## 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 $f &lt; n$.... [Read More]

## Encrypted Blockchain Databases (Part II)

In this second part of the series on Encrypted Blockchain Databases, we are going to describe three schemes to store dynamic encrypted multi-maps (EMMs) on blockchains, each of which achieves different tradeoffs between query, add and delete efficiency. [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]