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Vitalik

Vitalik

3 years ago

An approximate introduction to how zk-SNARKs are possible (part 1)

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

  1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
  2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.


It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.

see part 2

(Edited)

More on Web3 & Crypto

Jeff John Roberts

Jeff John Roberts

3 years ago

Jack Dorsey and  Jay-Z Launch 'Bitcoin Academy' in Brooklyn rapper's home

The new Bitcoin Academy will teach Jay-Marcy Z's Houses neighbors "What is Cryptocurrency."
Jay-Z grew up in Brooklyn's Marcy Houses. The rapper and Block CEO Jack Dorsey are giving back to his hometown by creating the Bitcoin Academy.

The Bitcoin Academy will offer online and in-person classes, including "What is Money?" and "What is Blockchain?"
The program will provide participants with a mobile hotspot and a small amount of Bitcoin for hands-on learning.

Students will receive dinner and two evenings of instruction until early September. The Shawn Carter Foundation will help with on-the-ground instruction.

Jay-Z and Dorsey announced the program Thursday morning. It will begin at Marcy Houses but may be expanded.

Crypto Blockchain Plug and Black Bitcoin Billionaire, which has received a grant from Block, will teach the classes.

Jay-Z, Dorsey reunite

Jay-Z and Dorsey have previously worked together to promote a Bitcoin and crypto-based future.

In 2021, Dorsey's Block (then Square) acquired the rapper's streaming music service Tidal, which they propose using for NFT distribution.

Dorsey and Jay-Z launched an endowment in 2021 to fund Bitcoin development in Africa and India.

Dorsey is funding the new Bitcoin Academy out of his own pocket (as is Jay-Z), but he's also pushed crypto-related charitable endeavors at Block, including a $5 million fund backed by corporate Bitcoin interest.


This post is a summary. Read full article here

CyberPunkMetalHead

CyberPunkMetalHead

2 years ago

I talked to ChatGPT about the adoption of cryptocurrencies.

OpenAI's ChatGPT is an amazing AI-powered chatbot. It can write poetry, fiction, and marketing ideas. I was impressed how well ChatGPT followed the interview, albeit there were a few classics “I’m afraid I can’t do that”.

Full interview below.

Me: I'm your interviewer. We'll discuss crypto. Thanks for being interviewed. What do you think about cryptocurrency?

CGPT: Cryptocurrency is an innovative technology that could transform money and financial activities. It might boost the efficiency and security of financial institutions and let consumers deal directly without banks. Cryptocurrency is still a new and untested technology with many unknowns and hurdles before it can be broadly accepted.

Me: Over 22,000 cryptocurrencies exist, and many have little use. We need how much cryptocurrencies?

CGPT: The appropriate quantity will rely on a multitude of factors, including each cryptocurrency's use cases, adoption rate, and market rivalry. Only a few cryptocurrencies will likely receive widespread adoption and be successful. Many existing cryptocurrencies may not survive since they can't deliver new or valued solutions or compete with more established cryptocurrencies.

Me: Will cryptocurrencies grow? What's next for worldwide adoption?

CGPT: It's hard to forecast the future of cryptocurrencies because the acceptance of new technologies is unpredictable. I believe cryptocurrencies will expand and acquire popularity in the future years. Regulatory ambiguity, security concerns, and scalability issues must be overcome for this to happen. Cryptocurrency companies and organizations must engage together with governments and authorities to address these obstacles and establish a growth-friendly climate. Continued innovation and improvement of the technology, including public education and awareness, will drive acceptance.

Me: Do bear markets affect bitcoin adoption?

CGPT: On the one hand, a bear market might induce uncertainty and hesitation among potential consumers. Bear markets can present opportunities for long-term investors who can acquire cryptocurrencies at cheaper prices and are more likely to hang onto their assets. A bear market can also test the tenacity and power of the underlying technology and community, which can boost long-term confidence and adoption. A bear market might have profound and nuanced effects on bitcoin adoption.

Me: What are some likely outcomes if Bitcoin reaches $100,000 by next year?

