Here is the ugly stuff, read this if you have a founder in your life or are trying to become one. Your call.

#1 You'll try to talk yourself to sleep, but it won't always work.

As founders, we're all driven. Good and bad, you're restless. Success requires resistance and discipline. Your startup will be on your mind 24/7, and not everyone will have the patience to listen to your worries, ideas, and coffee runs. You become more self-sufficient than ever before.

#2 No one will understand what you're going through unless they've been a founder.

Some of my closest friends don't understand the work that goes into starting a business, and we can't blame them.

#3 You'll feel alienated.

Your problems aren't common; calling your bestie won't help. You must search hard for the right resources. It alienates you from conversations you no longer relate to. (No 4th of July, no long weekends!)

#4 Since you're your "own boss," people assume you have lots of free time.

Do you agree? I was on a webinar with lots of new entrepreneurs, and one woman said, "I started my own business so I could have more time for myself." This may be true for some lucky people, and you can be flexible with your schedule. If you want your business to succeed, you'll probably be its slave for a while.

#5 No time for illness or family emergencies.

Both last month. Oh, no! Physically and emotionally withdrawing at the worst times will give you perspective. I learned this the hard way because I was too stubborn to postpone an important interview. I thought if I rested all day and only took one call, I'd be fine. Nope. I had a fever and my mind wasn't as sharp, so my performance and audience interaction suffered. Nope. Better to delay than miss out.

Oh, and setting a "OoO" makes you cringe.

#6 Good luck with your mental health, perfectionists.

When building a startup, it's difficult to accept that there won't be enough time to do everything. You can't make them all, not perfectly. You must learn to accept things that are done but not perfect.

#7 As a founder, you'll make mistakes, but you'll want to make them quickly so you can learn.

Hard lessons are learned quicker. You'll need to pivot and try new things often; some won't work, and it's best to discover them sooner rather than later.

#8 Pyramid schemes abound.

I didn't realize how bad it was until I started a company. You must spy and constantly research. As a founder, you'll receive many emails from people claiming to "support" you. Be wary and keep your eyes open. When it's too good to be true. Some "companies" will try to get you to pay for "competitions" to "pitch at events." Don't do it.

#9 Keep your competitor research to a minimum.

Actually, competition is good. It means there's a market for those solutions. However, this can be mentally exhausting too. Learn about their geography and updates, but that's it.

#10 You'll feel guilty taking vacation.

I don't know what to say, but I no longer enjoy watching TV, and that's okay. Pay attention to things that enrich you, bring you joy, and have fun. It boosts creativity.

Being a startup founder may be one of the hardest professional challenges you face, but it's also a great learning experience. Your passion will take you places you never imagined and open doors to opportunities you wouldn't have otherwise. You'll meet amazing people. No regrets, no complaints. It's a roller coaster, but the good days are great.

Miss anything? Comment below

I've always bucked social media norms. YouTube doesn't compare. Traditional video made me zig when everyone zagged. Audio, picture personality animation, thought movies, and slide show videos are most popular and profitable.

YouTube's business is shifting. While most video experts swear by the idea that YouTube success is all about making personal and professional Face-Share-Videos, those who use YouTube for business know things are different.

In this article, I will share concepts from my mini master class Figures to Followers: Prioritizing Purposeful Profits Over Popularity on YouTube to Create the Win-Win for You, Your Audience & More and my forthcoming publication The WOWTUBE-PRENEUR FACTOR EVOLUTION: The Basics of Powerfully & Profitably Positioning Yourself as a Video Communications Authority to Broadcast Your WOW Effect as a Video Entrepreneur.

I've researched the psychology, anthropology, and anatomy of significant social media platforms as an entrepreneur and social media marketing expert. While building my YouTube empire, I've paid particular attention to what works for short, mid, and long-term success, whether it's a niche-focused, lifestyle, or multi-interest channel.

Most new, semi-new, and seasoned YouTubers feel vlog-style or live-on-camera videos are popular. Faceless, animated, music-text-based, and slideshow videos do well for businesses.

Buyer-consumer vs. content-consumer thinking is totally different when absorbing content. Profitability and popularity are closely related, however most people become popular with traditional means but not profitable.

In my experience, Faceless videos are more profitable, although it depends on the channel's style. Several professionals are now teaching in their courses that non-traditional films are making the difference in their business success and popularity.

Face-Share-Personal-Touch videos make audiences feel like they know the personality, but they're not profitable.

Most spend hours creating articles, videos, and thumbnails to seem good. That's how most YouTubers gained their success in the past, but not anymore.

Looking the part and performing a typical role in videos doesn't convert well, especially for newbie channels.

