Everyone wants a scalable startup.

Innovation helps launch a startup. The secret to a scalable business is growth trials (from 1 to 100).

Growth marketing combines marketing and product development for long-term growth.

Today, I'll explain growth hacking strategies popular startups used to scale.

1/ A Facebook user's social value is proportional to their friends.

Facebook built its user base using content marketing and paid ads. Mark and his investors feared in 2007 when Facebook's growth stalled at 90 million users.

Chamath Palihapitiya was brought in by Mark.

The team tested SEO keywords and MAU chasing. The growth team introduced “people you may know”

This feature reunited long-lost friends and family. Casual users became power users as the retention curve flattened.

Growth Hack Insights: With social network effect the value of your product or platform increases exponentially if you have users you know or can relate with.

2/ Airbnb - Focus on your value propositions

Airbnb nearly failed in 2009. The company's weekly revenue was $200 and they had less than 2 months of runway.

Enter Paul Graham. The team noticed a pattern in 40 listings. Their website's property photos sucked.

Why?

Because these photos were taken with regular smartphones. Users didn't like the first impression.

Graham suggested traveling to New York to rent a camera, meet with property owners, and replace amateur photos with high-resolution ones.

A week later, the team's weekly revenue doubled to $400, indicating they were on track.

Growth Hack Insights: When selling an “online experience” ensure that your value proposition is aesthetic enough for users to enjoy being associated with them.

3/ Zomato - A company's smartphone push ensured growth.

Zomato delivers food. User retention was a challenge for the founders. Indian food customers are notorious for switching brands at the drop of a hat.

Zomato wanted users to order food online and repeat orders throughout the week.

Zomato created an attractive website with “near me” keywords for SEO indexing.

Zomato gambled to increase repeat orders. They only allowed mobile app food orders.

Zomato thought mobile apps were stickier. Product innovations in search/discovery/ordering or marketing campaigns like discounts/in-app notifications/nudges can improve user experience.

Zomato went public in 2021 after users kept ordering food online.

Growth Hack Insights: To improve user retention try to build platforms that build user stickiness. Your product and marketing team will do the rest for them.

4/ Hotmail - Signaling helps build premium users.

Ever sent or received an email or tweet with a sign — sent from iPhone?

Hotmail did it first! One investor suggested Hotmail add a signature to every email.

Overnight, thousands joined the company. Six months later, the company had 1 million users.

When serving an existing customer, improve their social standing. Signaling keeps the top 1%.

5/ Dropbox - Respect loyal customers

Dropbox is a company that puts people over profits. The company prioritized existing users.

Dropbox rewarded loyal users by offering 250 MB of free storage to anyone who referred a friend. The referral hack helped Dropbox get millions of downloads in its first few months.

Growth Hack Insights: Think of ways to improve the social positioning of your end-user when you are serving an existing customer. Signaling goes a long way in attracting the top 1% to stay.

These experiments weren’t hacks. Hundreds of failed experiments and user research drove these experiments. Scaling up experiments is difficult.

Contact me if you want to grow your startup's user base.

> Say Hello To The Lean-Hedge Model

People think starting a business requires significant debt and investment. Like Shark Tank, you need a world-changing idea. I'm not saying to avoid investors or brilliant ideas.

Investing is essential to build a genuinely profitable company. Think Apple or Starbucks.

Entrepreneurship is risky because many people go bankrupt from debt. As starters, we shouldn't do it. Instead, use lean-hedge.

Simply defined, you construct a cash-flow business to hedge against long-term investment-heavy business expenses.

What the “fx!$rench-toast” is the lean-hedge model?

When you start a business, your money should move down, down, down, then up when it becomes profitable.

Many people don't survive the business's initial losses and debt. What if, we created a cash-flow business BEFORE we started our Starbucks to hedge against its initial expenses?

Lean-hedge has two sections. Start a cash-flow business. A cash-flow business takes minimal investment and usually involves sweat and time.

