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. [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]

The First Blockchain or How to Time-Stamp a Digital Document

This post is about the work of Stuart Haber and W. Scott Stornetta from 1991 on How to Time-Stamp a Digital Document and their followup paper Improving the Efficiency and Reliability of Digital Time-Stamping. In many ways, this work introduced the idea of a chain of hashes to create a total order of commitments to a dynamically growing set of documents. It’s no wonder these two papers are cited by... [Read More]

On the Optimality of Optimistic Responsiveness

Synchronous consensus protocols tolerating Byzantine failures depend on the maximum network delay $\Delta$ for their safety and progress. The delay, $\Delta$ is usually much larger than actual network delay $\delta$ since $\Delta$ is a pessimistic value. While synchronous protocols tolerating more than one-third will have executions with at least a $\Delta$ latency, recent synchronous protocols such as Sync HotStuff have been trying to reduce the reliance on $\Delta$ as much... [Read More]