Working with video marketers and YouTubers for years, I've noticed that most struggle to be consistent with content publishing since they exclusively use formats that need extensive development. Camera and green screen set ups, shooting/filming, and editing for post productions require their time, making it less appealing to post consistently, especially if they're doing all the work themselves.

Because they won't make simple format videos or audio videos with an overlay image, they overcomplicate the procedure (even with YouTube Shorts), and they leave their channels for weeks or months. Again, they believe YouTube only allows specific types of videos. Even though this procedure isn't working, they plan to keep at it.

A successful YouTube channel needs multiple video formats to suit viewer needs, I teach. Face-Share-Personal Touch and Faceless videos are both useful.

How people engage with YouTube content has changed over the years, and the average customer is no longer interested in an all-video channel.

Face-Share-Personal-Touch videos are great

• Google Live

• Online training

• Giving listeners a different way to access your podcast that is being broadcast on sites like Anchor, BlogTalkRadio, Spreaker, Google, Apple Store, and others Many people enjoy using a video camera to record themselves while performing the internet radio, Facebook, or Instagram Live versions of their podcasts.

• Video Blog Updates

• even more

Faceless videos are popular for business and benefit both entrepreneurs and audiences.

For the business owner/entrepreneur…

• Less production time results in time dollar savings.

• enables the business owner to demonstrate the diversity of content development

For the Audience…

• The channel offers a variety of appealing content options.

• The same format is not monotonous or overly repetitive for the viewers.

Below are a couple videos from YouTube guru Make Money Matt's channel, which has over 347K subscribers.

Enjoy

24 Best Niches to Make Money on YouTube Without Showing Your Face

Make Money on YouTube Without Making Videos (Free Course)

In conclusion, you have everything it takes to build your own YouTube brand and empire. Learn the rules, then adapt them to succeed.

Please reread this and the other suggested articles for optimal benefit.

I hope this helped. How has this article helped you? Follow me for more articles like this and more multi-mission expressions.

I thought it would be interesting to share how much TikTok paid me in 2021.

Onward!

Oh, you get paid by TikTok?

Yes.

They compensate thousands of creators. My Tik Tok account

I launched my account in March 2020 and generally post about money, finance, and side hustles.

TikTok creators are paid in several ways.

• Fund for TikTok creators

• Sponsorships (aka brand deals)

• Affiliate promotion

• My own creations

Only one, the TikTok Creator Fund, pays me.

The TikTok Creator Fund: What Is It?

TikTok's initiative pays creators.

YouTube's Shorts Fund, Snapchat Spotlight, and other platforms have similar programs.

Creator Fund doesn't pay everyone. Some prerequisites are:

• age requirement of at least 18 years

• In the past 30 days, there must have been 100,000 views.

• a minimum of 10,000 followers

If you qualify, you can apply using your TikTok account, and once accepted, your videos can earn money.

My earnings from the TikTok Creator Fund

Since 2020, I've made $273.65. My 2021 payment is $77.36.

Yikes!

I made between $4.91 to around $13 payout each time I got paid.

TikTok reportedly pays 3 to 5 cents per thousand views.

To live off the Creator Fund, you'd need billions of monthly views.

Top personal finance creator Sara Finance has millions (if not billions) of views and over 700,000 followers yet only received $3,000 from the TikTok Creator Fund.

Goals for 2022

TikTok pays me in different ways, as listed above.

My largest TikTok account isn't my only one.

In 2022, I'll revamp my channel.

It's been a tumultuous year on TikTok for my account, from getting shadow-banned to being banned from the Creator Fund to being accepted back (not at my wish).

What I've experienced isn't rare. I've read about other creators' experiences.

So, some quick goals for this account…

• 200,000 fans by the year 2023

• Consistent monthly income of $5,000

• two brand deals each month

For now, that's all.

Perovskite solar cells will revolutionize everything.

Humanity is in a climatic Armageddon. Our widespread ecological crimes of the previous century are catching up with us, and planet-scale karma threatens everyone. We must adjust to new technologies and lifestyles to avoid this fate. Even solar power, a renewable energy source, has climate problems. A recent discovery could boost solar power's eco-friendliness and affordability. Perovskite solar cells are amazing.

Perovskite is a silicon-like semiconductor. Semiconductors are used to make computer chips, LEDs, camera sensors, and solar cells. Silicon makes sturdy and long-lasting solar cells, thus it's used in most modern solar panels.

Perovskite solar cells are far better. First, they're easy to make at room temperature, unlike silicon cells, which require long, intricate baking processes. This makes perovskite cells cheaper to make and reduces their carbon footprint. Perovskite cells are efficient. Most silicon panel solar farms are 18% efficient, meaning 18% of solar radiation energy is transformed into electricity. Perovskite cells are 25% efficient, making them 38% more efficient than silicon.

