“Poor distribution, not poor goods, is the main reason for failure” — Peter Thiel.

Here's an easy way to conceptualize "go-to-market" for your distribution plan.

One equation captures the concept:

Distribution = Ecosystem Participants + Incentives

Draw your customers' ecosystem. Set aside your goods and consider your consumer's environment. Who do they deal with daily? 

1. First, list each participant. You want an exhaustive list, but here are some broad categories.

• In-person media services

• Websites

• Events\Networks

• Financial education and banking

• Shops

• Staff

• Advertisers

• Twitter influencers

1. Draw influence arrows. Who's affected? I'm not just talking about Instagram selfie-posters. Who has access to your consumer and could promote your product if motivated?

The thicker the arrow, the stronger the relationship. Include more "influencers" if needed. Customer ecosystems are complex.

3. Incentivize ecosystem players. “Show me the incentive and I will show you the result.“, says Warren Buffet's business partner Charlie Munger.

Strong distribution strategies encourage others to promote your product to your target market by incentivizing the most prominent players. Incentives can be financial or non-financial.

Financial rewards

Usually, there's money. If you pay Facebook, they'll run your ad. Salespeople close deals for commission. Giving customers bonus credits will encourage referrals.

Most businesses underuse non-financial incentives.

Non-cash incentives

Motivate key influencers without spending money to expand quickly and cheaply. What can you give a client-connector for free?

Here are some ideas:

Are there any other features or services available?

Titles or status? Tinder paid college "ambassadors" for parties to promote its dating service.

Can I get early/free access? Facebook gave a select group of developers "exclusive" early access to their AR platform.

Are you a good host? Pharell performed at YPlan's New York launch party.

Distribution? Apple's iPod earphones are white so others can see them.

Have an interesting story? PR rewards journalists by giving them a compelling story to boost page views.

Prioritize distribution.

More time spent on distribution means more room in your product design and business plan. Once you've identified the key players in your customer's ecosystem, talk to them.

Money isn't your only resource. Creative non-monetary incentives may be more effective and scalable. Give people something useful and easy to deliver.

I've spent over 50 hours researching one-person firms, which interest me. I've found countless one-person enterprises that made millions on the founder's determination and perseverance.

Throughout my investigation, I found three of the most outstanding one-person enterprises. These enterprises show that people who work hard and dedicate themselves to their ideas may succeed.

Eric Barone (@ConcernedApe) created Stardew Valley in 2011 to better his job prospects. Eric loved making the game, in which players inherit a farm, grow crops, raise livestock, make friends with the villagers, and form a family.

Eric handled complete game production, including 3D graphics, animations, and music, to maintain creative control. He stopped job hunting and worked 8-15 hours a day on the game.

Eric developed a Stardew Valley website and subreddit to engage with gamers and get feedback. Eric's devoted community helped him meet Steam's minimum vote requirement for single creators.

Stardew Valley sold 1 million copies in two months after Eric launched it for $15 in 2016. The game has sold 20 million copies and made $300 million.

The game's inexpensive price, outsourcing of PR, marketing, and publication, and loyal player base helped it succeed. Eric has turned down million-dollar proposals from Sony and Nintendo to sell the game and instead updates and improves it. Haunted Chocolatier is Eric's new game.

Is farming not profitable? Ask Stardew Valley creator Eric Barone.

Gary Brewer established BuiltWith to assist users find website technologies and services. BuiltWith boasts 3000 paying customers and $14 million in yearly revenue, making it a significant resource for businesses wishing to generate leads, do customer analytics, obtain business insight, compare websites, or search websites by keyword.

BuiltWith has one full-time employee, Gary, and one or two part-time contractors that help with the blog. Gary handles sales, customer service, and other company functions alone.

BuiltWith acquired popularity through blog promotions and a top Digg ranking. About Us, a domain directory, connected to BuiltWith on every domain page, boosting it. Gary introduced $295–$995 monthly subscriptions to search technology, keywords, and potential consumers in response to customer demand.