CGPT: If Bitcoin saw rapid growth, it would undoubtedly have repercussions for the cryptocurrency market and economy. Possible scenarios include increased public interest and awareness of cryptocurrency, a surge in demand for Bitcoin and other cryptocurrencies, and a growth in the cryptocurrency industry's market value. By shifting their focus and cash to the cryptocurrency market, investors and traders may also affect other asset classes, such as traditional equities and commodities. Governments and financial organizations may focus more on the cryptocurrency sector as they try to grasp Bitcoin's rapid rise.

Me: Will other countries accept crypto as currency?

CGPT: It's hard to say if additional governments will adopt cryptocurrencies as legal tender. Some countries have recognized the promise of bitcoin and are exploring its use, while others are cautious. Adoption of bitcoin as legal cash may vary by country, based on financial infrastructure, rules, and political atmosphere. As cryptocurrency technology evolves and becomes more accepted, more governments may embrace it as legal tender.

Me: Final question: will the recent cryptocurrency hacks affect long term adoption?

CGPT: Hacks might tarnish cryptocurrency's reputation and public faith in its security, the technology underpinning it is continually improving. Many cryptocurrency projects have developed strong security mechanisms to prevent hacks and other dangers, and these safeguards will undoubtedly improve over time. The decentralized nature of cryptocurrency makes it more resistant to attacks. Hacks and other security breaches are a concern, but they may not affect cryptocurrency adoption.

Jayden Levitt

Jayden Levitt

3 years ago

The country of El Salvador's Bitcoin-obsessed president lost $61.6 million.

It’s only a loss if you sell, right?

Created by Author — Using Toonme

Nayib Bukele proclaimed himself “the world’s coolest dictator”.

His jokes aren't clear.

El Salvador's 43rd president self-proclaimed “CEO of El Salvador” couldn't be less presidential.

His thin jeans, aviator sunglasses, and baseball caps like a cartel lord.

He's popular, though.

Bukele won 53% of the vote by fighting violent crime and opposition party corruption.

El Salvador's 6.4 million inhabitants are riding the cryptocurrency volatility wave.

They were powerless.

Their autocratic leader, a former Yamaha Motors salesperson and Bitcoin believer, wants to help 70% unbanked locals.

He intended to give the citizens a way to save money and cut the country's $200 million remittance cost.

Transfer and deposit costs.

This makes logical sense when the president’s theatrics don’t blind you.

El Salvador's Bukele revealed plans to make bitcoin legal tender.

Remittances total $5.9 billion (23%) of the country's expenses.

Anything that reduces costs could boost the economy.

The country’s unbanked population is staggering. Here’s the data by % of people who either have a bank account (Blue) or a mobile money account (Black).

Source — statista.com

According to Bukele, 46% of the population has downloaded the Chivo Bitcoin Wallet.

In 2021, 36% of El Salvadorans had bank accounts.


Large rural countries like Kenya seem to have resolved their unbanked dilemma.

An economy surfaced where village locals would sell, trade and store network minutes and data as a store of value.

Kenyan phone networks realized unbanked people needed a safe way to accumulate wealth and have an emergency fund.

96% of Kenyans utilize M-PESA, which doesn't require a bank account.

The software involves human agents who hang out with cash and a phone.

These people are like ATMs.

You offer them cash to deposit money in your mobile money account or withdraw cash.

In a country with a faulty banking system, cash availability and a safe place to deposit it are important.

William Jack and Tavneet Suri found that M-PESA brought 194,000 Kenyan households out of poverty by making transactions cheaper and creating a safe store of value.

2016 Science paper

Mobile money, a service that allows monetary value to be stored on a mobile phone and sent to other users via text messages, has been adopted by most Kenyan households. We estimate that access to the Kenyan mobile money system M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty.

The impacts, which are more pronounced for female-headed households, appear to be driven by changes in financial behaviour — in particular, increased financial resilience and saving. Mobile money has therefore increased the efficiency of the allocation of consumption over time while allowing a more efficient allocation of labour, resulting in a meaningful reduction of poverty in Kenya.


Currently, El Salvador has 2,301 Bitcoin.

At publication, it's worth $44 million. That remains 41% of Bukele's original $105.6 million.

