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Muthinja

Muthinja

3 years ago

Why don't you relaunch my startup projects?

More on Entrepreneurship/Creators

Aaron Dinin, PhD

Aaron Dinin, PhD

3 years ago

There Are Two Types of Entrepreneurs in the World Make sure you are aware of your type!

Know why it's important.

Photo by Brendan Church on Unsplash

The entrepreneur I was meeting with said, "I should be doing crypto, or maybe AI? Aren't those the hot spots? I should look there for a startup idea.”

I shook my head. Yes, they're exciting, but that doesn't mean they're best for you and your business.

“There are different types of entrepreneurs?” he asked.

I said "obviously." Two types, actually. Knowing what type of entrepreneur you are helps you build the right startup.

The two types of businesspeople

The best way for me to describe the two types of entrepreneurs is to start by telling you exactly the kinds of entrepreneurial opportunities I never get excited about: future opportunities.

In the early 1990s, my older brother showed me the World Wide Web and urged me to use it. Unimpressed, I returned to my Super Nintendo.

My roommate tried to get me to join Facebook as a senior in college. I remember thinking, This is dumb. Who'll use it?

In 2011, my best friend tried to convince me to buy bitcoin and I laughed.

Heck, a couple of years ago I had to buy a new car, and I never even considered buying something that didn’t require fossilized dinosaur bones.

I'm no visionary. I don't anticipate the future. I focus on the present.

This tendency makes me a problem-solving entrepreneur. I identify entrepreneurial opportunities by spotting flaws and/or inefficiencies in the world and devising solutions.

There are other ways to find business opportunities. Visionary entrepreneurs also exist. I don't mean visionary in the hyperbolic sense that implies world-changing impact. I mean visionary as an entrepreneur who identifies future technological shifts that will change how people work and live and create new markets.

Problem-solving and visionary entrepreneurs are equally good. But the two approaches to building companies are very different. Knowing the type of entrepreneur you are will help you build a startup that fits your worldview.

What is the distinction?

Let's use some simple hypotheticals to compare problem-solving and visionary entrepreneurship.

Imagine a city office building without nearby restaurants. Those office workers love to eat. Sometimes they'd rather eat out than pack a lunch. As an entrepreneur, you can solve the lack of nearby restaurants. You'd open a restaurant near that office, say a pizza parlor, and get customers because you solved the lack of nearby restaurants. Problem-solving entrepreneurship.

Imagine a new office building in a developing area with no residents or workers. In this scenario, a large office building is coming. The workers will need to eat then. As a visionary entrepreneur, you're excited about the new market and decide to open a pizzeria near the construction to meet demand.

Both possibilities involve the same product. You opened a pizzeria. How you launched that pizza restaurant and what will affect its success are different.

Why is the distinction important?

Let's say you opened a pizzeria near an office. You'll probably get customers. Because people are nearby and demand isn't being met, someone from a nearby building will stop in within the first few days of your pizzeria's grand opening. This makes solving the problem relatively risk-free. You'll get customers unless you're a fool.

The market you're targeting existed before you entered it, so you're not guaranteed success. This means people in that market solved the lack of nearby restaurants. Those office workers are used to bringing their own lunches. Why should your restaurant change their habits? Even when they eat out, they're used to traveling far. They've likely developed pizza preferences.

To be successful with your problem-solving startup, you must convince consumers to change their behavior, which is difficult.

Unlike opening a pizza restaurant near a construction site. Once the building opens, workers won't have many preferences or standardized food-getting practices. Your pizza restaurant can become the incumbent quickly. You'll be the first restaurant in the area, so you'll gain a devoted following that makes your food a routine.

Great, right? It's easier than changing people's behavior. The benefit comes with a risk. Opening a pizza restaurant near a construction site increases future risk. What if builders run out of money? No one moves in? What if the building's occupants are the National Association of Pizza Haters? Then you've opened a pizza restaurant next to pizza haters.

Which kind of businessperson are you?

This isn't to say one type of entrepreneur is better than another. Each type of entrepreneurship requires different skills.

As my simple examples show, a problem-solving entrepreneur must operate in markets with established behaviors and habits. To be successful, you must be able to teach a market a new way of doing things.

Conversely, the challenge of being a visionary entrepreneur is that you have to be good at predicting the future and getting in front of that future before other people.

Both are difficult in different ways. So, smart entrepreneurs don't just chase opportunities. Smart entrepreneurs pursue opportunities that match their skill sets.

