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.

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. [Read More]
Tags: polynomials

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... [Read More]
Tags: consensus MPC

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... [Read More]

Blockchains + TEEs Day 1 Summary

Our workshop on Blockchains + TEEs concluded last week. We had a fantastic series of talks and discussions on both days of the workshop. In this two part post, we highlight some key takeaways from each of the days. [Read More]

Randomization and Consensus - synchronous binary agreement for minority omission failures

Continuing the series on simple ways where randomization can help solve consensus. The model is lock-step (synchrony) with $f<n/2$ omission failures. We know that in the worst case reaching agreement takes at least $f+1$ rounds. Can randomization help reduce the expected number of rounds? In the post, we show a simple randomized consensus algorithm including a simple weak coin protocol. [Read More]

Can we Obtain Player Replaceability and Forensic Support Simultaneously?

Forensic support is an important property of BFT protocols that addresses the other side of security: what happens when the number of malicious parties exceeds the allowable threshold? In a previous post, we systematically studied different BFT protocols to assess their ability to detect and prove malicious behavior when safety is violated. We learned that protocols such as PBFT and HotStuff with ${\sf poly}(n)$ communication have strong forensic support, meaning... [Read More]

What are Blockchains Useful for, Really?

Blockchains, or the decentralized ledger, are touted as the next big disruptive technology, as big as the Internet was in the 90s. What are these blockchains useful for, really? While there are relevant use cases, many examples people use that are either far too academic to be useful or are scenarios where blockchains are not the right solution in the first place. Thus, in this post, I am trying to... [Read More]
Tags: blockchain

Pairing-based Anonymous Credentials and the Power of Re-randomization

David Chaum wrote in 1985: Large-scale automated transaction systems are imminent. The architecture chosen for these systems may have a long-term impact on the centralization of our economic system, on some of our basic liberties, and even on our democracy. The initial choice of direction will gather economic and societal momentum, making reversal increasingly less likely. [Read More]

Responsiveness under omission failures

In this post, we discuss log replication responsiveness in the context of omission failures. We show how to transform the protocol in our previous post to a multi-shot version of Paxos for omission faults. The Byzantine failure case uses similar ideas and is covered in the next post of this series. [Read More]

Set Replication - fault tolerance without total ordering

While state machine replication is the gold standard for implementing any (public) ideal functionality, its power comes at the cost of needing to totally order all transactions and as a consequence solve (Byzantine) agreement. In some cases this overhead is unnecessary. [Read More]
Tags: dist101

What is Responsiveness?

In asynchronous protocols, latency to commit is a function of the actual maximum network delay $\delta$. In synchronous protocols, message delay is bounded by $\Delta$, and for $n/3 \leq f < n/2$, the $\Delta$ bound is used to obtain both safety and liveness. In partial synchrony, message delay is bounded by $\Delta$ after GST, and the $\Delta$ bound is used to obtain liveness. [Read More]
Tags: dist101