Here's how to be clear.

“I have only made this letter longer because I have not had the time to make it shorter.” — French mathematician, physicist, inventor, philosopher, and writer Blaise Pascal

Concise.

People want this. We tend to repeat ourselves and use unnecessary words.

Being vague frustrates readers. It focuses their limited attention span on figuring out what you're saying rather than your message.

Edit carefully.

“Examine every word you put on paper. You’ll find a surprising number that don’t serve any purpose.” — American writer, editor, literary critic, and teacher William Zinsser

How do you write succinctly?

Here are three ways to polish your writing.

1. Delete

Your readers will appreciate it if you delete unnecessary words. If a word or phrase is essential, keep it. Don't force it.

Many readers dislike bloated sentences. Ask yourself if cutting a word or phrase will change the meaning or dilute your message.

For example, you could say, “It’s absolutely essential that I attend this meeting today, so I know the final outcome.” It’s better to say, “It’s critical I attend the meeting today, so I know the results.”

Key takeaway

Delete actually, completely, just, full, kind of, really, and totally. Keep the necessary words, cut the rest.

2. Just Do It

Don't tell readers your plans. Your readers don't need to know your plans. Who are you?

Don't say, "I want to highlight our marketing's problems." Our marketing issues are A, B, and C. This cuts 5–7 words per sentence.

Keep your reader's attention on the essentials, not the fluff. What are you doing? You won't lose readers because you get to the point quickly and don't build up.

Key takeaway

Delete words that don't add to your message. Do something, don't tell readers you will.

3. Cut Overlap

You probably repeat yourself unintentionally. You may add redundant sentences when brainstorming. Read aloud to detect overlap.

Remove repetition from your writing. It's important to edit our writing and thinking to avoid repetition.

Key Takeaway

If you're repeating yourself, combine sentences to avoid overlap.

4. Simplify

Write as you would to family or friends. Communicate clearly. Don't use jargon. These words confuse readers.

Readers want specifics, not jargon. Write simply. Done.

Most adults read at 8th-grade level. Jargon and buzzwords make speech fluffy. This confuses readers who want simple language.

Key takeaway

Ensure all audiences can understand you. USA Today's 5th-grade reading level is intentional. They want everyone to understand.

5. Active voice

Subjects perform actions in active voice. When you write in passive voice, the subject receives the action.

For example, “the board of directors decided to vote on the topic” is an active voice, while “a decision to vote on the topic was made by the board of directors” is a passive voice.

Key takeaway

Active voice clarifies sentences. Active voice is simple and concise.

Bringing It All Together

Five tips help you write clearly. Delete, just do it, cut overlap, use simple language, and write in an active voice.

Clear writing is effective. It's okay to occasionally use unnecessary words or phrases. Realizing it is key. Check your writing.

Adding words costs.

Write more concisely. People will appreciate it and read your future articles, emails, and messages. Spending extra time will increase trust and influence.

“Not that the story need be long, but it will take a long while to make it short.” — Naturalist, essayist, poet, and philosopher Henry David Thoreau

Digital influences that mimic humans are rising.

Lil Miquela has 3M Instagram followers, 3.6M TikTok followers, and 30K Twitter followers. She's been on the covers of Prada, Dior, and Calvin Klein magazines. Miquela released Not Mine in 2017 and launched Hard Feelings at Lollapazoolas this year. This isn't surprising, given the rise of influencer marketing.

This may be unexpected. Miquela's fake. Brud, a Los Angeles startup, produced her in 2016.

Lil Miquela is one of many rising virtual influencers in the new era of social media marketing. She acts like a real person and performs the same tasks as sports stars and models.

The emergence of online influencers

Before 2018, computer-generated characters were rare. Since the virtual human industry boomed, they've appeared in marketing efforts worldwide.

In 2020, the WHO partnered up with Atlanta-based virtual influencer Knox Frost (@knoxfrost) to gather contributions for the COVID-19 Solidarity Response Fund.

Lu do Magalu (@magazineluiza) has been the virtual spokeswoman for Magalu since 2009, using social media to promote reviews, product recommendations, unboxing videos, and brand updates. Magalu's 10-year profit was $552M.

In 2020, PUMA partnered with Southeast Asia's first virtual model, Maya (@mayaaa.gram). She joined Singaporean actor Tosh Zhang in the PUMA campaign. Local virtual influencer Ava Lee-Graham (@avagram.ai) partnered with retail firm BHG to promote their in-house labels.

In Japan, Imma (@imma.gram) is the face of Nike, PUMA, Dior, Salvatore Ferragamo SpA, and Valentino. Imma's bubblegum pink bob and ultra-fine fashion landed her on the cover of Grazia magazine.

