How to overcome public speaking fear and give a killer presentation

"Public speaking is people's biggest fear, according to studies. Death's second. The average person is better off in the casket than delivering the eulogy."  — American comedian, actor, writer, and producer Jerry Seinfeld

People fear public speaking, according to research. Public speaking can be intimidating.

Most professions require public speaking, whether to 5, 50, 500, or 5,000 people. Your career will require many presentations. In a small meeting, company update, or industry conference.

You can improve your public speaking skills. You can reduce your anxiety, improve your performance, and feel more comfortable speaking in public.

“If I returned to college, I'd focus on writing and public speaking. Effective communication is everything.” — 38th president Gerald R. Ford

You can deliver a great presentation despite your fear of public speaking. There are ways to stay calm while speaking and become a more effective public speaker.

Seven tips to improve your public speaking today. Let's help you overcome your fear (no pun intended).

Know your audience.

"You're not being judged; the audience is." — Entrepreneur, author, and speaker Seth Godin

Understand your audience before speaking publicly. Before preparing a presentation, know your audience. Learn what they care about and find useful.

Your presentation may depend on where you're speaking. A classroom is different from a company meeting.

Determine your audience before developing your main messages. Learn everything about them. Knowing your audience helps you choose the right words, information (thought leadership vs. technical), and motivational message.

2. Be Observant

Observe others' speeches to improve your own. Watching free TED Talks on education, business, science, technology, and creativity can teach you a lot about public speaking.

What worked and what didn't?

• What would you change?

• Their strengths

• How interesting or dull was the topic?

Note their techniques to learn more. Studying the best public speakers will amaze you.

Learn how their stage presence helped them communicate and captivated their audience. Please note their pauses, humor, and pacing.

3. Practice

"A speaker should prepare based on what he wants to learn, not say." — Author, speaker, and pastor Tod Stocker

Practice makes perfect when it comes to public speaking. By repeating your presentation, you can find your comfort zone.

When you've practiced your presentation many times, you'll feel natural and confident giving it. Preparation helps overcome fear and anxiety. Review notes and important messages.

When you know the material well, you can explain it better. Your presentation preparation starts before you go on stage.

Keep a notebook or journal of ideas, quotes, and examples. More content means better audience-targeting.

4. Self-record

Videotape your speeches. Check yourself. Body language, hands, pacing, and vocabulary should be reviewed.

Best public speakers evaluate their performance to improve.

Write down what you did best, what you could improve and what you should stop doing after watching a recording of yourself. Seeing yourself can be unsettling. This is how you improve.

5. Remove text from slides

"Humans can't read and comprehend screen text while listening to a speaker. Therefore, lots of text and long, complete sentences are bad, bad, bad.” —Communications expert Garr Reynolds

Presentation slides shouldn't have too much text. 100-slide presentations bore the audience. Your slides should preview what you'll say to the audience.

Use slides to emphasize your main point visually.

If you add text, use at least 40-point font. Your slides shouldn't require squinting to read. You want people to watch you, not your slides.

6. Body language

"Body language is powerful." We had body language before speech, and 80% of a conversation is read through the body, not the words." — Dancer, writer, and broadcaster Deborah Bull

Nonverbal communication dominates. Our bodies speak louder than words. Don't fidget, rock, lean, or pace.

Relax your body to communicate clearly and without distraction through nonverbal cues. Public speaking anxiety can cause tense body language.

Maintain posture and eye contact. Don’t put your hand in your pockets, cross your arms, or stare at your notes. Make purposeful hand gestures that match what you're saying.

7. Beginning/ending Strong

Beginning and end are memorable. Your presentation must start strong and end strongly. To engage your audience, don't sound robotic.

Begin with a story, stat, or quote. Conclude with a summary of key points. Focus on how you will start and end your speech.

You should memorize your presentation's opening and closing. Memorize something naturally. Excellent presentations start and end strong because people won't remember the middle.

Bringing It All Together

Seven simple yet powerful ways to improve public speaking. Know your audience, study others, prepare and rehearse, record yourself, remove as much text as possible from slides, and start and end strong.

Follow these tips to improve your speaking and audience communication. Prepare, practice, and learn from great speakers to reduce your fear of public speaking.

"Speaking to one person or a thousand is public speaking." — Vocal coach Roger Love

He built a $40M hip-hop empire from street drug dealing.

50 Cent was nearly killed by 9mm bullets.

Before 50 Cent, Curtis Jackson sold drugs.

He sold coke to worried addicts after being orphaned at 8.

Pursuing police. Murderous hustlers and gangs. Unwitting informers.

Despite his hard life, his hip-hop career was a success.

An assassination attempt ended his career at the start.