Gary uses numerous methods to manage a firm without staff. He spends one to two hours every day answering user queries, most of which are handled quickly by linking to BuiltWiths knowledge store. Gary creates step-by-step essays or videos for complex problems. Gary can focus on providing new features based on customer comments and requests since he makes it easy to unsubscribe.

BuiltWith is entirely automated and successful due to its unique approach and useful offerings. It works for Google, Meta, Amazon, and Twitter.

Digital Inspiration develops Google Documents, Sheets, and Slides plugins. Digital Inspiration, founded by Amit Agarwal, receives 5 million monthly visits and earns $10 million. 40 million individuals have downloaded Digital Inspirations plugins.

Amit started Digital Inspiration by advertising his blog at tech events and getting Indian filter blogs and other newspapers to promote his articles. Amit built plugins and promoted them on the blog once the blog acquired popularity, using ideas from comments, friends, and Reddit. Digital Inspiration has over 20 free and premium plugins.

Mail Merge, Notifications for Google Forms, YouTube Uploader, and Document Studio are some of Digital Inspiration's most popular plugins. Mail Merge allows users to send personalized emails in bulk and track email opens and clicks.

Since Amits manages Digital Inspiration alone, his success is astounding. Amit developed a successful company via hard work and creativity, despite platform dependence. His tale inspires entrepreneurs.

This is for young entrepreneurs, especially in tech.

People give useless success advice on TikTok and Reddit. Early risers, bookworms, etc. Entrepreneurship courses. Work hard and hustle.

False. These aren't successful traits.

I mean, organization is good. As someone who founded several businesses and now works at a VC firm, I find these tips to be clichés.

Based on founding four successful businesses and working with other successful firms, here's my best actionable advice:

1. Choose a sector or a niche and become an expert in it.

This is more generic than my next tip, but it's a must-do that's often overlooked. Become an expert in the industry or niche you want to enter. Discover everything.

Buy (future) competitors' products. Understand consumers' pain points. Market-test. Target keyword combos. Learn technical details.

The most successful businesses I've worked with were all formed by 9-5 employees. They knew the industry's pain points. They started a business targeting these pain points.

2. Choose a niche or industry crossroads to target.

How do you choose an industry or niche? What if your industry is too competitive?

List your skills and hobbies. Randomness is fine. Find an intersection between two interests or skills.

Say you build websites well. You like cars.

Web design is a *very* competitive industry. Cars and web design?

Instead of web design, target car dealers and mechanics. Build a few fake demo auto mechanic websites, then cold call shops with poor websites. Verticalize.

I've noticed a pattern:

• Person works in a particular industry for a corporation.

• Person gains expertise in the relevant industry.

• Person quits their job and launches a small business to address a problem that their former employer was unwilling to address.

I originally posted this on Reddit and it seemed to have taken off so I decided to share it with you all.

Focus on the product. When someone buys from you, you convince them the product's value exceeds the price. It's not fair and favors the buyer.

Creating a superior product or service will win. Narrowing this helps you outcompete others.

You may be their only (lucky) option.

Looking back into the past can help you understand what's happening today and why.

"Creator economy" conjures up images of originality, sincerity, and passion. Where do Michelangelos and da Vincis push advancement with their gifts without battling for bread and proving themselves posthumously? 

Creativity has been as long as humanity, but it's just recently become a new economic paradigm. We even talk about Web3 now.

Let's examine the creative economy's history to better comprehend it. What brought us here? Looking back can help you understand what's happening now.

No yawning, I promise 😉.

Creator Economy's history

Long, uneven transition to creator economy. Let's examine the economic and societal changes that led us there.

1. Agriculture to industry

Mid-18th-century Industrial Revolution led to shift from agriculture to manufacturing. The industrial economy lasted until World War II.

The industrial economy's principal goal was to provide more affordable, accessible commodities.

Unlike today, products were scarce and inaccessible.

To fulfill its goals, industrialization triggered enormous economic changes, moving power from agrarians to manufacturers. Industrialization brought hard work, rivalry, and new ideas connected to production and automation. Creative thinkers focused on that then.