Jim Siwek

Jim Siwek

3 years ago

In 2022, can a lone developer be able to successfully establish a SaaS product?

Photo by Austin Distel on Unsplash

In the early 2000s, I began developing SaaS. I helped launch an internet fax service that delivered faxes to email inboxes. Back then, it saved consumers money and made the procedure easier.

Google AdWords was young then. Anyone might establish a new website, spend a few hundred dollars on keywords, and see dozens of new paying clients every day. That's how we launched our new SaaS, and these clients stayed for years. Our early ROI was sky-high.

Changing times

The situation changed dramatically after 15 years. Our paid advertising cost $200-$300 for every new customer. Paid advertising takes three to four years to repay.

Fortunately, we still had tens of thousands of loyal clients. Good organic rankings gave us new business. We needed less sponsored traffic to run a profitable SaaS firm.

Is it still possible?

Since selling our internet fax firm, I've dreamed about starting a SaaS company. One I could construct as a lone developer and progressively grow a dedicated customer base, as I did before in a small team.

It seemed impossible to me. Solo startups couldn't afford paid advertising. SEO was tough. Even the worst SaaS startup ideas attracted VC funding. How could I compete with startups that could hire great talent and didn't need to make money for years (or ever)?

The One and Only Way to Learn

After years of talking myself out of SaaS startup ideas, I decided to develop and launch one. I needed to know if a solitary developer may create a SaaS app in 2022.

Thus, I did. I invented webwriter.ai, an AI-powered writing tool for website content, from hero section headlines to blog posts, this year. I soft-launched an MVP in July.

Considering the Issue

Now that I've developed my own fully capable SaaS app for site builders and developers, I wonder if it's still possible. Can webwriter.ai be successful?

I know webwriter.ai's proposal is viable because Jasper.ai and Grammarly are also AI-powered writing tools. With competition comes validation.

To Win, Differentiate

To compete with well-funded established brands, distinguish to stand out to a portion of the market. So I can speak directly to a target user, unlike larger competition.

I created webwriter.ai to help web builders and designers produce web content rapidly. This may be enough differentiation for now.

Budget-Friendly Promotion

When paid search isn't an option, we get inventive. There are more tools than ever to promote a new website.

  • Organic Results

  • on social media (Twitter, Instagram, TikTok, LinkedIn)

  • Marketing with content that is compelling

  • Link Creation

  • Listings in directories

  • references made in blog articles and on other websites

  • Forum entries

The Beginning of the Journey

As I've labored to construct my software, I've pondered a new mantra. Not sure where that originated from, but I like it. I'll live by it and teach my kids:

“Do the work.”

cdixon

cdixon

3 years ago

2000s Toys, Secrets, and Cycles

During the dot-com bust, I started my internet career. People used the internet intermittently to check email, plan travel, and do research. The average internet user spent 30 minutes online a day, compared to 7 today. To use the internet, you had to "log on" (most people still used dial-up), unlike today's always-on, high-speed mobile internet. In 2001, Amazon's market cap was $2.2B, 1/500th of what it is today. A study asked Americans if they'd adopt broadband, and most said no. They didn't see a need to speed up email, the most popular internet use. The National Academy of Sciences ranked the internet 13th among the 100 greatest inventions, below radio and phones. The internet was a cool invention, but it had limited uses and wasn't a good place to build a business. 

A small but growing movement of developers and founders believed the internet could be more than a read-only medium, allowing anyone to create and publish. This is web 2. The runner up name was read-write web. (These terms were used in prominent publications and conferences.) 

Web 2 concepts included letting users publish whatever they want ("user generated content" was a buzzword), social graphs, APIs and mashups (what we call composability today), and tagging over hierarchical navigation. Technical innovations occurred. A seemingly simple but important one was dynamically updating web pages without reloading. This is now how people expect web apps to work. Mobile devices that could access the web were niche (I was an avid Sidekick user). 

The contrast between what smart founders and engineers discussed over dinner and on weekends and what the mainstream tech world took seriously during the week was striking. Enterprise security appliances, essentially preloaded servers with security software, were a popular trend. Many of the same people would talk about "serious" products at work, then talk about consumer internet products and web 2. It was tech's biggest news. Web 2 products were seen as toys, not real businesses. They were hobbies, not work-related. 