Lotte Home Shopping created Lucy (@here.me.lucy) in September 2020. She made her TV debut as a Christmas show host in 2021. Since then, she has 100K Instagram followers and 13K TikTok followers.

Liu Yiexi gained 3 million fans in five days on Douyin, China's TikTok, in 2021. Her two-minute video went viral overnight. She's posted 6 videos and has 830 million Douyin followers.

China's virtual human industry was worth $487 million in 2020, up 70% year over year, and is expected to reach $875.9 million in 2021.

Investors worldwide are interested. Immas creator Aww Inc. raised $1 million from Coral Capital in September 2020, according to Bloomberg. Superplastic Inc., the Vermont-based startup behind influencers Janky and Guggimon, raised $16 million by 2020. Craft Ventures, SV Angels, and Scooter Braun invested. Crunchbase shows the company has raised $47 million.

The industries they represent, including Augmented and Virtual reality, were worth $14.84 billion in 2020 and are projected to reach $454.73 billion by 2030, a CAGR of 40.7%, according to PR Newswire.

Advantages for brands

Forbes suggests brands embrace computer-generated influencers. Examples:

1. Unlimited creative opportunities: Because brands can personalize everything—from a person's look and activities to the style of their content—virtual influencers may be suited to a brand's needs and personalities.

2. 100% brand control: Brand managers now have more influence over virtual influencers, so they no longer have to give up and rely on content creators to include brands into their storytelling and style. Virtual influencers can constantly produce social media content to promote a brand's identity and ideals because they are completely scandal-free.

3. Long-term cost savings: Because virtual influencers are made of pixels, they may be reused endlessly and never lose their beauty. Additionally, they can move anywhere around the world and even into space to fit a brand notion. They are also always available. Additionally, the expense of creating their content will not rise in step with their expanding fan base.

4. Introduction to the metaverse: Statista reports that 75% of American consumers between the ages of 18 and 25 follow at least one virtual influencer. As a result, marketers that support virtual celebrities may now interact with younger audiences that are more tech-savvy and accustomed to the digital world. Virtual influencers can be included into any digital space, including the metaverse, as they are entirely computer-generated 3D personas. Virtual influencers can provide brands with a smooth transition into this new digital universe to increase brand trust and develop emotional ties, in addition to the young generations' rapid adoption of the metaverse.

5. Better engagement than in-person influencers: A Hype Auditor study found that online influencers have roughly three times the engagement of their conventional counterparts. Virtual influencers should be used to boost brand engagement even though the data might not accurately reflect the entire sector.

Concerns about influencers created by computers

Virtual influencers could encourage excessive beauty standards in South Korea, which has a $10.7 billion plastic surgery industry.

A classic Korean beauty has a small face, huge eyes, and pale, immaculate skin. Virtual influencers like Lucy have these traits. According to Lee Eun-hee, a professor at Inha University's Department of Consumer Science, this could make national beauty standards more unrealistic, increasing demand for plastic surgery or cosmetic items.

Other parts of the world raise issues regarding selling items to consumers who don't recognize the models aren't human and the potential of cultural appropriation when generating influencers of other ethnicities, called digital blackface by some.

Meta, Facebook and Instagram's parent corporation, acknowledges this risk.

“Like any disruptive technology, synthetic media has the potential for both good and harm. Issues of representation, cultural appropriation and expressive liberty are already a growing concern,” the company stated in a blog post. “To help brands navigate the ethical quandaries of this emerging medium and avoid potential hazards, (Meta) is working with partners to develop an ethical framework to guide the use of (virtual influencers).”

Despite theoretical controversies, the industry will likely survive. Companies think virtual influencers are the next frontier in the digital world, which includes the metaverse, virtual reality, and digital currency.

In conclusion

Virtual influencers may garner millions of followers online and help marketers reach youthful audiences. According to a YouGov survey, the real impact of computer-generated influencers is yet unknown because people prefer genuine connections. Virtual characters can supplement brand marketing methods. When brands are metaverse-ready, the author predicts virtual influencer endorsement will continue to expand.

This resulted to obimy's new audience.

Hi! obimy's official account. Here, we'll teach app developers and marketers. In 2022, our downloads increased dramatically, so we'll share what we learned.

obimy is what we call a ‘senseger’. It's a new method to communicate digitally. Instead of text, obimy users connect through senses and moods. Feeling playful? Flirt with your partner, pat a pal, or dump water on a classmate. Each feeling is an interactive animation with vibration. It's a wordless app. App Store and Google Play have obimy.

We had 20,000 users in 2022. Two to five thousand of them opened the app monthly. Our DAU metric was 500.

We have 6 million users after 6 months. 500,000 individuals use obimy daily. obimy was the top lifestyle app this week in the U.S.

And TikTok helped.