Let’s take a look at some examples:

A Translation company

Personal portfolio website (you make a site then you do cold e-mail marketing)

FREELANCE (UpWork, Fiverr).

Educational business.

Infomarketing. (You design a knowledge-based product. You sell the info).

Online fitness/diet/health coaching ($50-$300/month, calls, training plan)

Amazon e-book publishing. (Medium writers do this)

YouTube, cash-flow channel

A web development agency (I'm a dev, but if you're not, a graphic design agency, etc.) (Sell your time.)

Digital Marketing

Online paralegal (A million lawyers work in the U.S).

Some dropshipping (Organic Tik Tok dropshipping, where you create content to drive traffic to your shopify store instead of spend money on ads).

(Disclaimer: My first two cash-flow enterprises, which were language teaching, failed terribly. My translation firm is now booming because B2B e-mail marketing is easy.)

Crossover occurs. Your long-term business starts earning more money than your cash flow business.

My cash-flow business (freelancing, translation) makes $7k+/month.

I’ve decided to start a slightly more investment-heavy digital marketing agency

Here are the anticipated business's time- and money-intensive investments:

1. ($$$) Top Front-End designer's Figma/UI-UX design (in negotiation)

2. (Time): A little copywriting (I will do this myself)

3. ($$) Creating an animated webpage with HTML (in negotiation)

4. Backend Development (Duration) (I'll carry out this myself using Laravel.)

5. Logo Design ($$)

6. Logo Intro Video for $

7. Video Intro (I’ll edit this myself with Premiere Pro)

etc.

Then evaluate product, place, price, and promotion. Consider promotion and pricing.

The lean-hedge model's point is:

Don't gamble. Avoid debt. First create a cash-flow project, then grow it steadily.

Check read my previous posts on “Nightmare Mode” (which teaches you how to make work as interesting as video games) and Why most people can't escape a 9-5 to learn how to develop a cash-flow business.

Do you want to build and launch your own software company? To do this, all you need is a product that solves a problem.

Coming up with profitable ideas is not that easy. But you’re in luck because you got me!

I’ll give you the idea for free. All you need to do is execute it properly.

If you’re ready, let’s jump right into it! Starting with the problem.

Problem

Youtube has many creators. Every day, they think of new ways to entertain or inform us.

They work hard to make videos. Many of their efforts go to waste. They limit their revenue and reach.

Solution

Content repurposing solves this problem.

One video can become several TikToks. Creating YouTube videos from a podcast episode.

Or, one video might become a blog entry.

By turning videos into blog entries, Youtubers may develop evergreen SEO content, attract a new audience, and reach a non-YouTube audience.

Many YouTube creators want this easy feature.

Let's build it!

Implementation

We identified the problem, and we have a solution. All that’s left to do is see how it can be done.

Monitoring new video uploads

First, watch when a friend uploads a new video. Everything should happen automatically without user input.

YouTube Webhooks make this easy. Our server listens for YouTube Webhook notifications.

After publishing a new video, we create a conversion job.

Creating a Blog Post from a Video

Next, turn a video into a blog article.

To convert, we must extract the video's audio (which can be achieved by using FFmpeg on the server).

Once we have the audio channel, we can use speech-to-text.

Services can accomplish this easily.

• Speech-to-text on Google

• Google Translate

• Deepgram

Deepgram's affordability and integration make it my pick.

After conversion, the blog post needs formatting, error checking, and proofreading.

After this, a new blog post will appear in our web app's dashboard.

Completing a blog post

After conversion, users must examine and amend their blog posts.

Our application dashboard would handle all of this. It's a dashboard-style software where users can:

• Link their Youtube account

• Check out the converted videos in the future.

• View the conversions that are ongoing.

• Edit and format converted blog articles.

It's a web-based app.

It doesn't matter how it's made but I'd choose Next.js.

Next.js is a React front-end standard. Vercel serverless functions could conduct the conversions.

