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]

The Lock-Commit Paradigm: Multi-shot and Mixed Faults

In this follow to our Lock-Commit post, we show two important extensions. The first is how to extend from single-shot to multi-shot. Multi-shot is the bases of State Machine Replication. The second is how to tolerate mix faluts: both $f$ omission failures and $k$ crash failures given k+2f < n. [Read More]
Tags: dist101

The Lock-Commit Paradigm

In this post, we explore one of the most celebrated and widely used techniques for reaching consensus: the Lock-Commit paradigm. This approach is a key technique of DLS88, Lamport’s Paxos, and many subsequent protocols. Protocols like Raft, PBFT, Tendermint, SBFT, Casper FFG, HotStuff, etc., are all based on this paradigm. [Read More]
Tags: dist101

BFT Protocol Forensics

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]

Living with Asynchrony: Bracha's Reliable Broadcast

In this series of posts, we explore what can be done in the Asynchronous model. This model seems challenging because the adversary can delay messages by any bounded time. By the end of this series, you will see that almost everything that can be done in synchrony can be obtained in asynchrony. The next posts in this series are about gather, round complexity, and finally our series on Asynchronous Agreement.... [Read More]

Private Set Intersection #2

In the first post on Private Set Intersection, I presented the problem of Private Set Intersection, its applications and the simple protocol of [KMRS14], that allows Alice and Bob to learn the intersection of their sets with the aid of an untrusted third party Steve who is assumed to not collude with Alice or with Bob. [Read More]

Polynomial Secret Sharing and the Lagrange Basis

In this post, we highlight an amazing result: Shamir’s secret sharing scheme. This is one of the most powerful uses of polynomials over a finite field in distributed computing. Intuitively, this scheme allows a $Dealer$ to commit to a secret $s$ by splitting it into shares distributed to $n$ parties. The secret is hidden and requires a threshold of $f+1$ parties in order to be reconstructed, where $f < n$.... [Read More]

The Marvels of Polynomials over a Field

In this series of posts, we explore the mathematical foundations of polynomials over a field. These objects are at the heart of several results in computer science: secret sharing, Multi Party Computation, Complexity, and Zero Knowledge protocols. [Read More]