Unknown if the country has sold Bitcoin, but Bukeles keeps purchasing the dip.

It's still falling.

Source — Nayib Bukele — Twitter

This might be a fantastic move for the impoverished country over the next five years, if they can live economically till Bitcoin's price recovers.

The evidence demonstrates that a store of value pulls individuals out of poverty, but others say Bitcoin is premature.

You may regard it as an aggressive endeavor to front run the next wave of adoption, offering El Salvador a financial upside.

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Joe Procopio

Joe Procopio

3 years ago

Provide a product roadmap that can withstand startup velocities

This is how to build a car while driving.

Building a high-growth startup is compared to building a car while it's speeding down the highway.

How to plan without going crazy? Or, without losing team, board, and investor buy-in?

I just delivered our company's product roadmap for the rest of the year. Complete. Thorough. Page-long. I'm optimistic about its chances of surviving as everything around us changes, from internal priorities to the global economy.

It's tricky. This isn't the first time I've created a startup roadmap. I didn't invent a document. It took time to deliver a document that will be relevant for months.

Goals matter.

Although they never change, goals are rarely understood.

This is the third in a series about a startup's unique roadmapping needs. Velocity is the intensity at which a startup must produce to survive.

A high-growth startup moves at breakneck speed, which I alluded to when I said priorities and economic factors can change daily or weekly.

At that speed, a startup's roadmap must be flexible, bend but not break, and be brief and to the point. I can't tell you how many startups and large companies develop a product roadmap every quarter and then tuck it away.

Big, wealthy companies can do this. It's suicide for a startup.

The drawer thing happens because startup product roadmaps are often valid for a short time. The roadmap is a random list of features prioritized by different company factions and unrelated to company goals.

It's not because the goals changed that a roadmap is shelved or ignored. Because the company's goals were never communicated or documented in the context of its product.

In the previous post, I discussed how to turn company goals into a product roadmap. In this post, I'll show you how to make a one-page startup roadmap.

In a future post, I'll show you how to follow this roadmap. This roadmap helps you track company goals, something a roadmap must do.

Be vague for growth, but direct for execution.

Here's my plan. The real one has more entries and more content in each.

You can open this as an image at 1920 pixels

Let's discuss smaller boxes.

Product developers and engineers know that the further out they predict, the more wrong they'll be. When developing the product roadmap, this rule is ignored. Then it bites us three, six, or nine months later when we haven't even started.

Why do we put everything in a product roadmap like a project plan?

Yes, I know. We use it when the product roadmap isn't goal-based.

A goal-based roadmap begins with a document that outlines each goal's idea, execution, growth, and refinement.

You can open this as an image at 960 pixels

Once the goals are broken down into epics, initiatives, projects, and programs, only the idea and execution phases should be modeled. Any goal growth or refinement items should be vague and loosely mapped.

Why? First, any idea or execution-phase goal will result in growth initiatives that are unimaginable today. Second, internal priorities and external factors will change, but the goals won't. Locking items into calendar slots reduces flexibility and forces deviation from the single source of truth.

No soothsayers. Predicting the future is pointless; just prepare.

A map is useless if you don't know where you're going.

As we speed down the road, the car and the road will change. Goals define the destination.

This quarter and next quarter's roadmap should be set. After that, you should track destination milestones, not how to get there.

When you do that, even the most critical investors will understand the roadmap and buy in. When you track progress at the end of the quarter and revise your roadmap, the destination won't change.

Jared Heyman

Jared Heyman

2 years ago

The survival and demise of Y Combinator startups

I've written a lot about Y Combinator's success, but as any startup founder or investor knows, many startups fail.

Rebel Fund invests in the top 5-10% of new Y Combinator startups each year, so we focus on identifying and supporting the most promising technology startups in our ecosystem. Given the power law dynamic and asymmetric risk/return profile of venture capital, we worry more about our successes than our failures. Since the latter still counts, this essay will focus on the proportion of YC startups that fail.

Since YC's launch in 2005, the figure below shows the percentage of active, inactive, and public/acquired YC startups by batch.