There's a strong correlation between rich product design spaces and what smart people find interesting, which took me some time to learn and led to blog posts like "The next big thing will start out looking like a toy" Web 2's novel product design possibilities sparked dinner and weekend conversations. Imagine combining these features. What if you used this pattern elsewhere? What new product ideas are next? This excited people. "Serious stuff" like security appliances seemed more limited. 

The small and passionate web 2 community also stood out. I attended the first New York Tech meetup in 2004. Everyone fit in Meetup's small conference room. Late at night, people demoed their software and chatted. I have old friends. Sometimes I get asked how I first met old friends like Fred Wilson and Alexis Ohanian. These topics didn't interest many people, especially on the east coast. We were friends. Real community. Alex Rampell, who now works with me at a16z, is someone I met in 2003 when a friend said, "Hey, I met someone else interested in consumer internet." Rare. People were focused and enthusiastic. Revolution seemed imminent. We knew a secret nobody else did. 

My web 2 startup was called SiteAdvisor. When my co-founders and I started developing the idea in 2003, web security was out of control. Phishing and spyware were common on Internet Explorer PCs. SiteAdvisor was designed to warn users about security threats like phishing and spyware, and then, using web 2 concepts like user-generated reviews, add more subjective judgments (similar to what TrustPilot seems to do today). This staged approach was common at the time; I called it "Come for the tool, stay for the network." We built APIs, encouraged mashups, and did SEO marketing. 

Yahoo's 2005 acquisitions of Flickr and Delicious boosted web 2 in 2005. By today's standards, the amounts were small, around $30M each, but it was a signal. Web 2 was assumed to be a fun hobby, a way to build cool stuff, but not a business. Yahoo was a savvy company that said it would make web 2 a priority. 

As I recall, that's when web 2 started becoming mainstream tech. Early web 2 founders transitioned successfully. Other entrepreneurs built on the early enthusiasts' work. Competition shifted from ideation to execution. You had to decide if you wanted to be an idealistic indie bar band or a pragmatic stadium band. 

Web 2 was booming in 2007 Facebook passed 10M users, Twitter grew and got VC funding, and Google bought YouTube. The 2008 financial crisis tested entrepreneurs' resolve. Smart people predicted another great depression as tech funding dried up. 

Many people struggled during the recession. 2008-2011 was a golden age for startups. By 2009, talented founders were flooding Apple's iPhone app store. Mobile apps were booming. Uber, Venmo, Snap, and Instagram were all founded between 2009 and 2011. Social media (which had replaced web 2), cloud computing (which enabled apps to scale server side), and smartphones converged. Even if social, cloud, and mobile improve linearly, the combination could improve exponentially. 

This chart shows how I view product and financial cycles. Product and financial cycles evolve separately. The Nasdaq index is a proxy for the financial sentiment. Financial sentiment wildly fluctuates. 

Next row shows iconic startup or product years. Bottom-row product cycles dictate timing. Product cycles are more predictable than financial cycles because they follow internal logic. In the incubation phase, enthusiasts build products for other enthusiasts on nights and weekends. When the right mix of technology, talent, and community knowledge arrives, products go mainstream. (I show the biggest tech cycles in the chart, but smaller ones happen, like web 2 in the 2000s and fintech and SaaS in the 2010s.) 

Tech has changed since the 2000s. Few tech giants dominate the internet, exerting economic and cultural influence. In the 2000s, web 2 was ignored or dismissed as trivial. Entrenched interests respond aggressively to new movements that could threaten them. Creative patterns from the 2000s continue today, driven by enthusiasts who see possibilities where others don't. Know where to look. Crypto and web 3 are where I'd start. 

Today's negative financial sentiment reminds me of 2008. If we face a prolonged downturn, we can learn from 2008 by preserving capital and focusing on the long term. Keep an eye on the product cycle. Smart people are interested in things with product potential. This becomes true. Toys become necessities. Hobbies become mainstream. Optimists build the future, not cynics.


Full article is available here

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Cory Doctorow

Cory Doctorow

3 years ago

The downfall of the Big Four accounting companies is just one (more) controversy away.

Economic mutual destruction.

Multibillion-dollar corporations never bothered with an independent audit, and they all lied about their balance sheets.

It's easy to forget that the Big Four accounting firms are lousy fraud enablers. Just because they sign off on your books doesn't mean you're not a hoax waiting to erupt.

This is *crazy* Capitalism depends on independent auditors. Rich folks need to know their financial advisers aren't lying. Rich folks usually succeed.