It doesn't mean music, poetry, or painting had no place back then. They weren't top priority. Artists were independent. The creative field wasn't considered a different economic subdivision.

2. The consumer economy

Manufacturers produced more things than consumers desired after World War II. Stuff was no longer scarce.

The economy must make customers want to buy what the market offers.

The consumer economic paradigm supplanted the industrial one. Customers (or consumers) replaced producers as the new economic center.

Salesmen, marketing, and journalists also played key roles (TV, radio, newspapers, etc.). Mass media greatly boosted demand for goods, defined trends, and changed views regarding nearly everything.

Mass media also gave rise to pop culture, which focuses on mass-market creative products. Design, printing, publishing, multi-media, audio-visual, cinematographic productions, etc. supported pop culture.

The consumer paradigm generated creative occupations and activities, unlike the industrial economy. Creativity was limited by the need for wide appeal.

Most creators were corporate employees.

Creating a following and making a living from it were difficult.

Paul Saffo said that only journalists and TV workers were known. Creators who wished to be known relied on producers, publishers, and other gatekeepers. To win their favor was crucial. Luck was the best tactic.

3. The creative economy

Consumer economy was digitized in the 1990s. IT solutions transformed several economic segments. This new digital economy demanded innovative, digital creativity.

Later, states declared innovation a "valuable asset that creates money and jobs." They also introduced the "creative industries" and the "creative economy" (not creator!) and tasked themselves with supporting them. Australia and the UK were early adopters.

Individual skill, innovation, and intellectual property fueled the creative economy. Its span covered design, writing, audio, video material, etc. The creative economy required IT-powered activity.

The new challenge was to introduce innovations to most economic segments and meet demand for digital products and services.

Despite what the title "creative economy" may imply, it was primarily oriented at meeting consumer needs. It didn't provide inventors any new options to become entrepreneurs. Instead of encouraging innovators to flourish on their own, the creative economy emphasized "employment-based creativity."

4. The creator economy

Next, huge IT platforms like Google, Facebook, YouTube, and others competed with traditional mainstream media.

During the 2008 global financial crisis, these mediums surpassed traditional media. People relied on them for information, knowledge, and networking. That was a digital media revolution. The creator economy started there.

The new economic paradigm aimed to engage and convert clients. The creator economy allowed customers to engage, interact, and provide value, unlike the consumer economy. It gave them instruments to promote themselves as "products" and make money.

Writers, singers, painters, and other creators have a great way to reach fans. Instead of appeasing old-fashioned gatekeepers (producers, casting managers, publishers, etc.), they can use the platforms to express their talent and gain admirers. Barriers fell.

It's not only for pros. Everyone with a laptop and internet can now create.

2022 creator economy:

Since there is no academic description for the current creator economy, we can freestyle.

The current (or Web2) creator economy is fueled by interactive digital platforms, marketplaces, and tools that allow users to access, produce, and monetize content.

No entry hurdles or casting in the creative economy. Sign up and follow platforms' rules. Trick: A platform's algorithm aggregates your data and tracks you. This is the payment for participation.

The platforms offer content creation, design, and ad distribution options. This is platforms' main revenue source.

The creator economy opens many avenues for creators to monetize their work. Artists can now earn money through advertising, tipping, brand sponsorship, affiliate links, streaming, and other digital marketing activities.

Even if your content isn't digital, you can utilize platforms to promote it, interact and convert your audience, and more. No limits. However, some of your income always goes to a platform (well, a huge one).

The creator economy aims to empower online entrepreneurship by offering digital marketing tools and reducing impediments.

Barriers remain. They are just different. Next articles will examine these.

Why update the creator economy for Web3?

I could address this question by listing the present creator economy's difficulties that led us to contemplate a Web3 upgrade.

I don't think these difficulties are the main cause. The mentality shift made us see these challenges and understand there was a better reality without them.

Crypto drove this thinking shift. It promoted disintermediation, independence from third-party service providers, 100% data ownership, and self-sovereignty. Crypto has changed the way we view everyday things.

