The idea of decomposing a hard problem into easier problems is a fundamental algorithm design pattern in Computer Science. Divide and Conquer is used in so many domains: sorting, multiplication, and FFT, to mention a few. But what about distributed computing?
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## HotStuff-1 and the Prefix Speculation Dilemma in BFT Consensus

Several approaches aim to reduce the number of network hops to reach finality in BFT Consensus protocols through speculation. They differ in their methods and in their guarantees, yet they all face a common phenomenon referred to as the prefix speculation dilemma.
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## The SAP theorem for storing secret keys

Public key cryptography (PKC) is a fundamental technology that is a key enabler to the Internet and the whole client-server paradigm. Without public key cryptography there would be no cryptocurrencies, no online bank accounts, no online retail, etc.
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## What is Verifiable Information Dispersal?

Verifiable Information Dispersal (or VID) has its roots in the work of Michael Rabin, 1989 which introduced the notion of Information Dispersal (ID). Adding verifiability (referred to as binding in this post) to obtain VIDs was done by Garay, Gennaro, Jutla, and Rabin, 1998 (called SSRI). Cachin and Tessaro, 2004 introduced the notion of Asynchronous VID (or AVID). See LDDRVXG21 for state-of-the-art.
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## Shoal++: High Throughput DAG-BFT Can Be Fast!

TL;DR: Shoal++ is a novel DAG-BFT system that supercharges Shoal to achieve near-optimal theoretical latency while preserving the high throughput and robustness of state-of-the-art certified DAG BFT protocols.
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## Sailfish: Improving the Latency of DAG-based BFT

In this blog post, we will explain the core ideas behind Sailfish, a latency-efficient DAG-based protocol. In essence, Sailfish is a reliable-broadcast (RBC) based DAG protocol that supports leaders in every RBC round. It commits leader vertices within 1RBC + $\delta$ time and non-leader vertices within 2RBC + $\delta$ time, outperforming the state-of-the-art in terms of these latencies (where $\delta$ represents the actual network delay).
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## Decentralization of Ethereum Builder Market

Decentralization is a core underpinning of blockchains. Is today’s blockchain really decentralized?
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## Consensus tolerating one mobile crash in synchrony or one crash is asynchrony must have infinite executions for the same simple reason

In a consensus protocol parties have an input (at least two possible values, say 0 or 1) and may output a decision value such that:
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## In between Crash and Omission failures

In this post we explore adversary failure models that are in between crash and omission:
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## Early Stopping is same but different: two rounds are needed even in failure free executions

Many systems try to optimize executions that are failure free. If we absolutely knew that there will be no failures, parties could simply send each other messages with our inputs and reach consensus by outputting, say, the majority value. Thus completing the protocol after one round. What happens if there may be a crash failure? Say you have 100 servers and at most one can crash, can you devise a...
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## Gather with Binding and Verifiability

We extend the Gather protocol with two important properties: Binding and Verifiability. This post is based on and somewhat simplifies the information theoretic gather protocol in our recent ACS work with Gilad Asharov and Arpita Patra.
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## Simpler Security proof for Nakamoto Consensus

Four years ago (time flies!), I made a post on a simple security proof for Nakamoto consensus. While the proof intuition, as outlined in that post, is still reasonably simple, the actual proof has become quite delicate and crafty over the years. What happened was that some colleagues – Chen Feng at UBC and Dongning Guo at Northwestern – identified very subtle flaws in the proof, and clever mathematical maneuvers...
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## Scaling Blockchains: the Power of Batching

A few years ago if you asked “Can blockchains scale?” most people would give three reasons why, fundamentally, the answer is “No!”
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## The Fast Fourier Transform over finite fields

The Fast Fourier Transform (FFT) developed by Cooley and Tukey in 1965 has its origins in the work of Gauss. The FFT, its variants and extensions to finite fields, are a fundamental algorithmic tool and a beautiful example of interplay between algebra and combinatorics. There are many great resources on FFT, see ingopedia’s curated list.
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## Asynchronous Agreement on a Core Set

A challenging step in many asynchronous protocols is agreeing on a set of parties that completed some task. For example, an asynchronous protocol might start off with parties reliably broadcasting a value. Due to asynchrony and having $\leq f$ corruptions, honest parties can only wait for $n-f$ parties to complete the task. Parties may need to agree on a core set of $n-f$ such broadcasts and use them in the...
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## Can we Obtain Privacy in a Private Proof-of-Stake Blockchain? Part-II

This is Part-II of a two-part post on privacy in private proof-of-stake blockchains. In Part-I, we explored attacks on existing private PoS approaches. In this post, we will discuss some ways to obtain privacy (at the expense of safety and/or liveness).
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## Can we Obtain Privacy in a Private Proof-of-Stake Blockchain? Part-I

In this two-part post, we focus on the challenges and subtleties involved in obtaining privacy in private proof-of-stake (PoS) blockchains. For instance, designs that attempt to obtain privacy for transaction details while still relying on PoS, such as Ouroboros Crypsinous. The first part explains attacks on existing approaches, and the second part focuses on potential workarounds using differential privacy. These posts explain the intuitive ideas behind the works of Madathil...
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## The CAP Theorem and why State Machine Replication for Two Servers and One Crash Failure is Impossible in Partial Synchrony

In 1999, Fox and Brewer published a paper on the CAP principle, where they wrote:
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## $3f+1$ is needed in Partial Synchrony even against a Rollback adversary

We covered the classic DLS88 split brain impossibility result against a Byzantine adversary in a previous post:
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## Blockchains + TEEs Day 2 Summary

This is the second of the two part post on the workshop on Blockchains + TEEs that concluded last week. Here are the key ideas from Day 2. You can find the post summarizing Day 1 here.
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