Who is AMTD Digital?

An unknown Hong Kong corporation joined the global megacaps worth over $500 billion on Tuesday.

The American Depository Share (ADS) with the ticker code HKD gapped at the open, soaring 25% over the previous closing price as trading began, before hitting an intraday high of $2,555.

At its peak, its market cap was almost $450 billion, more than Facebook parent Meta or Alibaba.

Yahoo Finance reported a daily volume of 350,500 shares, the lowest since the ADS began trading and much below the average of 1.2 million.

Despite losing a fifth of its value on Wednesday, it's still worth more than Toyota, Nike, McDonald's, or Walt Disney.

The company sold 16 million shares at $7.80 each in mid-July, giving it a $1 billion market valuation.

Why the boom?

That market cap seems unjustified.

According to SEC reports, its income-generating assets barely topped $400 million in March. Fortune's emails and calls went unanswered.

Website discloses little about company model. Its one-minute business presentation film uses a Star Wars–like design to sell the company as a "one-stop digital solutions platform in Asia"

The SEC prospectus explains.

AMTD Digital sells a "SpiderNet Ecosystems Solutions" kind of club membership that connects enterprises. This is the bulk of its $25 million annual revenue in April 2021.

Pretax profits have been higher than top line over the past three years due to fair value accounting gains on Appier, DayDayCook, WeDoctor, and five Asian fintechs.

AMTD Group, the company's parent, specializes in investment banking, hotel services, luxury education, and media and entertainment. AMTD IDEA, a $14 billion subsidiary, is also traded on the NYSE.

“Significant volatility”

Why AMTD Digital listed in the U.S. is unknown, as it informed investors in its share offering prospectus that could delist under SEC guidelines.

Beijing's red tape prevents the Sarbanes-Oxley Board from inspecting its Chinese auditor.

This frustrates Chinese stock investors. If the U.S. and China can't achieve a deal, 261 Chinese companies worth $1.3 trillion might be delisted.

Calvin Choi left UBS to become AMTD Group's CEO.

His capitalist background and status as a Young Global Leader with the World Economic Forum don't stop him from praising China's Communist party or celebrating the "glory and dream of the Great Rejuvenation of the Chinese nation" a century after its creation.

Despite having an executive vice chairman with a record of battling corruption and ties to Carrie Lam, Beijing's previous proconsul in Hong Kong, Choi is apparently being targeted for a two-year industry ban by the city's securities regulator after an investor accused Choi of malfeasance.

Some CMIG-funded initiatives produced money, but he didn't give us the proceeds, a corporate official told China's Caixin in October 2020. We don't know if he misappropriated or lost some money.

A seismic anomaly

In fundamental analysis, where companies are valued based on future cash flows, AMTD Digital's mind-boggling market cap is a statistical aberration that should occur once every hundred years.

AMTD Digital doesn't know why it's so valuable. In a thank-you letter to new shareholders, it said it was confused by the stock's performance.

Since its IPO, the company has seen significant ADS price volatility and active trading volume, it said Tuesday. "To our knowledge, there have been no important circumstances, events, or other matters since the IPO date."

Permabears awoke after the jump. Jim Chanos asked if "we're all going to ignore the $400 billion meme stock in the room," while Nate Anderson called AMTD Group "sketchy."

It happened the same day SEC Chair Gary Gensler praised the 20th anniversary of the Sarbanes-Oxley Act, aimed to restore trust in America's financial markets after the Enron and WorldCom accounting fraud scandals.

The run-up revived unpleasant memories of Robinhood's decision to limit retail investors' ability to buy GameStop, regarded as a measure to protect hedge funds invested in the meme company.

Why wasn't HKD's buy button removed? Because retail wasn't behind it?" tweeted Gensler on Tuesday. "Real stock fraud. "You're worthless."

What quarterly bank earnings reveal

Big banks know the economy best. Unless we’re talking about a housing crisis in 2007…

Banks are crucial to the U.S. economy. The Fed, communities, and investments exchange money.

An economy depends on money flow. Banks' views on the economy can affect their decision-making.

Most large banks released quarterly earnings and forward guidance last week. Others were pessimistic about the future.

What Makes Banks Confident

Bank of America's profit decreased 30% year-over-year, but they're optimistic about the economy. Comparatively, they're bullish.

