Two Round HotStuff

In the first part of this post we describe a single-shot variation of Two Round HotStuff (see the HotStuff v1 paper) using Locked Broadcast that follows a similar path as our previous post on Paxos and Linear PBFT. In the second part, we describe a fully pipelined multi-shot State Machine Replication version of Two Round HotStuff that is similar to Casper FFG and Streamlet. [Read More]
Tags: dist101

On PBFT from Locked Broadcast

We describe a variation of the authenticated version of PBFT using Locked Broadcast that follows a similar path as our previous post on Paxos using Recoverable Broadcast. I call this protocol linear PBFT and variants of it are used by SBFT and Tusk. A later post will show how to extend this approach for Two Round HotStuff using Locked Broadcast and Three Round HotStuff using Keyed Broadcast. [Read More]
Tags: dist101

From Single-Shot Agreement to State Machine Replication

In this post we explore the path from Single-Shot Agreement, via Write-Once Registers, to Log Replication, and finally to State Machine Replication. We begin by defining all four problems assuming minority omission failures and partial synchrony. This post continues our previous posts on Paxos from Recoverable Broadcast and on State Machine Replication. [Read More]
Tags: dist101

Provable Broadcast

We explore a family of broadcast protocols in the authenticated setting in which a designated sender wants to create a delivery-certificate of its input value. After describing the base protocol we call Provable Broadcast ($PB$), we explore the surprising power of simply running $PB$ two times in a row, then three times, and finally four times in a row. [Read More]
Tags: dist101

Dining Cryptographers and the additivity of polynomial secret sharing

David Chaum’s dining cryptographer problem is a pioneering work on the foundations of privacy. It shows the amazing power of information-theoretic Secure Multi Party Computation. The original paper from 1988 is super accessible and fun to read. Many systems in the last 20 years for anonymity and privacy-preserving communication are based on the Dining Cryptographers problem. Herbivore, Dissent, Riposte, Blinder, and many others. [Read More]

The BGW Verifiable Secret Sharing Protocol

In this post, we present the classic Ben-or, Goldwasser, and Wigderson, 1988 (BGW) Verifiable Secret Sharing protocol (VSS) with the simplifications of Feldman, 1988. The analysis and notation in this post are based on the full proof of the BGW MPC protocol of Asharov and Lindell. This post is a continuation of our previous posts on secret sharing for passive and crash failures. [Read More]

Polynomial Secret Sharing with crash failures

We continue our series on polynomial secret sharing. In the previous post of this series we discussed secret sharing with a passive adversary. In this post we assume crash failures and in later posts we will extend to malicious failures. As before, we must assume parties have private channels: the adversary cannot see the content of messages sent between two non-faulty parties. [Read More]

A new Dolev-Reischuk style Lower Bound

In a previous post we discussed Crusader Broadcast and showed a $O(n^2)$ words, $O(1)$ time solution for $f<n$ and assuming a PKI. In this post, we overview a new Dolev-Reischuk style bower bound (see our full paper): [Read More]

He-HTLC - Revisiting Incentives in HTLC

Hashed Time-locked Contracts (HTLC) find many useful applications in the L2 Layer such as the lightning network and atomic swaps. In this post, we will focus on discussing protocols for implementing HTLC when taking into consideration incentives for parties in the system. We will discuss a line of work — WHF’19, MAD-HTLC, He-HTLC — towards developing an HTLC protocol secure in the presence of rational parties. [Read More]

DAG Meets BFT - The Next Generation of BFT Consensus

This post explains in simple words a recent development in the theory and practice of directed acyclic graph-based (DAG-based) Byzantine Fault Tolerance (BFT) consensus, published in three prestigious peer-reviewed conferences, and currently being implemented by several Blockchain companies, e.g., Aptos, Celo, Mysten Labs, and Somelier. [Read More]
Tags: consensus

Safe Permissionless Consensus

Nakamoto’s consensus protocol works in a permissionless model, where nodes can join and leave without notice. However, it guarantees agreement only probabilistically. Is this weaker guarantee a necessary concession to the severe demands of supporting a permissionless model? [Read More]

Crusader Broadcast

In previous posts we showed that the classic Dolev-Strong broadcast protocol takes $O(n^3)$ words and $t+1$ rounds and that Dolev Reischuk show that $\Omega(n^2)$ is needed and it is also known that $t+1$ rounds are needed. So while the number of rounds is optimal, to this day it remains an open question of obtaining $O(n^2)$ broadcast against a strongly adaptive adversary (see post for recent progress). [Read More]
Tags: dist101

Phase-King through the lens of Gradecast: A simple unauthenticated synchronous Byzantine Agreement protocol

In this post we overview a simple unauthenticated synchronous Byzantine Agreement protocol that is based on the Phase-King protocol of Berman, Garay, and Perry 1989-92. We refer also to Jonathan Katz’s excellent write-up on this same protocol from 2013. We offer a modern approach that decomposes the Phase-King protocol into a Gradecast building block. [Read More]
Tags: dist101

Asynchronous Agreement Part Three: a Modern version of Ben-Or's protocol

In this series of posts, we explore the marvelous world of consensus in the Asynchronous model. In this third post, we present a modern version of Ben-Or’s classic protocol that is part of our new work on Asynchronous Agreement. In the first post we defined the problem and in the second post we presented Ben-Or’s protocol. This is a simplified version extracted from our paper. [Read More]

Asynchronous Agreement Part Two: Ben-Or's protocol

We continue to explore the marvelous world of consensus in the Asynchronous model. In this post, we present Ben-Or’s classic protocol from 1983. In the next post, we will present a more modern version that is a simplified version from our paper. [Read More]