# Window Based BFT Blockchain Consensus

## TL;DR

This paper introduces Musch, a BFT blockchain protocol that significantly reduces communication complexity to linear levels while maintaining low latency, addressing scalability issues without sacrificing fault tolerance.

## Contribution

Musch is the first BFT blockchain protocol to achieve linear communication complexity with low latency under failures by using exponentially increasing windows for reporting complaints.

## Key findings

- Achieves $O(f n + n)$ communication complexity for $f < n/3$ failures.
- Maintains low latency despite reduced communication overhead.
- Addresses scalability limitations of traditional BFT protocols.

## Abstract

There is surge of interest to the blockchain technology not only in the scientific community but in the business community as well. Proof of Work (PoW) and Byzantine Fault Tolerant (BFT) are the two main classes of consensus protocols that are used in the blockchain consensus layer. PoW is highly scalable but very slow with about 7 (transactions/second) performance. BFT based protocols are highly efficient but their scalability are limited to only tens of nodes. One of the main reasons for the BFT limitation is the quadratic $O(n^2)$ communication complexity of BFT based protocols for $n$ nodes that requires $n \times n$ broadcasting. In this paper, we present the {\em Musch} protocol which is BFT based and provides communication complexity $O(f n + n)$ for $f$ failures and $n$ nodes, where $f < n/3$, without compromising the latency. Hence, the performance adjusts to $f$ such that for constant $f$ the communication complexity is linear. Musch achieves this by introducing the notion of exponentially increasing windows of nodes to which complains are reported, instead of broadcasting to all the nodes. To our knowledge, this is the first BFT-based blockchain protocol which efficiently addresses simultaneously the issues of communication complexity and latency under the presence of failures.