This would let me host the software for free and reduce server expenditures.

Taking It One Step Further

SaaS in a nutshell. Future improvements include integrating with WordPress or Ghost.

Our app users could then publish blog posts. Streamlining the procedure.

MVPs don't need this functionality.

Final Thoughts

Repurposing content helps you post more often, reach more people, and develop faster.

Many agencies charge a fortune for this service. Handmade means pricey.

Content creators will go crazy if you automate and cheaply solve this problem.

Just execute this idea!

From 1984 until 2011, he ran Apple using the same template.

What is a founder CEO's most crucial skill?

Presentation, communication, and sales

As a Business Angel Investor, I saw many pitch presentations and met with investors one-on-one to promote my companies.

There is always the conception of “Investors have to invest,” so there is no need to care about the presentation.

It's false. Nobody must invest. Many investors believe that entrepreneurs must convince them to invest in their business.

Sometimes — like in 2018–2022 — too much money enters the market, and everyone makes good money.

Do you recall the Buy Now, Pay Later Movement? This amazing narrative had no return potential. Only buyers who couldn't acquire financing elsewhere shopped at these companies.

Klarna's failing business concept led to high valuations.

Investors become more cautious when the economy falters. 2022 sees rising inflation, interest rates, wars, and civil instability. It's like the apocalypse's four horsemen have arrived.

Storytelling is important in rough economies.

When investors draw back, how can entrepreneurs stand out?

In Q2/2022, every study I've read said:

Investors cease investing

Deals are down in almost all IT industries from previous quarters.

What do founders need to do?

Differentiate yourself.

Storytelling talents help.

The Steve Jobs Way

Every time I watch a Steve Jobs presentation, I'm enthralled.

I'm a techie. Everything technical interests me. But, I skim most presentations.

What's Steve Jobs's secret?

Steve Jobs created Apple in 1976 and made it a profitable software and hardware firm in the 1980s. Macintosh goods couldn't beat IBM's. This mistake sacked him in 1985.

Before rejoining Apple in 1997, Steve Jobs founded Next Inc. and Pixar.

From then on, Apple became America's most valuable firm.

Steve Jobs understood people's needs. He said:

“People don’t know what they want until you show it to them. That’s why I never rely on market research. Our task is to read things that are not yet on the page.”

In his opinion, people talk about problems. A lot. Entrepreneurs must learn what the population's pressing problems are and create a solution.

Steve Jobs showed people what they needed before they realized it.

I'll explain:

Present a Big Vision

Steve Jobs starts every presentation by describing his long-term goals for Apple.

1984's Macintosh presentation set up David vs. Goliath. In a George Orwell-style dystopia, IBM computers were bad. It was 1984.

Apple will save the world, like Jedis.

Why do customers and investors like Big Vision?

People want a wider perspective, I think. Humans love improving the planet.

Apple users often cite emotional reasons for buying the brand.

Revolutionizing several industries with breakthrough inventions

Establish Authority

Everyone knows Apple in 2022. It's hard to find folks who confuse Apple with an apple around the world.

Apple wasn't as famous as it is today until Steve Jobs left in 2011.

Most entrepreneurs lack experience. They may market their company or items to folks who haven't heard of it.

Steve Jobs presented the company's historical accomplishments to overcome opposition.

In his presentation of the first iPhone, he talked about the Apple Macintosh, which altered the computing sector, and the iPod, which changed the music industry.

People who have never heard of Apple feel like they're seeing a winner. It raises expectations that the new product will be game-changing and must-have.

The Big Reveal

A pitch or product presentation always has something new.

Steve Jobs doesn't only demonstrate the product. I don't think he'd skip the major point of a company presentation.

He consistently discusses present market solutions, their faults, and a better consumer solution.

No solution exists yet.

It's a multi-faceted play:

• It's comparing the new product to something familiar. This makes novelty and the product more relatable.

• Describe a desirable solution.

• He's funny. He demonstrated an iPod with an 80s phone dial in his iPhone presentation.

