Decentralized Thoughts is a group blog on decentralization, by decentralized thinkers, for decentralized thoughts, of decentralized matters. Decentralized Thoughts is a group blog on decentralization, by decentralized thinkers, for decentralized thoughts, of decentralized matters.

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]

EIP-1559 In Retrospect

On August 5, 2021, Ethereum implemented Ethereum Improvement Proposal 1559 (EIP-1559) on its mainnet as part of the London Hardfork, which modified the transaction fee mechanism on Ethereum from a first price auction to one that involves blocks of varying sizes, separating transaction fees as history-dependent base fees and tips, and burning of the base fees. How does such a mechanism fare in practice? [Read More]

Colordag: From always-almost to almost-always 50% selfish mining resilience

The Selfish mining attack against blockchain protocols was discovered and formalized in 2013 by Eyal and Sirer (also see our blog post). The Bitcoin community has mentioned similar types of attacks in 2010. This attack remains a vulnerability of all operational blockchains we are aware of. For Bitcoin’s blockchain algorithm (under reasonable network assumptions), a coalition controlling over 1/4 of the mining power can improve its revenue using this attack.... [Read More]

Blockchain Resource Pools and a CAP-esque Impossibility Result

The consensus layers of different blockchain protocols can look very different from one another. For example, to achieve sybil-resistance, some protocols use proof-of-work (selecting each block producer randomly, with probability proportional to its computational power), while some use proof-of-stake (with probabilities proportional to the amount of locked-up stake). To achieve consensus, some blockchain protocols use a longest-chain rule to resolve forks in-protocol, while others use BFT-style consensus to (with high... [Read More]