Who banks serve affects what they see. Bank of America supports customers.

They think consumers' future is bright. They believe this for many reasons.

The average customer has decent credit, unless the system is flawed. Bank of America's new credit card and mortgage borrowers averaged 771. New-car loan and home equity borrower averages were 791 and 797.

2008's housing crisis affected people with scores below 620.

Bank of America and the economy benefit from a robust consumer. Major problems can be avoided if individuals maintain spending.

Reasons Other Banks Are Less Confident

Spending requires income. Many companies, mostly in the computer industry, have announced they will slow or freeze hiring. Layoffs are frequently an indication of poor times ahead.

BOA is positive, but investment banks are bearish.

Jamie Dimon, CEO of JPMorgan, outlined various difficulties our economy could confront.

But geopolitical tension, high inflation, waning consumer confidence, the uncertainty about how high rates have to go and the never-before-seen quantitative tightening and their effects on global liquidity, combined with the war in Ukraine and its harmful effect on global energy and food prices are very likely to have negative consequences on the global economy sometime down the road.

That's more headwinds than tailwinds.

JPMorgan, which helps with mergers and IPOs, is less enthusiastic due to these concerns. Incoming headwinds signal drying liquidity, they say. Less business will be done.

Final Reflections

I don't think we're done. Yes, stocks are up 10% from a month ago. It's a long way from old highs.

I don't think the stock market is a strong economic indicator.

Many executives foresee a 2023 recession. According to the traditional definition, we may be in a recession when Q2 GDP statistics are released next week.

Regardless of criteria, I predict the economy will have a terrible year.

Weekly layoffs are announced. Inflation persists. Will prices return to 2020 levels if inflation cools? Perhaps. Still expensive energy. Ukraine's war has global repercussions.

I predict BOA's next quarter earnings won't be as bullish about the consumer's strength.

ZERO GRACE/ZERO MALICE

Big companies and wealthy people make stupid mistakes too.

Your ancestors kept snakes and drank bad water. You (probably) don't because you've learnt from their failures via instinct+, the ultimate life-lessons streaming network in your head. Instincts foretell the future. If you approach a lion, it'll eat you. Our society's nuanced/complex decisions have surpassed instinct. Human growth depends on how we handle these issues. 80% of people believe they are above-average drivers, yet few believe they make many incorrect mistakes that make them risky. Stupidity hurts others like death. Basic Laws of Human Stupidity by Carlo Cipollas:

1. Everyone underestimates the prevalence of idiots in our society.

2. Any other trait a person may have has no bearing on how likely they are to be stupid.

3. A dumb individual is one who harms someone without benefiting themselves and may even lose money in the process.

4. Non-dumb people frequently underestimate how destructively powerful stupid people can be.

5. The most dangerous kind of person is a moron.

Professor Cippola defines stupid as bad for you and others. We underestimate the corporate world's and seemingly successful people's ability to make bad judgments that harm themselves and others. Success is an intoxication that makes you risk-aggressive and blurs your peripheral vision.

Stupid companies and decisions:

Big Dumber

Big-company bad ideas have more bulk and inertia. The world's most valuable company recently showed its board a VR headset. Jony Ive couldn't destroy Apple's terrible idea in 2015. Mr. Ive said that VR cut users off from the outer world, made them seem outdated, and lacked practical uses. Ives' design team doubted users would wear headsets for lengthy periods.

VR has cost tens of billions of dollars over a decade to prove nobody wants it. The next great SaaS startup will likely come from Florence, not Redmond or San Jose.

Apple Watch and Airpods have made the Cupertino company the world's largest jewelry maker. 10.5% of Apple's income, or $38 billion, comes from wearables in 2021. (seven times the revenue of Tiffany & Co.). Jewelry makes you more appealing and useful. Airpods and Apple Watch do both.

Headsets make you less beautiful and useful and promote isolation, loneliness, and unhappiness among American teenagers. My sons pretend they can't hear or see me when on their phones. VR headsets lack charisma.

Coinbase disclosed a plan to generate division and tension within its workplace weeks after Apple was pitched $2,000 smokes. The crypto-trading platform is piloting a program that rates staff after every interaction. If a coworker says anything you don't like, you should tell them how to improve. Everyone gets a 110-point scorecard. Coworkers should evaluate a person's rating while deciding whether to listen to them. It's ridiculous.

