# My Presentation on Proof-of-Work vs. Proof-of-Stake Blockchain Protocols

I gave a talk in our seminar about the proof-of-work vs. the proof-of-stake blockchain paradigm. Although I don’t have an audio/video recording, here is a Google Slides rendering of my original Powerpoint slides. Some of the animations are out of place/order, but in general, it feels okay.

I intended this talk to be accessible in nature, so I intentionally skipped many details and strived not to flaunt any equation in it.

Advertised Summary: Bitcoin is a blockchain protocol where finalized transactions need a “proof of work”. Such protocols have been criticized for a high demand for computing power i.e., electricity. There is another family of protocols which deals with a “proof of stake”. In these protocols, the ability to make a transaction depends on your “stake” in the system instead of your computing power. In both cases, it is notoriously difficult to mathematically prove that these protocols are secure. Only a handful of provably secure protocols exist today. In this talk, I will tell a lighthearted story about the basics of the proof-of-work vs. proof-of-stake protocols. No equations but a lot of movie references.

# Ouroboros Proof-of-Stake Blockchain Protocol: Assumptions and Main Theorems

A blockchain protocol is essentially a distributed consensus protocol. A Proof-of-Work protocol such as Bitcoin requires a user to show a proof  — such as making a large number of computations — before he can add a block to an existing chain. Proof-of-Stake protocols, on the other hand, would not require “burning electricity” since the ability to “mine” a coin would depend only on the user’s current stake at the system.

The growing computing power of the bitcoin miners is already consuming a significant amount of electricity. One can easily see the necessity of a provably secure and efficient cryptocurrency without the heavy energy requirement. However, it is easier said than done. So far, I am aware of only three Proof-of-Stake protocols which give provable security guarantees. These are Ouroboros, led by Aggelos Kiayias, Alex Russell, and others; Snow White, led by Rafael Pass and Elaine Shi; Ouroboros Praos from the Ouroboros team; and Algorand, led by Silvio Micali. There is also an open-source initiative to implement Ourorboros, named Cardano.

In this post, I am going to present the main theorems of Ouroboros.

# Forkable Strings are Rare

In a blockchain protocol such as Bitcoin, the users see the world as a sequence of states. A simple yet functional view of this world, for the purpose of analysis, is a Boolean string $w = w_1, w_2, \cdots$ of zeros and ones, where each bit is independently biased towards $1$ favoring the “bad guys.”

A bad guy is activated when $w_t = 1$ for some $t$. He may try to present the good guys with a conflicting view of the world, such as presenting multiple candidate blockchains of equal length. This view is called a “fork”. A string $w$ that allows the bad guy to fork (with nonnegligible probability) is called a “forkable string”. Naturally, we would like to show that forkable strings are rare: that the manipulative power of the bad guys over the good guys is negligible.

Claim ([1], Bound 2). Suppose $w =w_1, \cdots, w_n$ is a Boolean string, with every bit independently set to $1$ with probability $(1-\epsilon)/2$ for some $\epsilon < 1$. The probability that $w$ is forkable is at most $\exp(-\epsilon^3n/2)$.

In this post, we present a commentary on the proof that forkable strings are rare. I like the proof because it uses simple facts about random walks, generating functions, and stochastic domination to bound an apparently difficult random process.