiring correct…

### Lessons from HotStuff

- Computer Science
- 2023

This article will take you on a journey to the core of blockchains, their Byzantine consensus engine, where HotStuff emerged as a new algorithmic foundation for the classical Byzantine generals…

### Every Bit Counts in Consensus

- Computer Science, Mathematics
- 2023

A new algorithm, DARE (Disperse, Agree, REtrieve), is presented, that improves upon the O(n^2 L) term via a novel dispersal primitive and employs heavier cryptographic primitives, namely STARK proofs, to devise DARE-Stark, a version of DARE which achieves the near-optimal bit complexity of O( n L + n^2 poly(kappa).

## 27 References

### Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR

- Computer ScienceDISC
- 2020

This work presents an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency, and existing protocols can use this algorithm to solve Byzantine SMR with the same asymptotic performance.

### The Next 700 BFT Protocols

- Computer ScienceOPODIS
- 2008

We present Abstract (ABortable STate mAChine replicaTion), a new abstraction for designing and reconfiguring generalized replicated state machines that are, unlike traditional state machines, allowed…

### Cogsworth: Byzantine View Synchronization.

- Computer Science
- 2019

The Byzantine View Synchronization problem is defined, which is responsible for eventually bringing all nodes to the same view for a sufficiently long time, and a third protocol is introduced, named Cogsworth, that has optimistically linear communication complexity and constant latency, and faced with benign failures, has expected linear communication and constantLatency.

### Consensus in the presence of partial synchrony

- Computer Science, MathematicsJACM
- 1988

Fault-tolerant consensus protocols are given for various cases of partial synchrony and various fault models that allow partially synchronous processors to reach some approximately common notion of time.

### Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement Using Cryptography

- Computer Science, MathematicsJournal of Cryptology
- 2005

A new protocol for Byzantine agreement in a completely asynchronous network is presented that makes use of new cryptographic protocols, specifically protocols for threshold signatures and coin-tossing based on the Diffie-Hellman problem.

### Bounds on information exchange for Byzantine agreement

- Computer ScienceJACM
- 1985

The amount of information exchange necessary to ensure Byzantine Agreement is studied and a lower bound is shown for the number of signatures for any algorithm using authentication and algorithms that achieve this bound are presented.

### Reaching Agreement in the Presence of Faults

- Computer ScienceJACM
- 1980

It is shown that the problem is solvable for, and only for, n ≥ 3m + 1, where m is the number of faulty processors and n is the total number and this weaker assumption can be approximated in practice using cryptographic methods.

### SBFT: A Scalable and Decentralized Trust Infrastructure

- Computer Science2019 49th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN)
- 2019

The results show that SBFT simultaneously provides almost 2x better throughput and about 1.5x better latency relative to a highly optimized system that implements the PBFT protocol.

### Optimal Communication Complexity of Authenticated Byzantine Agreement

- Computer Science, MathematicsDISC
- 2021

The first protocol achieves the optimal resilience of f < n/2 but requires a trusted setup for threshold signature, and the second protocol achieves near optimal resilience f ≤ (1/2 − ε)n in the standard PKI model.

### State Machine Replication for the Masses with BFT-SMART

- Computer Science2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks
- 2014

BFT-SMART is an open-source Java-based library implementing robust BFT state machine replication with improved reliability, modularity as a first-class property, multicore-awareness, reconfiguration support and a flexible programming interface.