Organizations leverage our superpower of cooperation. This encourages non-cooperation, period. Bridgewater's founder Ray Dalio designed the approach to promote extreme transparency. Dalio has 223 billion reasons his managerial style works. There's reason to suppose only a small group of people, largely traders, will endure a granular scorecard. Bridgewater has 20% first-year turnover. Employees cry in bathrooms, and sex scandals are settled by ignoring individuals with poor believability levels. Coinbase might take solace that the stock is 80% below its initial offering price.

Poor Stupid

Fools' ledgers are valuable. More valuable are lists of foolish rich individuals.

Robinhood built a $8 billion corporation on financial ignorance. The firm's median account value is $240, and its stock has dropped 75% since last summer. Investors, customers, and society lose. Stupid. Luna published a comparable list on the blockchain, grew to $41 billion in market cap, then plummeted.

A podcast presenter is recruiting dentists and small-business owners to invest in Elon Musk's Twitter takeover. Investors pay a 7% fee and 10% of the upside for the chance to buy Twitter at a 35% premium to the current price. The proposal legitimizes CNBC's Trade Like Chuck advertising (Chuck made $4,600 into $460,000 in two years). This is stupid because it adds to the Twitter deal's desperation. Mr. Musk made an impression when he urged his lawyers to develop a legal rip-cord (There are bots on the platform!) to abandon the share purchase arrangement (for less than they are being marketed by the podcaster). Rolls-Royce may pay for this list of the dumb affluent because it includes potential Cullinan buyers.

Worst company? Flowcarbon, founded by WeWork founder Adam Neumann, operates at the convergence of carbon and crypto to democratize access to offsets and safeguard the earth's natural carbon sinks. Can I get an ayahuasca Big Gulp?

Neumann raised $70 million with their yogababble drink. More than half of the consideration came from selling GNT. Goddess Nature Token. I hope the company gets an S-1. Or I'll start a decentralized AI Meta Renewable NFTs company. My Community Based Ebitda coin will fund the company. Possible.

Stupidity inside oneself

This weekend, I was in NYC with my boys. My 14-year-old disappeared. He's realized I'm not cool and is mad I let the charade continue. When out with his dad, he likes to stroll home alone and depart before me. Friends told me hell would return, but I was surprised by how fast the eye roll came.

Not so with my 11-year-old. We went to The Edge, a Hudson Yards observation platform where you can see the city from 100 storeys up for $38. This is hell's seventh ring. Leaning into your boys' interests is key to engaging them (dad tip). Neither loves Crossfit, WW2 history, or antitrust law.

We take selfies on the Thrilling Glass Floor he spots. Dad, there's a bar! Coke? I nod, he rushes to the bar, stops, runs back for money, and sprints back. Sitting on stone seats, drinking Atlanta Champagne, he turns at me and asks, Isn't this amazing? I'll never reach paradise.

Later that night, the lads are asleep and I've had two Zacapas and Cokes. I SMS some friends about my day and how I feel about sons/fatherhood/etc. How I did. They responded and approached. The next morning, I'm sober, have distance from my son, and feel ashamed by my texts. Less likely to impulsively share my emotions with others. Stupid again.

"Don't let technology control you; manage your phone."

"Don't become a slave to technology," said Richard Branson. "Manage your phone, don't let it manage you."

Unfortunately, most people are addicted to smartphones.

Worrying smartphone statistics:

• 46% of smartphone users spend 5–6 hours daily on their device.

• The average adult spends 3 hours 54 minutes per day on mobile devices.

• We check our phones 150–344 times per day (every 4 minutes).

• During the pandemic, children's daily smartphone use doubled.

Having a list of productive, healthy, and fulfilling replacement activities is an effective way to reduce smartphone use.

The more you practice these smartphone replacements, the less time you'll waste.

Skills Development

Most people say they 'don't have time' to learn new skills or read more. Lazy justification. The issue isn't time, but time management. Distractions and low-quality entertainment waste hours every day.

The majority of time is spent in low-quality ways, according to Richard Koch, author of The 80/20 Principle.

What if you swapped daily phone scrolling for skill-building?

There are dozens of skills to learn, from high-value skills to make more money to new languages and party tricks.