As more startups finish, the blue bars (active) decrease significantly. By 12 years, 88% of startups have closed or exited. Only 7% of startups reach resolution each year.

YC startups by status after 12 years:

Half the startups have failed, over one-third have exited, and the rest are still operating.

In venture investing, it's said that failed investments show up before successful ones. This is true for YC startups, but only in their early years.

Below, we only present resolved companies from the first chart. Some companies fail soon after establishment, but after a few years, the inactive vs. public/acquired ratio stabilizes around 55:45. After a few years, a YC firm is roughly as likely to quit as fail, which is better than I imagined.

I prepared this post because Rebel investors regularly question me about YC startup failure rates and how long it takes for them to exit or shut down.

Early-stage venture investors can overlook it because 100x investments matter more than 0x investments.

YC founders can ignore it because it shouldn't matter if many of their peers succeed or fail ;)

Florian Wahl

Florian Wahl

3 years ago

An Approach to Product Strategy

I've been pondering product strategy and how to articulate it. Frameworks helped guide our thinking.

If your teams aren't working together or there's no clear path to victory, your product strategy may not be well-articulated or communicated (if you have one).

Before diving into a product strategy's details, it's important to understand its role in the bigger picture — the pieces that move your organization forward.

the overall picture

A product strategy is crucial, in my opinion. It's part of a successful product or business. It's the showpiece.

The Big Picture: Vision, Product Strategy, Goals, Roadmap

To simplify, we'll discuss four main components:

  1. Vision

  2. Product Management

  3. Goals

  4. Roadmap

Vision

Your company's mission? Your company/product in 35 years? Which headlines?

The vision defines everything your organization will do in the long term. It shows how your company impacted the world. It's your organization's rallying cry.

An ambitious but realistic vision is needed.

Without a clear vision, your product strategy may be inconsistent.

Product Management

Our main subject. Product strategy connects everything. It fulfills the vision.

In Part 2, we'll discuss product strategy.

Goals

This component can be goals, objectives, key results, targets, milestones, or whatever goal-tracking framework works best for your organization.

These product strategy metrics will help your team prioritize strategies and roadmaps.

Your company's goals should be unified. This fuels success.

Roadmap

The roadmap is your product strategy's timeline. It provides a prioritized view of your team's upcoming deliverables.

A roadmap is time-bound and includes measurable goals for your company. Your team's steps and capabilities for executing product strategy.

If your team has trouble prioritizing or defining a roadmap, your product strategy or vision is likely unclear.

Formulation of a Product Strategy

Now that we've discussed where your product strategy fits in the big picture, let's look at a framework.

Product Strategy Framework: Challenges, Decided Approach, Actions

A product strategy should include challenges, an approach, and actions.

Challenges

First, analyze the problems/situations you're solving. It can be customer- or company-focused.

The analysis should explain the problems and why they're important. Try to simplify the situation and identify critical aspects.

Some questions:

  • What issues are we attempting to resolve?

  • What obstacles—internal or otherwise—are we attempting to overcome?

  • What is the opportunity, and why should we pursue it, in your opinion?

Decided Method

Second, describe your approach. This can be a set of company policies for handling the challenge. It's the overall approach to the first part's analysis.

The approach can be your company's bets, the solutions you've found, or how you'll solve the problems you've identified.

Again, these questions can help:

  • What is the value that we hope to offer to our clients?

  • Which market are we focusing on first?

  • What makes us stand out? Our benefit over rivals?

Actions

Third, identify actions that result from your approach. Second-part actions should be these.

Coordinate these actions. You may need to add products or features to your roadmap, acquire new capabilities through partnerships, or launch new marketing campaigns. Whatever fits your challenges and strategy.

Final questions:

  • What skills do we need to develop or obtain?

  • What is the chosen remedy? What are the main outputs?

  • What else ought to be added to our road map?

Put everything together

… and iterate!

Strategy isn't one-and-done. Changes occur. Economies change. Competitors emerge. Customer expectations change.

One unexpected event can make strategies obsolete quickly. Muscle it. Review, evaluate, and course-correct your strategies with your teams. Quarterly works. In a new or unstable industry, more often.