However, perovskite cells are nowhere near as durable. A normal silicon panel will lose efficiency after 20 years. The first perovskite cells were ineffective since they lasted barely minutes.

Recent research from Princeton shows that perovskite cells can endure 30 years. The cells kept their efficiency, therefore no sacrifices were made.

No electrical or chemical engineer here, thus I can't explain how they did it. But strangely, the team said longevity isn't the big deal. In the next years, perovskite panels will become longer-lasting. How do you test a panel if you only have a month or two? This breakthrough technique needs a uniform method to estimate perovskite life expectancy fast. The study's key milestone was establishing a standard procedure.

Lab-based advanced aging tests are their solution. Perovskite cells decay faster at higher temperatures, so scientists can extrapolate from that. The test heated the panel to 110 degrees and waited for its output to reduce by 20%. Their panel lasted 2,100 hours (87.5 days) before a 20% decline.

They did some math to extrapolate this data and figure out how long the panel would have lasted in different climates, and were shocked to find it would last 30 years in Princeton. This made perovskite panels as durable as silicon panels. This panel could theoretically be sold today.

This technology will soon allow these brilliant panels to be released into the wild. This technology could be commercially viable in ten, maybe five years.

Solar power will be the best once it does. Solar power is cheap and low-carbon. Perovskite is the cheapest renewable energy source if we switch to it. Solar panel manufacturing's carbon footprint will also drop.

Perovskites' impact goes beyond cost and carbon. Silicon panels require harmful mining and contain toxic elements (cadmium). Perovskite panels don't require intense mining or horrible materials, making their production and expiration more eco-friendly.

Solar power destroys habitat. Massive solar farms could reduce biodiversity and disrupt local ecology by destroying vital habitats. Perovskite cells are more efficient, so they can shrink a solar farm while maintaining energy output. This reduces land requirements, making perovskite solar power cheaper, and could reduce solar's environmental impact.

Perovskite solar power is scalable and environmentally friendly. Princeton scientists will speed up the development and rollout of this energy.

Why bother with fusion, fast reactors, SMRs, or traditional nuclear power? We're close to developing a nearly perfect environmentally friendly power source, and we have the tools and systems to do so quickly. It's also affordable, so we can adopt it quickly and let the developing world use it to grow. Even I struggle to justify spending billions on fusion when a great, cheap technology outperforms it. Perovskite's eco-credentials and cost advantages could save the world and power humanity's future.

I use a conceptual and practical system I developed decades ago as an example.

Since childhood, I've been interested in the brain-mind connection, so I developed a system using scientific breakthroughs, experiments, and the experiences of successful people in my circles.

This story provides a high-level overview of a custom system to inform and inspire readers. Creating a mind gym was one of my best personal and professional investments.

Such a complex system may not be possible for everyone or appear luxurious at first. However, the process and approach may help you find more accessible and viable solutions.

Visualizing the brain as a muscle, I learned to stimulate it with physical and mental exercises, applying a new mindset and behavioral changes.

My methods and practices may not work for others because we're all different. I focus on the approach's principles and highlights so you can create your own program.

Some create a conceptual and practical system intuitively, and others intellectually. Both worked. I see intellect and intuition as higher selves.

The mental tools I introduce are based on lifestyle changes and can be personalized by anyone, barring physical constraints or underlying health conditions.

Some people can't meditate despite wanting to due to mental constraints. This story lacks exceptions.

People's systems may vary. Many have used my tools successfully. All have scientific backing because their benefits attracted scientists. None are unethical or controversial.

My focus is cognition, which is the neocortex's ability. These practices and tools can affect the limbic and reptilian brain regions.

A previous article discussed brain health's biological aspects. This article focuses on psychology.

Thinking, learning, and remembering are cognitive abilities. Cognitive abilities determine our health and performance.

Cognitive health is the ability to think, concentrate, learn, and remember. Cognitive performance boosting involves various tools and processes. My system and protocols address cognitive health and performance.

As a biological organ, the brain's abilities decline with age, especially if not used regularly. Older people have more neurodegenerative disorders like dementia.

As aging is inevitable, I focus on creating cognitive reserves to remain mentally functional as we age and face mental decline or cognitive impairment.

My protocols focus on neurogenesis, or brain growth and maintenance. Neurons and connections can grow at any age.

Metacognition refers to knowing our cognitive abilities, like thinking about thinking and learning how to learn.

In the following sections, I provide an overview of my system, mental tools, and protocols.

This system summarizes my 50-year career. Some may find it too abstract, so I give examples.

First, explain the system. Section 2 introduces activities. Third, how to measure and maintain mental growth.

1 — Developed a practical mental gym.

The mental gym is a metaphor for the physical fitness gym to improve our mental muscles.

This concept covers brain and mind functionality. Integrated biological and psychological components.