Learning a new skill will last for years, if not a lifetime, compared to scrolling through your phone.

Watch Docs

Love documentaries. It's educational and relaxing. A good documentary helps you understand the world, broadens your mind, and inspires you to change.

Recent documentaries I liked include:

• 14 Peaks: Nothing Is Impossible

• The Social Dilemma

• Jim & Andy: The Great Beyond

• Fantastic Fungi

Make money online

If you've ever complained about not earning enough money, put away your phone and get to work.

Instead of passively consuming mobile content, start creating it. Create something worthwhile. Freelance.

Internet makes starting a business or earning extra money easier than ever.

(Grand)parents didn't have this. Someone made them work 40+ hours. Few alternatives existed.

Today, all you need is internet and a monetizable skill. Use the internet instead of letting it distract you. Profit from it.

Bookworm

Jack Canfield, author of Chicken Soup For The Soul, said, "Everyone spends 2–3 hours a day watching TV." If you read that much, you'll be in the top 1% of your field."

Few people have more than two hours per day to read.

If you read 15 pages daily, you'd finish 27 books a year (as the average non-fiction book is about 200 pages).

Jack Canfield's quote remains relevant even though 15 pages can be read in 20–30 minutes per day. Most spend this time watching TV or on their phones.

What if you swapped 20 minutes of mindless scrolling for reading? You'd gain knowledge and skills.

Favorite books include:

• The 7 Habits of Highly Effective People — Stephen R. Covey

• The War of Art — Steven Pressfield

• The Psychology of Money — Morgan Housel

• A New Earth — Eckart Tolle

Get Organized

All that screen time could've been spent organizing. It could have been used to clean, cook, or plan your week.

If you're always 'behind,' spend 15 minutes less on your phone to get organized.

"Give me six hours to chop down a tree, and I'll spend the first four sharpening the ax," said Abraham Lincoln. Getting organized is like sharpening an ax, making each day more efficient.

Creativity

Why not be creative instead of consuming others'? Do something creative, like:

• Painting

• Musically

• Photography\sWriting

• Do-it-yourself

• Construction/repair

Creative projects boost happiness, cognitive functioning, and reduce stress and anxiety. Creative pursuits induce a flow state, a powerful mental state.

This contrasts with smartphones' effects. Heavy smartphone use correlates with stress, depression, and anxiety.

Hike

People spend 90% of their time indoors, according to research. This generation is the 'Indoor Generation'

We lack an active lifestyle, fresh air, and vitamin D3 due to our indoor lifestyle (generated through direct sunlight exposure). Mental and physical health issues result.

Put away your phone and get outside. Go on nature walks. Explore your city on foot (or by bike, as we do in Amsterdam) if you live in a city. Move around! Outdoors!

You can't spend your whole life staring at screens.

Podcasting

Okay, a smartphone is needed to listen to podcasts. When you use your phone to get smarter, you're more productive than 95% of people.

Favorite podcasts:

• The Pomp Podcast (about cryptocurrencies)

• The Joe Rogan Experience

• Kwik Brain (by Jim Kwik)

Podcasts can be enjoyed while walking, cleaning, or doing laundry. Win-win.

Journalize

I find journaling helpful for mental clarity. Writing helps organize thoughts.

Instead of reading internet opinions, comments, and discussions, look inward. Instead of Twitter or TikTok, look inward.

“It never ceases to amaze me: we all love ourselves more than other people, but care more about their opinion than our own.” — Marcus Aurelius

Give your mind free reign with pen and paper. It will highlight important thoughts, emotions, or ideas.

Never write for another person. You want unfiltered writing. So you get the best ideas.

Find your best hobbies

List your best hobbies. I guarantee 95% of people won't list smartphone scrolling.

It's often low-quality entertainment. The dopamine spike is short-lived, and it leaves us feeling emotionally 'empty'

High-quality leisure sparks happiness. They make us happy and alive. Everyone has different interests, so these activities vary.

My favorite quality hobbies are:

• Nature walks (especially the mountains)

• Video game party

• Watching a film with my girlfriend

• Gym weightlifting

• Complexity learning (such as the blockchain and the universe)

This brings me joy. They make me feel more fulfilled and 'rich' than social media scrolling.

Make a list of your best hobbies to refer to when you're spending too much time on your phone.

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.