No accounting. EY, KPMG, PWC, and Deloitte make more money consulting firms than signing off on their accounts.

The Big Four sign off on phony books because failing to make friends with unscrupulous corporations may cost them consulting contracts.

The Big Four are the only firms big enough to oversee bankruptcy when they sign off on fraudulent books, as they did for Carillion in 2018. All four profited from Carillion's bankruptcy.

The Big Four are corrupt without any consequences for misconduct. Who can forget when KPMG's top management was fined millions for helping auditors cheat on ethics exams?

Consulting and auditing conflict. Consultants help a firm cover its evil activities, such as tax fraud or wage theft, whereas auditors add clarity to a company's finances. The Big Four make more money from cooking books than from uncooking them, thus they are constantly embroiled in scandals.

If a major scandal breaks, it may bring down the entire sector and substantial parts of the economy. Jim Peterson explains system risk for The Dig.

The Big Four are voluntary private partnerships where accountants invest their time, reputations, and money. If a controversy threatens the business, partners who depart may avoid scandal and financial disaster.

When disaster looms, each partner should bolt for the door, even if a disciplined stay-and-hold posture could weather the storm. This happened to Arthur Andersen during Enron's collapse, and a 2006 EU report recognized the risk to other corporations.

Each partner at a huge firm knows how much dirty laundry they've buried in the company's garden, and they have well-founded suspicions about what other partners have buried, too. When someone digs, everyone runs.

If a firm confronts substantial litigation damages or enforcement penalties, it could trigger the collapse of one of the Big Four. That would be bad news for the firm's clients, who would have trouble finding another big auditor.

Most of the world's auditing capacity is concentrated in four enormous, brittle, opaque, compromised organizations. If one of them goes bankrupt, the other three won't be able to take on its clients.

Peterson: Another collapse would strand many of the world's large public businesses, leaving them unable to obtain audit views for their securities listings and regulatory compliance.

Count Down: The Past, Present, and Uncertain Future of the Big Four Accounting Firms is in its second edition.

https://www.emerald.com/insight/publication/doi/10.1108/9781787147003

Julie Plavnik

Julie Plavnik

3 years ago

How to Become a Crypto Broker [Complying and Making Money]

Three options exist. The third one is the quickest and most fruitful.

How To Become a Cryptocurrency Broker?

You've mastered crypto trading and want to become a broker.

So you may wonder: Where to begin?

If so, keep reading.

Today I'll compare three different approaches to becoming a cryptocurrency trader.

What are cryptocurrency brokers, and how do they vary from stockbrokers?

A stockbroker implements clients' market orders (retail or institutional ones).

Brokerage firms are regulated, insured, and subject to regulatory monitoring.

Stockbrokers are required between buyers and sellers. They can't trade without a broker. To trade, a trader must open a broker account and deposit money. When a trader shops, he tells his broker what orders to place.

Crypto brokerage is trade intermediation with cryptocurrency.

In crypto trading, however, brokers are optional.

Crypto exchanges offer direct transactions. Open an exchange account (no broker needed) and make a deposit.

Question:

Since crypto allows DIY trading, why use a broker?

Let's compare cryptocurrency exchanges vs. brokers.

Broker versus cryptocurrency exchange

Most existing crypto exchanges are basically brokers.

Examine their primary services:

  • connecting purchasers and suppliers

  • having custody of clients' money (with the exception of decentralized cryptocurrency exchanges),

  • clearance of transactions.

Brokerage is comparable, don't you think?

There are exceptions. I mean a few large crypto exchanges that follow the stock exchange paradigm. They outsource brokerage, custody, and clearing operations. Classic exchange setups are rare in today's bitcoin industry.

Back to our favorite “standard” crypto exchanges. All-in-one exchanges and brokers. And usually, they operate under a broker or a broker-dealer license, save for the exchanges registered somewhere in a free-trade offshore paradise. Those don’t bother with any licensing.

What’s the sense of having two brokers at a time?

Better liquidity and trading convenience.

The crypto business is compartmentalized.

We have CEXs, DEXs, hybrid exchanges, and semi-exchanges (those that aggregate liquidity but do not execute orders on their sides). All have unique regulations and act as sovereign states.

There are about 18k coins and hundreds of blockchain protocols, most of which are heterogeneous (i.e., different in design and not interoperable).

A trader must register many accounts on different exchanges, deposit funds, and manage them all concurrently to access global crypto liquidity.

