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

I read 53 novels last year and hope to do so again.

Books are best if you love learning. You get a range of perspectives, unlike podcasts and YouTube channels where you get the same ones.

Book quality varies. I've read useless books. Most books teach me something.

These 9 novels have changed my outlook in recent years. They've made me rethink what I believed or introduced me to a fresh perspective that changed my worldview.

You can order these books yourself. Or, read my summaries to learn what I've synthesized.

Enjoy!

Fooled By Randomness

Nassim Taleb worked as a Wall Street analyst. He used options trading to bet on unlikely events like stock market crashes.

Using financial models, investors predict stock prices. The models assume constant, predictable company growth.

These models base their assumptions on historical data, so they assume the future will be like the past.

Fooled By Randomness argues that the future won't be like the past. We often see impossible market crashes like 2008's housing market collapse. The world changes too quickly to use historical data: by the time we understand how it works, it's changed.

Most people don't live to see history unfold. We think our childhood world will last forever. That goes double for stable societies like the U.S., which hasn't seen major turbulence in anyone's lifetime.

Fooled By Randomness taught me to expect the unexpected. The world is deceptive and rarely works as we expect. You can't always trust your past successes or what you've learned.

Antifragile

More Taleb. Some things, like the restaurant industry and the human body, improve under conditions of volatility and turbulence.

We didn't have a word for this counterintuitive concept until Taleb wrote Antifragile. The human body (which responds to some stressors, like exercise, by getting stronger) and the restaurant industry both benefit long-term from disorder (when economic turbulence happens, bad restaurants go out of business, improving the industry as a whole).

Many human systems are designed to minimize short-term variance because humans don't understand it. By eliminating short-term variation, we increase the likelihood of a major disaster.

Once, we put out every forest fire we found. Then, dead wood piled up in forests, causing catastrophic fires.

We don't like price changes, so politicians prop up markets with stimulus packages and printing money. This leads to a bigger crash later. Two years ago, we printed a ton of money for stimulus checks, and now we have double-digit inflation.

Antifragile taught me how important Plan B is. A system with one or two major weaknesses will fail. Make large systems redundant, foolproof, and change-responsive.

Reality is broken

We dread work. Work is tedious. Right?

Wrong. Work gives many people purpose. People are happiest when working. (That's why some are workaholics.)

Factory work saps your soul, office work is boring, and working for a large company you don't believe in and that operates unethically isn't satisfying.

Jane McGonigal says in Reality Is Broken that meaningful work makes us happy. People love games because they simulate good work. McGonigal says work should be more fun.

Some think they'd be happy on a private island sipping cocktails all day. That's not true. Without anything to do, most people would be bored. Unemployed people are miserable. Many retirees die within 2 years, much more than expected.

Instead of complaining, find meaningful work. If you don't like your job, it's because you're in the wrong environment. Find the right setting.

The Lean Startup

Before the airplane was invented, Harvard scientists researched flying machines. Who knew two North Carolina weirdos would beat them?

The Wright Brothers' plane design was key. Harvard researchers were mostly theoretical, designing an airplane on paper and trying to make it fly in theory. They'd build it, test it, and it wouldn't fly.

The Wright Brothers were different. They'd build a cheap plane, test it, and it'd crash. Then they'd learn from their mistakes, build another plane, and it'd crash.

They repeated this until they fixed all the problems and one of their planes stayed aloft.

Mistakes are considered bad. On the African savannah, one mistake meant death. Even today, if you make a costly mistake at work, you'll be fired as a scapegoat. Most people avoid failing.

In reality, making mistakes is the best way to learn.

Eric Reis offers an unintuitive recipe in The Lean Startup: come up with a hypothesis, test it, and fail. Then, try again with a new hypothesis. Keep trying, learning from each failure.

This is a great startup strategy. Startups are new businesses. Startups face uncertainty. Run lots of low-cost experiments to fail, learn, and succeed.

Don't fear failing. Low-cost failure is good because you learn more from it than you lose. As long as your worst-case scenario is acceptable, risk-taking is good.

The Sovereign Individual

Today, nation-states rule the world. The UN recognizes 195 countries, and they claim almost all land outside of Antarctica.

We agree. For the past 2,000 years, much of the world's territory was ungoverned.

Why today? Because technology has created incentives for nation-states for most of the past 500 years. The logic of violence favors nation-states, according to James Dale Davidson, author of the Sovereign Individual. Governments have a lot to gain by conquering as much territory as possible, so they do.