Crypto's disruptive mission has migrated to other economic segments. It's now called Web3. Web3's creator economy is unique.

Here's the essence of the Web3 economy:

• Eliminating middlemen between creators and fans.

• 100% of creators' data, brand, and effort.

• Business and money-making transparency.

• Authentic originality above ad-driven content.

In the next several articles, I'll explain. We'll also discuss the creator economy and Web3's remedies.

Final thoughts

The creator economy is the organic developmental stage we've reached after all these social and economic transformations.

The Web3 paradigm of the creator economy intends to allow creators to construct their own independent "open economy" and directly monetize it without a third party.

If this approach succeeds, we may enter a new era of wealth creation where producers aren't only the products. New economies will emerge.

This article is a summary. To read the full post, click here.

Jobs' secret emails became public due to a litigation with Samsung.

Steve Jobs sent Phil Schiller an email at the end of 2010. Top 100 A was the codename for Apple's annual Top 100 executive meetings. The 2011 one was scheduled.

Everything about this gathering is secret, even attendance. The location is hidden, and attendees can't even drive themselves. Instead, buses transport them to a 2-3 day retreat.

Due to a litigation with Samsung, this Top 100 meeting's agenda was made public in 2014. This was a critical milestone in Apple's history, not a Top 100 meeting. Apple had many obstacles in the 2010s to remain a technological leader. Apple made more money with non-PC goods than with its best-selling Macintosh series. This was the last Top 100 gathering Steve Jobs would attend before passing, and he wanted to make sure his messages carried on before handing over his firm to Tim Cook.

In this post, we'll discuss lessons from Jobs' meeting agenda. Two sorts of entrepreneurs can use these tips:

1. Those who manage a team in a business and must ensure that everyone is working toward the same goals, upholding the same principles, and being inspired by the same future.

2. Those who are sole proprietors or independent contractors and who must maintain strict self-discipline in order to stay innovative in their industry and adhere to their own growth strategy.

Here's Steve Jobs's email outlining the annual meeting agenda. It's an 11-part summary of the company's shape and strategy.

Steve Jobs outlines Apple's 2011 strategy, 10/24/10

1. Correct your data

Business leaders must comprehend their company's metrics. Jobs either mentions critical information he already knows or demands slides showing the numbers he wants. These numbers fall under 2 categories:

Metrics for growth and strategy

• As we will see, this was a crucial statistic for Apple since it signaled the beginning of the Post PC era and required them to make significant strategic changes in order to stay ahead of the curve. Post PC products now account for 66% of our revenues.

• Within six months, iPad outsold Mac, another sign of the Post-PC age. As we will see, Jobs thought the iPad would be the next big thing, and item number four on the agenda is one of the most thorough references to the iPad.

• Geographical analysis: Here, Jobs emphasizes China, where the corporation has a slower start than anticipated. China was dominating Apple's sales growth with 16% of revenue one year after this meeting.

Metrics for people & culture

• The individuals that make up a firm are more significant to its success than its headcount or average age. That holds true regardless of size, from a 5-person startup to a Fortune 500 firm. Jobs was aware of this, which is why his suggested agenda begins by emphasizing demographic data.

• Along with the senior advancements in the previous year's requested statistic, it's crucial to demonstrate that if the business is growing, the employees who make it successful must also grow.

2. Recognize the vulnerabilities and strengths of your rivals

Steve Jobs was known for attacking his competition in interviews and in his strategies and roadmaps. This agenda mentions 18 competitors, including:

• Google 7 times

• Android 3 times

• Samsung 2 times

Jobs' agenda email was issued 6 days after Apple's Q4 results call (2010). On the call, Jobs trashed Google and Android. His 5-minute intervention included:

• Google has acknowledged that the present iteration of Android is not tablet-optimized.

• Future Android tablets will not work (Dead On Arrival)

• While Google Play only has 90,000 apps, the Apple App Store has 300,000.

• Android is extremely fragmented and is continuing to do so.