It’s extremely inconvenient.

Crypto liquidity fragmentation is the largest obstacle and bottleneck blocking crypto from mass adoption.

Crypto brokers help clients solve this challenge by providing one-gate access to deep and diverse crypto liquidity from numerous exchanges and suppliers. Professionals and institutions need it.

Another killer feature of a brokerage may be allowing clients to trade crypto with fiat funds exclusively, without fiat/crypto conversion. It is essential for professional and institutional traders.

Who may work as a cryptocurrency broker?

Apparently, not anyone. Brokerage requires high-powered specialists because it involves other people's money.

Here's the essentials:

  • excellent knowledge, skills, and years of trading experience

  • high-quality, quick, and secure infrastructure

  • highly developed team

  • outstanding trading capital

  • High-ROI network: long-standing, trustworthy connections with customers, exchanges, liquidity providers, payment gates, and similar entities

  • outstanding marketing and commercial development skills.

What about a license for a cryptocurrency broker? Is it necessary?

Complex question.

If you plan to play in white-glove jurisdictions, you may need a license. For example, in the US, as a “money transmitter” or as a CASSP (crypto asset secondary services provider) in Australia.

Even in these jurisdictions, there are no clear, holistic crypto brokerage and licensing policies.

Your lawyer will help you decide if your crypto brokerage needs a license.

Getting a license isn't quick. Two years of patience are needed.

How can you turn into a cryptocurrency broker?

Finally, we got there! 🎉

Three actionable ways exist:

  1. To kickstart a regulated stand-alone crypto broker

  2. To get a crypto broker franchise, and

  3. To become a liquidity network broker.

Let's examine each.

1. Opening a regulated cryptocurrency broker

It's difficult. Especially If you're targeting first-world users.

You must comply with many regulatory, technical, financial, HR, and reporting obligations to keep your organization running. Some are mentioned above.

The licensing process depends on the products you want to offer (spots or derivatives) and the geographic areas you plan to service. There are no general rules for that.

In an overgeneralized way, here are the boxes you will have to check:

  • capital availability (usually a large amount of capital c is required)

  • You will have to move some of your team members to the nation providing the license in order to establish an office presence there.

  • the core team with the necessary professional training (especially applies to CEO, Head of Trading, Assistant to Head of Trading, etc.)

  • insurance

  • infrastructure that is trustworthy and secure

  • adopted proper AML/KYC/financial monitoring policies, etc.

Assuming you passed, what's next?

I bet it won’t be mind-blowing for you that the license is just a part of the deal. It won't attract clients or revenue.

To bring in high-dollar clientele, you must be a killer marketer and seller. It's not easy to convince people to give you money.

You'll need to be a great business developer to form successful, long-term agreements with exchanges (ideally for no fees), liquidity providers, banks, payment gates, etc. Persuade clients.

It's a tough job, isn't it?

I expect a Quora-type question here:

Can I start an unlicensed crypto broker?

Well, there is always a workaround with crypto!

You can register your broker in a free-trade zone like Seychelles to avoid US and other markets with strong watchdogs.

This is neither wise nor sustainable.

First, such experiments are illegal.

Second, you'll have trouble attracting clients and strategic partners.

A license equals trust. That’s it.

Even a pseudo-license from Mauritius matters.

Here are this method's benefits and downsides.

Cons first.

  • As you navigate this difficult and expensive legal process, you run the risk of missing out on business prospects. It's quite simple to become excellent compliance yet unable to work. Because your competitors are already courting potential customers while you are focusing all of your effort on paperwork.

  • Only God knows how long it will take you to pass the break-even point when everything with the license has been completed.

  • It is a money-burning business, especially in the beginning when the majority of your expenses will go toward marketing, sales, and maintaining license requirements. Make sure you have the fortitude and resources necessary to face such a difficult challenge.

Pros

  • It may eventually develop into a tool for making money. Because big guys who are professionals at trading require a white-glove regulated brokerage. You have every possibility if you work hard in the areas of sales, marketing, business development, and wealth. Simply put, everything must align.

Launching a regulated crypto broker is analogous to launching a crypto exchange. It's ROUGH. Sure you can take it?

2. Franchise for Crypto Broker (Crypto Sub-Brokerage)

A broker franchise is easier and faster than becoming a regulated crypto broker. Not a traditional brokerage.

A broker franchisee, often termed a sub-broker, joins with a broker (a franchisor) to bring them new clients. Sub-brokers market a broker's products and services to clients.