TikTok fuels obimys' growth. It's why our app exploded. How and what did we learn? Our Head of Marketing, Anastasia Avramenko, knows.

our actions prior to TikTok

We wanted to achieve product-market fit through organic expansion. Quora, Reddit, Facebook Groups, Facebook Ads, Google Ads, Apple Search Ads, and social media activity were tested. Nothing worked. Our CPI was sometimes $4, so unit economics didn't work.

We studied our markets and made audience hypotheses. We promoted our goods and studied our audience through social media quizzes. Our target demographic was Americans in long-distance relationships. I designed quizzes like Test the Strength of Your Relationship to better understand the user base. After each quiz, we encouraged users to download the app to enhance their connection and bridge the distance.

We got 1,000 responses for $50. This helped us comprehend the audience's grief and coping strategies (aka our rivals). I based action items on answers given. If you can't embrace a loved one, use obimy.

We also tried Facebook and Google ads. From the start, we knew it wouldn't work.

We were desperate to discover a free way to get more users.

Our journey to TikTok

TikTok is a great venue for emerging creators. It also helped reach people. Before obimy, my TikTok videos garnered 12 million views without sponsored promotion.

We had to act. TikTok was required.

I wasn't a TikTok user before obimy. Initially, I uploaded promotional content. Call-to-actions appear strange next to dancing challenges and my money don't jiggle jiggle. I learned TikTok. Watch TikTok for an hour was on my to-do list. What a dream job!

Our most popular movies presented the app alongside text outlining what it does. We started promoting them in Europe and the U.S. and got a 16% CTR and $1 CPI, an improvement over our previous efforts.

Somehow, we were expanding. So we came up with new hypotheses, calls to action, and content.

Four months passed, yet we saw no organic growth.

Russia attacked Ukraine.

Our app aimed to be helpful. For now, we're focusing on our Ukrainian audience. I posted sloppy TikToks illustrating how obimy can help during shelling or air raids.

In two hours, Kostia sent me our visitor count. Our servers crashed.

Initially, we had several thousand daily users. Over 200,000 users joined obimy in a week. They posted obimy videos on TikTok, drawing additional users. We've also resumed U.S. video promotion.

We gained 2,000,000 new members with less than $100 in ads, primarily in the U.S. and U.K.

TikTok helped.

The figures

We were confident we'd chosen the ideal tool for organic growth.

• Over 45 million people have viewed our own videos plus a ton of user-generated content with the hashtag #obimy.

• About 375 thousand people have liked all of our individual videos.

• The number of downloads and the virality of videos are directly correlated.

Where are we now?

TikTok fuels our organic growth. We post 56 videos every week and pay to promote viral content.

We use UGC and influencers. We worked with Universal Music Italy on Eurovision. They offered to promote us through their million-follower TikTok influencers. We thought their followers would improve our audience, but it didn't matter. Integration didn't help us. Users that share obimy videos with their followers can reach several million views, which affects our download rate.

After the dust settled, we determined our key audience was 13-18-year-olds. They want to express themselves, but it's sometimes difficult. We're searching for methods to better engage with our users. We opened a Discord server to discuss anime and video games and gather app and content feedback.

TikTok helps us test product updates and hypotheses. Example: I once thought we might raise MAU by prompting users to add strangers as friends. Instead of asking our team to construct it, I made a TikTok urging users to share invite URLs. Users share links under every video we upload, embracing people worldwide.

Key lessons

Don't direct-sell. TikTok isn't for Instagram, Facebook, or YouTube promo videos. Conventional advertisements don't fit. Most users will swipe up and watch humorous doggos.

More product videos are better. Finally. So what?

Encourage interaction. Tagging friends in comments or making videos with the app promotes it more than any marketing spend.

Be odd and risqué. A user mistakenly sent a French kiss to their mom in one of our most popular videos.

TikTok helps test hypotheses and build your user base. It also helps develop apps. In our upcoming blog, we'll guide you through obimy's design revisions based on TikTok. Follow us on Twitter, Instagram, and TikTok.

Overview

I'm happy to provide this important update. We've worked on this for a year and a half, so I'm glad to finally write it. We named the application AESIR because we’ve love Norse Mythology. AESIR automates and runs trading strategies.

• Volatility, technical analysis, oscillators, and other signals are currently supported by AESIR.

• Additionally, we enhanced AESIR's ability to create distinctive bespoke signals by allowing it to analyze many indicators and produce a single signal.

• AESIR has a significant social component that allows you to copy the best-performing public setups and use them right away.

Enter your email here to be notified when AEISR launches.

Views on algorithmic trading

First, let me clarify. Anyone who claims algorithmic trading platforms are money-printing plug-and-play devices is a liar. Algorithmic trading platforms are a collection of tools.

A trading algorithm won't make you a competent trader if you lack a trading strategy and yolo your funds without testing. It may hurt your trade. Test and alter your plans to account for market swings, but comprehend market signals and trends.