I'll describe my mental gym so my other points make sense. My mental gym has physical and mental tools.

Mindfulness, meditation, visualization, self-conversations, breathing exercises, expressive writing, working in a flow state, reading, music, dance, isometric training, barefoot walking, cold/heat exposure, CBT, and social engagements are regular tools.

Dancing, walking, and thermogenesis are body-related tools. As the brain is part of the body and houses the mind, these tools can affect mental abilities such as attention, focus, memory, task switching, and problem-solving.

Different people may like different tools. I chose these tools based on my needs, goals, and lifestyle. They're just examples. You can choose tools that fit your goals and personality.

2 — Performed tasks regularly.

These tools gave me clarity. They became daily hobbies. Some I did alone, others with others.

Some examples: I meditate daily. Even though my overactive mind made daily meditation difficult at first, I now enjoy it. Meditation three times a day sharpens my mind.

Self-talk is used for self-therapy and creativity. Self-talk was initially difficult, but neurogenesis rewired my brain to make it a habit.

Cold showers, warm baths with Epsom salts, fasting, barefoot walks on the beach or grass, dancing, calisthenics, trampoline hopping, and breathing exercises increase my mental clarity, creativity, and productivity.

These exercises can increase BDNF, which promotes nervous system growth. They improve mental capacity and performance by increasing blood flow and brain oxygenation.

I use weekly and occasional activities like dry saunas, talking with others, and community activities.

These activities stimulate the brain and mind, improving performance and cognitive capacity.

3 — Measured progress, set growth goals.

Measuring progress helps us stay on track. Without data, it's hard to stay motivated. When we face inevitable setbacks, we may abandon our dreams.

I created a daily checklist for a spreadsheet with macros. I tracked how often and long I did each activity.

I measured my progress objectively and subjectively. In the progress spreadsheet, I noted my meditation hours and subjective feelings.

In another column, I used good, moderate, and excellent to get qualitative data. It took time and effort. Later, I started benefiting from this automated structure.

Creating a page for each activity, such as meditation, self-talk, cold showers, walking, expressive writing, personal interactions, etc., gave me empirical data I could analyze, modify, and graph to show progress.

Colored charts showed each area's strengths and weaknesses.

Strengths motivate me to continue them. Identifying weaknesses helped me improve them.

As the system matured, data recording became a habit and took less time. I saw the result immediately because I automated the charts when I entered daily data. Early time investment paid off later.

Mind Gym Benefits, Effective Use, and Progress Measuring

This concept helped me move from comfort to risk. I accept things as they are.

Turnarounds were made. I stopped feeling "Fight-Flight-Freeze" and maintained self-control.

I tamed my overactive amygdala by strengthening my brain. Stress and anxiety decreased. With these shifts, I accepted criticism and turned envy into admiration. Clarity improved.

When the cognitive part of the brain became stronger and the primitive part was tamed, managing thoughts and emotions became easier. My AQ increased. I learned to tolerate people, physical, mental, and emotional obstacles.

Accessing vast information sources in my subconscious mind through an improved RAS allowed me to easily tap into my higher self and recognize flaws in my lower self.

Summary

The brain loves patterns and routines, so habits help. Observing, developing, and monitoring habits mindfully can be beneficial. Mindfulness helps us achieve this goal systematically.

As body and mind are connected, we must consider both when building habits. Consistent and joyful practices can strengthen neurons and neural connections.

Habits help us accomplish more with less effort. Regularly using mental tools and processes can improve our cognitive health and performance as we age.

Creating daily habits to improve cognitive abilities can sharpen our minds and boost our well-being.

Some apps monitor our activities and behavior to help build habits. If you can't replicate my system, try these apps. Some smartwatches and fitness devices include them.

Set aside time each day for mental activities you enjoy. Regular scheduling and practice can strengthen brain regions and form habits. Once you form habits, tasks become easy.

Improving our minds is a lifelong journey. It's easier and more sustainable to increase our efforts daily, weekly, monthly, or annually.

Despite life's ups and downs, many want to remain calm and cheerful.

This valuable skill is unrelated to wealth or fame. It's about our mindset, fueled by our biological and psychological needs.

Here are some lessons I've learned about staying calm and composed despite challenges and setbacks.

1 — Tranquillity starts with observing thoughts and feelings.

2 — Clear the mental clutter and emotional entanglements with conscious breathing and gentle movements.

3 — Accept situations and events as they are with no resistance.

4 — Self-love can lead to loving others and increasing compassion.

5 — Count your blessings and cultivate gratitude.

Clear thinking can bring joy and satisfaction. It's a privilege to wake up with a healthy body and clear mind, ready to connect with others and serve them.

Thank you for reading my perspectives. I wish you a healthy and happy life.

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.