What sane producer would want to deal with a man entrenched in crime?

Most would have drowned in self-pity and drank themselves to death.

But 50 Cent isn't most people. Life on the streets had given him fearlessness.

“Having a brush with death, or being reminded in a dramatic way of the shortness of our lives, can have a positive, therapeutic effect. So it is best to make every moment count, to have a sense of urgency about life.” ― 50 Cent, The 50th Law

50 released a series of mixtapes that caught Eminem's attention and earned him a $50 million deal!

50 Cents turned death into life.

Things happen; that is life.

We want problems solved.

Every human has problems, whether it's Jeff Bezos swimming in his billions, Obama in his comfortable retirement home, or Dan Bilzerian with his hired bikini models.

All problems.

Problems churn through life. solve one, another appears.

It's harsh. Life's unfair. We can face reality or run from it.

The latter will worsen your issues.

“The firmer your grasp on reality, the more power you will have to alter it for your purposes.” — 50 Cent, The 50th Law

In a fantasy-obsessed world, 50 Cent loves reality.

Wish for better problem-solving skills rather than problem-free living.

Don't wish, work.

We All Have the True Power of Alchemy

Humans are arrogant enough to think the universe cares about them.

That things happen as if the universe notices our nanosecond existences.

Things simply happen. Period.

By changing our perspective, we can turn good things bad.

The alchemists' search for the philosopher's stone may have symbolized the ability to turn our lead-like perceptions into gold.

Negativity bias tints our perceptions.

Normal sparring broke your elbow? Rest and rethink your training. Fired? You can improve your skills and get a better job.

Consider Curtis if he had fallen into despair.

The legend we call 50 Cent wouldn’t have existed.

The Best Lesson in Life Ever?

Neither avoid nor fear your reality.

That simple sentence contains every self-help tip and life lesson on Earth.

When reality is all there is, why fear it? avoidance?

Or worse, fleeing?

To accept reality, we must eliminate the words should be, could be, wish it were, and hope it will be.

It is. Period.

Only by accepting reality's chaos can you shape your life.

“Behind me is infinite power. Before me is endless possibility, around me is boundless opportunity. My strength is mental, physical and spiritual.” — 50 Cent

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

Amazon's Rings of Power is the most costly TV series ever made. This is merely a down payment towards Amazon's grand goal.

Here's a video:

Amazon bought J.R.R. Tolkien's fantasy novels for $250 million in 2017. This agreement allows Amazon to create a Tolkien series for Prime Video.

The business spent years developing and constructing a Lord of the Rings prequel. Rings of Power premiered on September 2, 2022.

It drew 25 million global viewers in 24 hours. Prime Video's biggest debut.

An Exorbitant Budget

The most expensive. First season cost $750 million to $1 billion, making it the most costly TV show ever.

Jeff Bezos has spent years looking for the next Game of Thrones, a critically and commercially successful original series. Rings of Power could help.

Why would Amazon bet $1 billion on one series?

It's Not Just About the Streaming War

It's simple to assume Amazon just wants to win. Since 2018, the corporation has been fighting Hulu, Netflix, HBO, Apple, Disney, and NBC. Each wants your money, talent, and attention. Amazon's investment goes beyond rivalry.

Subscriptions Are the Bait

Audible, Amazon Music, and Prime Video are subscription services, although the company's fundamental business is retail. Amazon's online stores contribute over 50% of company revenue. Subscription services contribute 6.8%. The company's master plan depends on these subscriptions.

Streaming videos on Prime increases membership renewals. Free trial participants are more likely to join. Members buy twice as much as non-members.

Amazon Studios doesn't generate original programming to earn from Prime Video subscriptions. It aims to retain and attract clients.

Amazon can track what you watch and buy. Its algorithm recommends items and services. Mckinsey says you'll use more Amazon products, shop at Amazon stores, and watch Amazon entertainment.

In 2015, the firm launched the first season of The Man in the High Castle, a dystopian alternate history TV series depicting a world ruled by Nazi Germany and Japan after World War II.

This $72 million production earned two Emmys. It garnered 1.15 million new Prime users globally.

When asked about his Hollywood investment, Bezos said, "A Golden Globe helps us sell more shoes."

Selling more footwear

Amazon secured a deal with DirecTV to air Thursday Night Football in restaurants and bars. First streaming service to have exclusive NFL games.

This isn't just about Thursday night football, says media analyst Ritchie Greenfield. This sells t-shirts. This may be a ticket. Amazon does more than stream games.

The Rings of Power isn't merely a production showcase, either. This sells Tolkien's fantasy novels such Lord of the Rings, The Hobbit, and The Silmarillion.

This tiny commitment keeps you in Amazon's ecosystem.

> 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.

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.