Status Report

Throughout closed beta testing, we've communicated closely with users to design a platform they want to use.

To celebrate, we're giving you free Aesir Viking NFTs and we cover gas fees.

Why use a trading Algorithm?

• Automating a successful manual approach

• experimenting with and developing solutions that are impossible to execute manually

One AESIR strategy lets you buy any cryptocurrency that rose by more than x% in y seconds.

AESIR can scan an exchange for coins that have gained more than 3% in 5 minutes. It's impossible to manually analyze over 1000 trading pairings every 5 minutes. Auto buy dips or DCA around a Dip

Sneak Preview

Here's the Leaderboard, where you can clone the best public settings.

As a tiny, self-funded team, we're excited to unveil our product. It's a beta release, so there's still more to accomplish, but we know where we stand.

If this sounds like a project that you might want to learn more about, you can sign up to our newsletter and be notified when AESIR launches.

Useful Links:

Join the Discord | Join our subreddit | Newsletter | Mint Free NFT

How I monetized and sold an abandoned side project for $20,000

The Origin Story

I've always wanted to be an entrepreneur but never succeeded. I often had business ideas, made a landing page, and told my buddies. Never got customers.

In April 2021, I decided to try again with a new strategy. I noticed that I had trouble acquiring an initial set of customers, so I wanted to start by acquiring a product that had a small user base that I could grow.

I found a SaaS marketplace called MicroAcquire.com where you could buy and sell SaaS products. I liked Shareit.video, an online Loom-like screen recorder.

Shareit.video didn't generate revenue, but 50 people visited daily to record screencasts.

Purchasing a Failed Side Project

I eventually bought Shareit.video for $12,000 from its owner.

$12,000 was probably too much for a website without revenue or registered users.

I thought time was most important. I could have recreated the website, but it would take months. $12,000 would give me an organized code base and a working product with a few users to monetize.

I considered buying a screen recording website and trying to grow it versus buying a new car or investing in crypto with the $12K.

Buying the website would make me a real entrepreneur, which I wanted more than anything.

Putting down so much money would force me to commit to the project and prevent me from quitting too soon.

A Year of Development

I rebranded the website to be called RecordJoy and worked on it with my cousin for about a year. Within a year, we made $5000 and had 3000 users.

We spent $3500 on ads, hosting, and software to run the business.

AppSumo promoted our $120 Life Time Deal in exchange for 30% of the revenue.

We put RecordJoy on maintenance mode after 6 months because we couldn't find a scalable user acquisition channel.

We improved SEO and redesigned our landing page, but nothing worked.

Despite not being able to grow RecordJoy any further, I had already learned so much from working on the project so I was fine with putting it on maintenance mode. RecordJoy still made $500 a month, which was great lunch money.

Getting Taken Over

One of our customers emailed me asking for some feature requests and I replied that we weren’t going to add any more features in the near future. They asked if we'd sell.

We got on a call with the customer and I asked if he would be interested in buying RecordJoy for 15k. The customer wanted around $8k but would consider it.

Since we were negotiating with one buyer, we put RecordJoy on MicroAcquire to see if there were other offers.

We quickly received 10+ offers. We got 18.5k. There was also about $1000 in AppSumo that we could not withdraw, so we agreed to transfer that over for $600 since about 40% of our sales on AppSumo usually end up being refunded.

Lessons Learned

First, create an acquisition channel

We couldn't discover a scalable acquisition route for RecordJoy. If I had to start another project, I'd develop a robust acquisition channel first. It might be LinkedIn, Medium, or YouTube.

Purchase Power of the Buyer Affects Acquisition Price

Some of the buyers we spoke to were individuals looking to buy side projects, as well as companies looking to launch a new product category. Individual buyers had less budgets than organizations.

Customers of AppSumo vary.

AppSumo customers value lifetime deals and low prices, which may not be a good way to build a business with recurring revenue. Designed for AppSumo users, your product may not connect with other users.

Try to increase acquisition trust

Acquisition often fails. The buyer can go cold feet, cease communicating, or run away with your stuff. Trusting the buyer ensures a smooth asset exchange. First acquisition meeting was unpleasant and price negotiation was tight. In later meetings, we spent the first few minutes trying to get to know the buyer’s motivations and background before jumping into the negotiation, which helped build trust.

Operating expenses can reduce your earnings.

Monitor operating costs. We were really happy when we withdrew the $5000 we made from AppSumo and Stripe until we realized that we had spent $3500 in operating fees. Spend money on software and consultants to help you understand what to build.

Don't overspend on advertising

We invested $1500 on Google Ads but made little money. For a side project, it’s better to focus on organic traffic from SEO rather than paid ads unless you know your ads are going to have a positive ROI.

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.