Late in 2018, I published my first Medium article, but I didn't start writing seriously until 2019. Since then, I've written more than 240 articles, earned over $50,000 through Medium's Partner Program, and had over 2.5 million page views.

Write A Lot

Most people don't have the patience and persistence for this simple writing secret:

Write + Write + Write = possible success

Writing more improves your skills.

The more articles you publish, the more likely one will go viral.

If you only publish once a month, you have no views. If you publish 10 or 20 articles a month, your success odds increase 10- or 20-fold.

Tim Denning, Ayodeji Awosika, Megan Holstein, and Zulie Rane. Medium is their jam. How are these authors alike? They're productive and consistent. They're prolific.

80% is publishable

Many writers battle perfectionism. 

To succeed as a writer, you must publish often. You'll never publish if you aim for perfection.

Adopt the 80 percent-is-good-enough mindset to publish more. It sounds terrible, but it'll boost your writing success.

Your work won't be perfect. Always improve. Waiting for perfection before publishing will take a long time.

Second, readers are your true critics, not you. What you consider "not perfect" may be life-changing for the reader. Don't let perfectionism hinder the reader.

Don't let perfectionism hinder the reader. ou don't want to publish mediocre articles. When the article is 80% done, publish it. Don't spend hours editing. Realize it. Get feedback. Only this will work.

Make Your Headline Irresistible

We all judge books by their covers, despite the saying. And headlines. Readers, including yourself, judge articles by their titles. We use it to decide if an article is worth reading.

Make your headlines irresistible. Want more article views? Then, whether you like it or not, write an attractive article title.

Many high-quality articles are collecting dust because of dull, vague headlines. It didn't make the reader click.

As a writer, you must do more than produce quality content. You must also make people click on your article. This is a writer's job. How to create irresistible headlines:

Curiosity makes readers click. Here's a tempting example...

• Example: What Women Actually Look For in a Guy, According to a Huge Study by Luba Sigaud

Use Numbers: Click-bait lists. I mean, which article would you click first? ‘Some ways to improve your productivity’ or ’17 ways to improve your productivity.’ Which would I click?

• Example: 9 Uncomfortable Truths You Should Accept Early in Life by Sinem Günel

Most headlines are dull. If you want clicks, get 'sexy'. Buzzword-ify. Invoke emotion. Trendy words.

• Example: 20 Realistic Micro-Habits To Live Better Every Day by Amardeep Parmar

Concise paragraphs

Our culture lacks focus. If your headline gets a click, keep paragraphs short to keep readers' attention.

Some writers use 6–8 lines per paragraph, but I prefer 3–4. Longer paragraphs lose readers' interest.

A writer should help the reader finish an article, in my opinion. I consider it a job requirement. You can't force readers to finish an article, but you can make it 'snackable'

Help readers finish an article with concise paragraphs, interesting subheadings, exciting images, clever formatting, or bold attention grabbers.

Work And Move On

I've learned over the years not to get too attached to my articles. Many writers report a strange phenomenon:

The articles you're most excited about usually bomb, while the ones you're not tend to do well.

This isn't always true, but I've noticed it in my own writing. My hopes for an article usually make it worse. The more objective I am, the better an article does.

Let go of a finished article. 40 or 40,000 views, whatever. Now let the article do its job. Onward. Next story. Start another project.

Disregard Haters

Online content creators will encounter haters, whether on YouTube, Instagram, or Medium. More views equal more haters. Fun, right?

As a web content creator, I learned:

Don't debate haters. Never.

It's a mistake I've made several times. It's tempting to prove haters wrong, but they'll always find a way to be 'right'. Your response is their fuel.

I smile and ignore hateful comments. I'm indifferent. I won't enter a negative environment. I have goals, money, and a life to build. "I'm not paid to argue," Drake once said.

Use Grammarly

Grammarly saves me as a non-native English speaker. You know Grammarly. It shows writing errors and makes article suggestions.

As a writer, you need Grammarly. I have a paid plan, but their free version works. It improved my writing greatly.

Put The Reader First, Not Yourself

Many writers write for themselves. They focus on themselves rather than the reader.

Ask yourself:

This article teaches what? How can they be entertained or educated?

Personal examples and experiences improve writing quality. Don't focus on yourself.

It's not about you, the content creator. Reader-focused. Putting the reader first will change things.

Extreme ownership: Stop blaming others

I remember writing a lot on Medium but not getting many views. I blamed Medium first. Poor algorithm. Poor publishing. All sucked.

Instead of looking at what I could do better, I blamed others.

When you blame others, you lose power. Owning your results gives you power.

As a content creator, you must take full responsibility. Extreme ownership means 100% responsibility for work and results.

You don’t blame others. You don't blame the economy, president, platform, founders, or audience. Instead, you look for ways to improve. Few people can do this.

Blaming is useless. Zero. Taking ownership of your work and results will help you progress. It makes you smarter, better, and stronger.