Then he reveals the new product. Macintosh presented itself.

Show the benefits

He outlines what Apple is doing differently after demonstrating the product.

How do you distinguish from others? The Big Breakthrough Presentation.

A few hundred slides might list all benefits.

Everyone would fall asleep. Have you ever had similar presentations?

When the brain is overloaded with knowledge, the limbic system changes to other duties, like lunch planning.

What should a speaker do? There's a classic proverb:

“Tell me and I forget, teach me and I may remember, involve me and I learn” (— Not Benjamin Franklin).

Steve Jobs showcased the product live.

Again, using ordinary scenarios to highlight the product's benefits makes it relatable.

The 2010 iPad Presentation uses this technique.

Invite the Team and Let Them Run the Presentation

CEOs spend most time outside the organization. Many companies elect to have only one presenter.

It sends the incorrect message to investors. Product presentations should always include the whole team.

Let me explain why.

Companies needing investment money frequently have shaky business strategies or no product-market fit or robust corporate structure.

Investors solely bet on a team's ability to implement ideas and make a profit.

Early team involvement helps investors understand the company's drivers. Travel costs are worthwhile.

But why for product presentations?

Presenters of varied ages, genders, social backgrounds, and skillsets are relatable. CEOs want relatable products.

Some customers may not believe a white man's message. A black woman's message may be more accepted.

Make the story relatable when you have the best product that solves people's concerns.

Best example: 1984 Macintosh presentation with development team panel.

What is the largest error people make when companies fail?

Saving money on the corporate and product presentation.

Invite your team to five partner meetings when five investors are shortlisted.

Rehearse the presentation till it's natural. Let the team speak.

Successful presentations require structure, rehearsal, and a team. Steve Jobs nailed it.

The human brain is amazing. As more scientists examine the brain, we learn how much it can store.

The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]

What if you could store and access more info, freeing up brain space for problem-solving and creativity?

Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.

Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.

How to construct a second brain to organize information and achieve goals.

What Is a Second Brain?

How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?

If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.

This is when the second brain comes in.

Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.

Digital tools are preferable to analog for building a second brain.

Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.

Brainware

Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult. 

Memory has three components in computing:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

For example:

Due to rigorous security settings, many websites need you to create complicated passwords with special characters.

You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).

Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.

It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.

It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.

Why You Need a Digital Brain

Dual minds are best. Birth brain is limited.

The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]

Building a second brain improves learning and memory.

Learn and store information effectively

Faster information recall

Organize information to see connections and patterns

Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings. 

Why you need a Digital Brain:

1. Use Brainpower Effectively

Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.

Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.

2. Staying Organized

Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.

Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.

You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.

3. Creativity Process

Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.

Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.

4. Transforming Your Knowledge Into Opportunities

This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.

Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.

5. Improving Thinking and Uncovering Connections

Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.

This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]

Your ability to recognize trends will help you stay ahead of the pack.

6. Credibility for a New Job or Business

Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.

This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.

7. Using Learning Resources

Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.

These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.

How does a second brain feel?

Digital Brain has helped me arrange my job and family life for years.

No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.

Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.

No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.

How to Develop Your Digital Brain (Your Second Brain)

It's cheap but requires work.

Digital Brain development requires:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

1. Decide what information matters before recording.

To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.

What information do you need to achieve your goals?

You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.

2. Use the Right Tool

We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.

This information isn't used. You must store information in a central location.

Different information needs different instruments.

Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.

Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design

Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.

To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.

3. Organize data for easy retrieval

How should you organize collected data?

When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.

Choosing the correct tools helps organize data. Here are some tools selection criteria:

• Can the tool sync across devices?

• Personal or team?

• Has a search function for easy information retrieval?

• Does it provide easy data categorization?

• Can users create lists or collections?

• Does it offer easy idea-information connections?

• Does it mind map and visually organize thoughts?

Conclusion

Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.

People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength. 

Reference

[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?

[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?

[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery

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.