Not always. During the Dark Ages, Europe was fragmented and had few central governments. Partly because of armor. With armor, a sword, and a horse, you couldn't be stopped. Large states were hard to form because they rely on the threat of violence.

When gunpowder became popular in Europe, violence changed. In a world with guns, assembling large armies and conquest are cheaper.

James Dale Davidson says the internet will make nation-states obsolete. Most of the world's wealth will be online and in people's heads, making capital mobile.

Nation-states rely on predatory taxation of the rich to fund large militaries and welfare programs.

When capital is mobile, people can live anywhere in the world, Davidson says, making predatory taxation impossible. They're not bound by their job, land, or factory location. Wherever they're treated best.

Davidson says that over the next century, nation-states will collapse because they won't have enough money to operate as they do now. He imagines a world of small city-states, like Italy before 1900. (or Singapore today).

We've already seen some movement toward a more Sovereign Individual-like world. The pandemic proved large-scale remote work is possible, freeing workers from their location. Many cities and countries offer remote workers incentives to relocate.

Many Western businesspeople live in tax havens, and more people are renouncing their US citizenship due to high taxes. Increasing globalization has led to poor economic conditions and resentment among average people in the West, which is why politicians like Trump and Sanders rose to popularity with angry rhetoric, even though Obama rose to popularity with a more hopeful message.

The Sovereign Individual convinced me that the future will be different than Nassim Taleb's. Large countries like the U.S. will likely lose influence in the coming decades, while Portugal, Singapore, and Turkey will rise. If the trend toward less freedom continues, people may flee the West en masse.

So a traditional life of college, a big firm job, hard work, and corporate advancement may not be wise. Young people should learn as much as possible and develop flexible skills to adapt to the future.

Sapiens

Sapiens is a history of humanity, from proto-humans in Ethiopia to our internet society today, with some future speculation.

Sapiens views humans (and Homo sapiens) as a unique species on Earth. We were animals 100,000 years ago. We're slowly becoming gods, able to affect the climate, travel to every corner of the Earth (and the Moon), build weapons that can kill us all, and wipe out thousands of species.

Sapiens examines what makes Homo sapiens unique. Humans can believe in myths like religion, money, and human-made entities like countries and LLCs.

These myths facilitate large-scale cooperation. Ants from the same colony can cooperate. Any two humans can trade, though. Even if they're not genetically related, large groups can bond over religion and nationality.

Combine that with intelligence, and you have a species capable of amazing feats.

Sapiens may make your head explode because it looks at the world without presupposing values, unlike most books. It questions things that aren't usually questioned and says provocative things.

It also shows how human history works. It may help you understand and predict the world. Maybe.

The 4-hour Workweek

Things can be done better.

Tradition, laziness, bad bosses, or incentive structures cause complacency. If you're willing to make changes and not settle for the status quo, you can do whatever you do better and achieve more in less time.

The Four-Hour Work Week advocates this. Tim Ferriss explains how he made more sales in 2 hours than his 8-hour-a-day colleagues.

By firing 2 of his most annoying customers and empowering his customer service reps to make more decisions, he was able to leave his business and travel to Europe.

Ferriss shows how to escape your 9-to-5, outsource your life, develop a business that feeds you with little time, and go on mini-retirement adventures abroad.

Don't accept the status quo. Instead, level up. Find a way to improve your results. And try new things.

Why Nations Fail

Nogales, Arizona and Mexico were once one town. The US/Mexico border was arbitrarily drawn.

Both towns have similar cultures and populations. Nogales, Arizona is well-developed and has a high standard of living. Nogales, Mexico is underdeveloped and has a low standard of living. Whoa!

Why Nations Fail explains how government-created institutions affect country development. Strong property rights, capitalism, and non-corrupt governments promote development. Countries without capitalism, strong property rights, or corrupt governments don't develop.

Successful countries must also embrace creative destruction. They must offer ordinary citizens a way to improve their lot by creating value for others, not reducing them to slaves, serfs, or peasants. Authors say that ordinary people could get rich on trading expeditions in 11th-century Venice.

East and West Germany and North and South Korea have different economies because their citizens are motivated differently. It explains why Chile, China, and Singapore grow so quickly after becoming market economies.

People have spent a lot of money on third-world poverty. According to Why Nations Fail, education and infrastructure aren't the answer. Developing nations must adopt free-market economic policies.

Elon Musk

Elon Musk is the world's richest man, but that’s not a good way to describe him. Elon Musk is the world's richest man, which is like calling Steve Jobs a turtleneck-wearer or Benjamin Franklin a printer.