• The App Store for iPad contains over 35,000 applications. The market share of the latest generation of tablets (which debuted in 2011) will be close to nil.

Jobs' aim in blasting the competition on that call was to reassure investors about the upcoming flood of new tablets. Jobs often criticized Google, Samsung, and Microsoft, but he also acknowledged when they did a better job. He was great at detecting his competitors' advantages and devising ways to catch up.

• Jobs doesn't hold back when he says in bullet 1 of his agenda: "We further lock customers into our ecosystem while Google and Microsoft are further along on the technology, but haven't quite figured it out yet tie all of our goods together."

• The plan outlined in bullet point 5 is immediately clear: catch up to Android where we are falling behind (notifications, tethering, and speech), and surpass them (Siri,). It's important to note that Siri frequently let users down and never quite lived up to expectations.

• Regarding MobileMe, see Bullet 6 Jobs admits that when it comes to cloud services like contacts, calendars, and mail, Google is far ahead of Apple.

3. Adapt or perish

Steve Jobs was a visionary businessman. He knew personal computers were the future when he worked on the first Macintosh in the 1980s.

Jobs acknowledged the Post-PC age in his 2010 D8 interview.

Will the tablet replace the laptop, Walt Mossberg questioned Jobs? Jobs' response:

“You know, when we were an agrarian nation, all cars were trucks, because that’s what you needed on the farm. As vehicles started to be used in the urban centers and America started to move into those urban and suburban centers, cars got more popular and innovations like automatic transmission and things that you didn’t care about in a truck as much started to become paramount in cars. And now, maybe 1 out of every 25 vehicles is a truck, where it used to be 100%. PCs are going to be like trucks. They’re still going to be around, still going to have a lot of value, but they’re going to be used by one out of X people.”

Imagine how forward-thinking that was in 2010, especially for the Macintosh creator. You have to be willing to recognize that things were changing and that it was time to start over and focus on the next big thing.

Post-PC is priority number 8 in his 2010 agenda's 2011 Strategy section. Jobs says Apple is the first firm to get here and that Post PC items account about 66% of our income. The iPad outsold the Mac in 6 months, and the Post-PC age means increased mobility (smaller, thinner, lighter). Samsung had just introduced its first tablet, while Apple was working on the iPad 3. (as mentioned in bullet 4).

4. Plan ahead (and different)

Jobs' agenda warns that Apple risks clinging to outmoded paradigms. Clayton Christensen explains in The Innovators Dilemma that huge firms neglect disruptive technologies until they become profitable. Samsung's Galaxy tab, released too late, never caught up to Apple.

Apple faces a similar dilemma with the iPhone, its cash cow for over a decade. It doesn't sell as much because consumers aren't as excited about new iPhone launches and because technology is developing and cell phones may need to be upgraded.

Large companies' established consumer base typically hinders innovation. Clayton Christensen emphasizes that loyal customers from established brands anticipate better versions of current products rather than something altogether fresh and new technologies.

Apple's marketing is smart. Apple's ecosystem is trusted by customers, and its products integrate smoothly. So much so that Apple can afford to be a disruptor by doing something no one has ever done before, something the world's largest corporation shouldn't be the first to try. Apple can test the waters and produce a tremendous innovation tsunami, something few corporations can do.

In March 2011, Jobs appeared at an Apple event. During his address, Steve reminded us about Apple's brand:

“It’s in Apple’s DNA, that technology alone is not enough. That it’s technology married with liberal arts, married with the humanities that yields us the results that make our hearts sink. And nowhere is that more true that in these Post-PC devices.“

More than a decade later, Apple remains one of the most innovative and trailblazing companies in the Post-PC world (industry-disrupting products like Airpods or the Apple Watch came out after that 2011 strategy meeting), and it has reinvented how we use laptops with its M1-powered line of laptops offering unprecedented performance.

A decade after Jobs' death, Apple remains the world's largest firm, and its former CEO had a crucial part in its expansion. If you can do 1% of what Jobs did, you may be 1% as successful.

Not bad.

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.