Sub-brokers are the middlemen between a broker and an investor.

Why is sub-brokering easier?

  • less demanding qualifications and legal complexity. All you need to do is keep a few certificates on hand (each time depends on the jurisdiction).

  • No significant investment is required

  • there is no demand that you be a trading member of an exchange, etc.

As a sub-broker, you can do identical duties without as many rights and certifications.

What about the crypto broker franchise?

Sub-brokers aren't common in crypto.

In most existing examples (PayBito, PCEX, etc.), franchises are offered by crypto exchanges, not brokers. Though we remember that crypto exchanges are, in fact, brokers, do we?

Similarly:

  • For a commission, a franchiser crypto broker receives new leads from a crypto sub-broker.

See above for why enrolling is easy.

Finding clients is difficult. Most crypto traders prefer to buy-sell on their own or through brokers over sub-broker franchises.

3. Broker of the Crypto Trading Network (or a Network Broker)

It's the greatest approach to execute crypto brokerage, based on effort/return.

Network broker isn't an established word. I wrote it for clarity.

Remember how we called crypto liquidity fragmentation the current crypto finance paradigm's main bottleneck?

Where there's a challenge, there's progress.

Several well-funded projects are aiming to fix crypto liquidity fragmentation. Instead of launching another crypto exchange with siloed trading, the greatest minds create trading networks that aggregate crypto liquidity from desynchronized sources and enable quick, safe, and affordable cross-blockchain transactions. Each project offers a distinct option for users.

Crypto liquidity implies:

  • One-account access to cryptocurrency liquidity pooled from network participants' exchanges and other liquidity sources

  • compiled price feeds

  • Cross-chain transactions that are quick and inexpensive, even for HFTs

  • link between participants of all kinds, and

  • interoperability among diverse blockchains

Fast, diversified, and cheap global crypto trading from one account.

How does a trading network help cryptocurrency brokers?

I’ll explain it, taking Yellow Network as an example.

Yellow provides decentralized Layer-3 peer-to-peer trading.

  • trade across chains globally with real-time settlement and

  • Between cryptocurrency exchanges, brokers, trading companies, and other sorts of network members, there is communication and the exchange of financial information.

Have you ever heard about ECN (electronic communication network)? If not, it's an automated system that automatically matches buy and sell orders. Yellow is a decentralized digital asset ECN.

Brokers can:

  • Start trading right now without having to meet stringent requirements; all you need to do is integrate with Yellow Protocol and successfully complete some KYC verification.

  • Access global aggregated crypto liquidity through a single point.

  • B2B (Broker to Broker) liquidity channels that provide peer liquidity from other brokers. Orders from the other broker will appear in the order book of a broker who is peering with another broker on the market. It will enable a broker to broaden his offer and raise the total amount of liquidity that is available to his clients.

  • Select a custodian or use non-custodial practices.

Comparing network crypto brokerage to other types:

  • A licensed stand-alone brokerage business is much more difficult and time-consuming to launch than network brokerage, and

  • Network brokerage, in contrast to crypto sub-brokerage, is scalable, independent, and offers limitless possibilities for revenue generation.

Yellow Network Whitepaper. has more details on how to start a brokerage business and what rewards you'll obtain.

Final thoughts

There are three ways to become a cryptocurrency broker, including the non-conventional liquidity network brokerage. The last option appears time/cost-effective.

Crypto brokerage isn't crowded yet. Act quickly to find your right place in this market.

Choose the way that works for you best and see you in crypto trading.

Discover Web3 & DeFi with Yellow Network!

Yellow, powered by Openware, is developing a cross-chain P2P liquidity aggregator to unite the crypto sector and provide global remittance services that aid people.

Join the Yellow Community and plunge into this decade's biggest product-oriented crypto project.

  • Observe Yellow Twitter

  • Enroll in Yellow Telegram

  • Visit Yellow Discord.

  • On Hacker Noon, look us up.

Yellow Network will expose development, technology, developer tools, crypto brokerage nodes software, and community liquidity mining.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

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? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

  • x+5
  • x^4
  • x^3+3x^2+3x+1
  • 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

  • A(0)+B(0)=C(0)
  • A(1)+B(1)=C(1)
  • A(2)+B(2)=C(2)
  • A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

  • 12+1=13
  • 10+8=18
  • 15+8=23
  • 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

  • A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
  • B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
  • C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

see part 3