Instead of blaming others, you'll learn writing, marketing, copywriting, content creation, productivity, and other skills. Game-changer.

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

Successful workers don't talk this way.

"I know it's unprofessional, but I can't stop." — Author Sandy Hall

Do you realize your unprofessionalism? Do you care? Self-awareness?

Everyone can improve their unprofessionalism. Some workplace phrases and words shouldn't be said.

People often say out loud what they're thinking. They show insecurity, incompetence, and disrespect.

"Think before you speak," goes the saying.

Some of these phrases are "okay" in certain situations, but you'll lose colleagues' respect if you use them often.

Your word choice. Your tone. Your intentions. They matter.

Choose your words carefully to build work relationships and earn peer respect. You should build positive relationships with coworkers and clients.

These 10 phrases are unprofessional. 

1. That Meeting Really Sucked

Wow! Were you there? You should be responsible if you attended. You can influence every conversation.

Alternatives

Improve the meeting instead of complaining afterward. Make it more meaningful and productive.

2. Not Sure if You Saw My Last Email

Referencing a previous email irritates people. Email follow-up can be difficult. Most people get tons of emails a day, so it may have been buried, forgotten, or low priority.

Alternatives

It's okay to follow up, but be direct, short, and let the recipient "save face"

3. Any Phrase About Sex, Politics, and Religion

Discussing sex, politics, and religion at work is foolish. If you discuss these topics, you could face harassment lawsuits.

Alternatives

Keep quiet about these contentious issues. Don't touch them.

4. I Know What I’m Talking About

Adding this won't persuade others. Research, facts, and topic mastery are key to persuasion. If you're knowledgeable, you don't need to say this.

Alternatives

Please don’t say it at all. Justify your knowledge.

5. Per Our Conversation

This phrase sounds like legal language. You seem to be documenting something legally. Cold, stern, and distant. "As discussed" sounds inauthentic.

Alternatives

It was great talking with you earlier; here's what I said.

6. Curse-Word Phrases

Swearing at work is unprofessional. You never know who's listening, so be careful. A child may be at work or on a Zoom or Teams call. Workplace cursing is unacceptable.

Alternatives

Avoid adult-only words.

7. I Hope This Email Finds You Well

This is a unique way to wish someone well. This phrase isn't as sincere as the traditional one. When you talk about the email, you're impersonal.

Alternatives

Genuinely care for others.

8. I Am Really Stressed

Happy, strong, stress-managing coworkers are valued. Manage your own stress. Exercise, sleep, and eat better.

Alternatives

Everyone has stress, so manage it. Don't talk about your stress.

9. I Have Too Much to Do

You seem incompetent. People think you can't say "no" or have poor time management. If you use this phrase, you're telling others you may need to change careers.

Alternatives

Don't complain about your workload; just manage it.

10. Bad Closing Salutations

"Warmly," "best," "regards," and "warm wishes" are common email closings. This conclusion sounds impersonal. Why use "warmly" for finance's payment status?

Alternatives

Personalize the closing greeting to the message and recipient. Use "see you tomorrow" or "talk soon" as closings.

Bringing It All Together

These 10 phrases are unprofessional at work. That meeting sucked, not sure if you saw my last email, and sex, politics, and religion phrases.

Also, "I know what I'm talking about" and any curse words. Also, avoid phrases like I hope this email finds you well, I'm stressed, and I have too much to do.

Successful workers communicate positively and foster professionalism. Don't waste chances to build strong work relationships by being unprofessional.

“Unprofessionalism damages the business reputation and tarnishes the trust of society.” — Pearl Zhu, an American author

This post is a summary. Read full article here

Homeownership isn't the only life pattern.

Want to irritate people?

My party trick is to say I used to own a house but no longer do.

I no longer wish to own a home, not because I lost it or because I'm moving.

It was a long-term plan. It was more deliberate than buying a home. Many people are committed for this reason.

Poppycock.

Anyone who told me that owning a house (or striving to do so) is a must is wrong.

Because, URGH.

One pattern for life is to own a home, but there are millions of others.

You can afford to buy a home? Go, buddy.

You think you need 1,000 square feet (or more)? You think it's non-negotiable in life?

Nope.

It's insane that society forces everyone to own real estate, regardless of income, wants, requirements, or situation. As if this trade brings happiness, stability, and contentment.

Take it from someone who thought this for years: drywall isn't happy. Living your way brings contentment.

That's in real estate. It may also be renting a small apartment in a city that makes your soul sing, but you can't afford the downpayment or mortgage payments.

Living or traveling abroad is difficult when your life savings are connected to something that eats your money the moment you sign.

#vanlife, which seems like torment to me, makes some people feel alive.

I've seen co-living, vacation rental after holiday rental, living with family, and more work.

Insisting that home ownership is the only path in life is foolish and reduces alternative options.

How little we question homeownership is a disgrace.

No one challenges a homebuyer's motives. We congratulate them, then that's it.