Elon Musk does cool sci-fi stuff to help humanity avoid existential threats.

Oil will run out. We've delayed this by developing better extraction methods. We only have so much nonrenewable oil.

Our society is doomed if it depends on oil. Elon Musk invested heavily in Tesla and SolarCity to speed the shift to renewable energy.

Musk worries about AI: we'll build machines smarter than us. We won't be able to stop these machines if something goes wrong, just like cows can't fight humans. Neuralink: we need to be smarter to compete with AI when the time comes.

If Earth becomes uninhabitable, we need a backup plan. Asteroid or nuclear war could strike Earth at any moment. We may not have much time to react if it happens in a few days. We must build a new civilization while times are good and resources are plentiful.

Short-term problems dominate our politics, but long-term issues are more important. Long-term problems can cause mass casualties and homelessness. Musk demonstrates how to think long-term.

The main reason people are impressed by Elon Musk, and why Ashlee Vances' biography influenced me so much, is that he does impossible things.

Electric cars were once considered unprofitable, but Tesla has made them mainstream. SpaceX is the world's largest private space company.

People lack imagination and dismiss ununderstood ideas as impossible. Humanity is about pushing limits. Don't worry if your dreams seem impossible. Try it.

Thanks for reading.

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

Writing for readers:

14 years of daily writing.

I post practically everything on social media. I authored hundreds of articles, thousands of tweets, and numerous volumes to almost no one.

Tens of thousands of readers regularly praise me.

I despised writing. I'm stuck now.

I've learned what readers like and what doesn't.

Here are some essential guidelines for writing with impact:

Readers won't understand your work if you can't.

Though obvious, this slipped me up. Share your truths.

Stories engage human brains.

Showing the journey of a person from worm to butterfly inspires the human spirit.

Overthinking hinders powerful writing.

The best ideas come from inner understanding in between thoughts.

Avoid writing to find it. Write.

Writing a masterpiece isn't motivating.

Write for five minutes to simplify. Step-by-step, entertaining, easy steps.

Good writing requires a willingness to make mistakes.

So write loads of garbage that you can edit into a good piece.

Courageous writing.

A courageous story will move readers. Personal experience is best.

Go where few dare.

Templates, outlines, and boundaries help.

Limitations enhance writing.

Excellent writing is straightforward and readable, removing all the unnecessary fat.

Use five words instead of nine.

Use ordinary words instead of uncommon ones.

Readers desire relatability.

Too much perfection will turn it off.

Write to solve an issue if you can't think of anything to write.

Instead, read to inspire. Best authors read.

Every tweet, thread, and novel must have a central idea.

What's its point?

This can make writing confusing.

️ Don't direct your reader.

Readers quit reading. Demonstrate, describe, and relate.

Even if no one responds, have fun. If you hate writing it, the reader will too.

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.

The Top 8 Growth Hacking Techniques for Startups

These startups, and how they used growth-hack marketing to flourish, are some of the more ethical ones, while others are less so.

Before the 1970 World Cup began, Puma paid footballer Pele $120,000 to tie his shoes. The cameras naturally focused on Pele and his Pumas, causing people to realize that Puma was the top football brand in the world.

Early workers of Uber canceled over 5,000 taxi orders made on competing applications in an effort to financially hurt any of their rivals.

PayPal developed a bot that advertised cheap goods on eBay, purchased them, and paid for them with PayPal, fooling eBay into believing that customers preferred this payment option. Naturally, Paypal became eBay's primary method of payment.

Anyone renting a space on Craigslist had their emails collected by AirBnB, who then urged them to use their service instead. A one-click interface was also created to list immediately on AirBnB from Craigslist.

To entice potential single people looking for love, Tinder developed hundreds of bogus accounts of attractive people. Additionally, for at least a year, users were "accidentally" linked.

Reddit initially created a huge number of phony accounts and forced them all to communicate with one another. It eventually attracted actual users—the real meaning of "fake it 'til you make it"! Additionally, this gave Reddit control over the tone of voice they wanted for their site, which is still present today.

To disrupt the conferences of their main rival, Salesforce recruited fictitious protestors. The founder then took over all of the event's taxis and gave a 45-minute pitch for his startup. No place to hide!

When a wholesaler required a minimum purchase of 10, Amazon CEO Jeff Bezos wanted a way to purchase only one book from them. A wholesaler would deliver the one book he ordered along with an apology for the other eight books after he discovered a loophole and bought the one book before ordering nine books about lichens. On Amazon, he increased this across all of the users.

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