Decentralized Thoughts is a group blog on decentralization, by decentralized thinkers, for decentralized thoughts, of decentralized matters. Decentralized Thoughts is a group blog on decentralization, by decentralized thinkers, for decentralized thoughts, of decentralized matters.

## The round complexity of Reliable Broadcast

Reliable Broadcast is an important building block of many Asynchronous protocols. There is a broadcaster that has some input value, $v$, and a non-faulty party that terminates needs to output a value. Reliable Broadcast is defined via two properties: [Read More]

## Optimal Communication Complexity of Authenticated Byzantine Agreement

Communication complexity of Byzantine Agreement (BA) has been studied for decades. Dolev and Reischuk showed that quadratic communication is necessary for BA with perfect security, i.e., without error. Berman, Garay, and Perry showed that this lower bound is tight for the unauthenticated setting (without signatures) with $f &lt; n/3$. However, for $f \ge n/3$, the best solution so far is still the Dolev-Strong protocol with cubic communication, so a linear... [Read More]

## Information Theoretic HotStuff (IT-HS): Part One

This post is the first of two on Information Theoretic HotStuff (IT-HS). Information Theoretic HotStuff is a Byzantine Consensus protocol in the partially synchronous model. It replaces all of HotStuff’s cryptographic signatures with simple information theoretic message passing techniques over authenticated channels. Information theoretic protocols are often easy to reason about, form a great introduction for learning the basics of consensus, have less of an attack surface, and highlight useful... [Read More]
Tags: dist101

## The Private Set Intersection (PSI) Protocol of the Apple CSAM Detection System

In this post, we will discuss the cryptographic construction used in Apple’s new system for detecting CSAM - Child Sexual Abuse Material. This cryptographic construction implements a new variant of PSI - Private Set Intersection. While a lot of attention has been paid to the broad implications of this system, the technical details of the PSI construction have not been highlighted, even though Apple published a detailed technical description of... [Read More]

## Simplifying Raft with Chaining

Raft is a consensus algorithm for deciding a sequence of commands to execute on a replicated state machine. Raft is famed for its understandability (relative to other consensus algorithms such as Paxos) yet some aspects of the protocol still require careful treatment. For instance, determining when it is safe for a leader to commit commands from previous leaders or when it is safe for servers to delete or overwrite commands... [Read More]

## Benign Hotstuff

In this post we describe a variant of Paxos (or Raft or Lock-Commit) that is inspired by looking through the lens of HotStuff and Blockchain protocols. The most noticeable difference is that while Paxos and Raft aim to maintain a stable Primary/Leader (and change views infrequently), in Benign Hotstuff (as in HotStuff), the Primary is rotated every round! A more subtle difference is that in Paxos and Raft each block... [Read More]

## Living with Asynchrony: the Gather protocol

A very useful tool in Asynchronus distributed computing is Reliable Broadcast, or simply called Broadcast. It allows a leader to send a message, knowing that all parties will eventually receive the same message, even if a malicious adversary control $f$ parties and $f&lt;n/3$. Broadcast is deterministic and takes just a constant number of rounds. [Read More]

## Good-case Latency of Byzantine Broadcast: the Synchronous Case

In our first post, we presented a summary of our good-case latency results for Byzantine broadcast (BB) and state machine replication (SMR), where the good case measures the latency to commit given that the broadcaster or leader is honest. In our second post, we discussed our results for partial synchrony, and described a new BFT SMR protocol named (5f-1)-SMR that can commit a decision within $2$ rounds in the good... [Read More]

## Raft does not Guarantee Liveness in the face of Network Faults

Last month, Cloudflare published a postmortem of a recent 6-hour outage caused by a partial switch failure which left etcd unavailable as it was unable to establish a stable leader. This outage has understandably led to discussion online about exactly what liveness guarantees are provided by the Raft consensus algorithm in the face of network failures. [Read More]
Tags: raft dist101

## A Simple and Succinct Zero Knowledge Proof

There is a popular belief that succinct proofs and zero-knowledge proofs are a type of moon math. In this post, our goal is to present a simple proof system that can provide an introduction and intuition to this space. Perhaps surprisingly, the only tool we will use is the Theorem that non-trivial degree-at-most-$d$ polynomials over a field have at most $d$ roots. [Read More]

An important property satisfied by any Byzantine fault tolerant consensus protocol is agreement, which requires non-faulty replicas to not decide on conflicting values. Depending on the network model, typical consensus protocols tolerate only a fraction of Byzantine replicas. In particular, under partial synchrony or asynchrony, no consensus protocol with $n$ replicas can tolerate more than $n/3$ Byzantine faults. If the number of Byzantine replicas exceed this number, the protocols do... [Read More]