When you offload one, you must answer every question, even if you have a loose screw.

• Why do you want to sell?

• Do you have any concerns about leaving the market?

• Why would you want to renounce what everyone strives for?

• Why would you want to abandon a beautiful place like that?

• Why would you mismanage your cash in such a way?

• But surely it's only temporary? RIGHT??

Incorrect questions. Buying a property requires several inquiries.

• The typical American has $4500 saved up. When something goes wrong with the house (not if, it’s never if), can you actually afford the repairs?

• Are you certain that you can examine a home in less than 15 minutes before committing to buying it outright and promising to pay more than twice the asking price on a 30-year 7% mortgage?

• Are you certain you're ready to leave behind friends, family, and the services you depend on in order to acquire something?

• Have you thought about the connotation that moving to a suburb, which more than half of Americans do, means you will be dependent on a car for the rest of your life?

Plus:

Are you sure you want to prioritize home ownership over debt, employment, travel, raising kids, and daily routines?

Homeownership entails that. This ex-homeowner says it will rule your life from the time you put the key in the door.

This isn't questioned. We don't question enough. The holy home-ownership grail was set long ago, and we don't challenge it.

Many people question after signing the deeds. 70% of homeowners had at least one regret about buying a property, including the expense.

Exactly. Tragic.

Homes are different from houses

We've been fooled into thinking home ownership will make us happy.

Some may agree. No one.

Bricks and brick hindered me from living the version of my life that made me most comfortable, happy, and steady.

I'm spending the next month in a modest apartment in southern Spain. Even though it's late November, today will be 68 degrees. My spouse and I will soon meet his visiting parents. We'll visit a Sherry store. We'll eat, nap, walk, and drink Sherry. Writing. Jerez means flamenco.

That's my home. This is such a privilege. Living a fulfilling life brings me the contentment that buying a home never did.

I'm happy and comfortable knowing I can make almost all of my days good. Rejecting home ownership is partly to blame.

I'm broke like most folks. I had to choose between home ownership and comfort. I said, I didn't find them together.

Feeling at home trumps owning brick-and-mortar every day.

The following is the reality of what it's like to turn the American Dream around.

Leaving the housing market.

Sometimes I wish I owned a home.

I miss having my own yard and bed. My kitchen, cookbooks, and pizza oven are missed.

But I rarely do.

Someone else's life plan pushed home ownership on me. I'm grateful I figured it out at 35. Many take much longer, and some never understand homeownership stinks (for them).

It's confusing. People will think you're dumb or suicidal.

If you read what I write, you'll know. You'll realize that all you've done is choose to live intentionally. Find a home beyond four walls and a picket fence.

Miss? As I said, they're not home. If it were, a pizza oven, a good mattress, and a well-stocked kitchen would bring happiness.

No.

If you can afford a house and desire one, more power to you.

There are other ways to discover home. Find calm and happiness. For fun.

For it, look deeper than your home's foundation.

Combining AIs creates realistic AI News Videos.

Powerful AI tools like Chat GPT-3 are trending. Have you combined AIs?

The 1-minute fake news video below is startlingly realistic. Artificial Intelligence developed NASA's Mars exploration breakthrough video (AI). However, integrating the aforementioned AIs generated it.

• AI-generated text for the Chat GPT-3 based on a succinct tagline

• DALL-E-2 AI generates an image from a brief slogan.

• Artificial intelligence-generated avatar and speech

This article shows how to use and mix the three AIs to make a realistic news video. First, watch the video (1 minute).

Talk GPT-3

Chat GPT-3 is an OpenAI NLP model. It can auto-complete text and produce conversational responses.

Try it at the playground. The AI will write a comprehensive text from a brief tagline. Let's see what the AI generates with "Breakthrough in Mars Project" as the headline.

Amazing. Our tagline matches our complete and realistic text. Fake news can start here.

DALL-E-2

OpenAI's huge transformer-based language model DALL-E-2. Its GPT-3 basis is geared for image generation. It can generate high-quality photos from a brief phrase and create artwork and images of non-existent objects.

DALL-E-2 can create a news video background. We'll use "Breakthrough in Mars project" again. Our AI creates four striking visuals. Last.

Synthesia

Synthesia lets you quickly produce videos with AI avatars and synthetic vocals.

Avatars are first. Rosie it is.

Upload and select DALL-backdrop. E-2's

Copy the Chat GPT-3 content and choose a synthetic voice.

Voice: English (US) Professional.

Finally, we generate and watch or download our video.

Synthesia AI completes the AI video.

Overview & Resources

We used three AIs to make surprisingly realistic NASA Mars breakthrough fake news in this post. Synthesia generates an avatar and a synthetic voice, therefore it may be four AIs.

These AIs created our fake news.

• AI-generated text for the Chat GPT-3 based on a succinct tagline

• DALL-E-2 AI generates an image from a brief slogan.

• Artificial intelligence-generated avatar and speech

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.