Price Intelligently put out amazing content on pricing your SaaS product. This blog's link to the whole report is worth reading. Our key takeaways are below.

Don't base prices on the competition. Competitor-based pricing has clear drawbacks. Their pricing approach is yours. Your company offers customers something unique. Otherwise, you wouldn't create it. This strategy is static, therefore you can't add value by raising prices without outpricing competitors. Look, but don't touch is the competitor-based moral. You want to know your competitors' prices so you're in the same ballpark, but they shouldn't guide your selections. Competitor-based pricing also drives down prices.

Value-based pricing wins. This is customer-based pricing. Value-based pricing looks outward, not inward or laterally at competitors. Your clients are the best source of pricing information. By valuing customer comments, you're focusing on buyers. They'll decide if your pricing and packaging are right. In addition to asking consumers about cost savings or revenue increases, look at data like number of users, usage per user, etc.

Value-based pricing increases prices. As you learn more about the client and your worth, you'll know when and how much to boost rates. Every 6 months, examine pricing.

Cloning top customers. You clone your consumers by learning as much as you can about them and then reaching out to comparable people or organizations. You can't accomplish this without knowing your customers. Segmenting and reproducing them requires as much detail as feasible. Offer pricing plans and feature packages for 4 personas. The top plan should state Contact Us. Your highest-value customers want more advice and support.

Question your 4 personas. What's the one item you can't live without? Which integrations matter most? Do you do analytics? Is support important or does your company self-solve? What's too cheap? What's too expensive?

Not everyone likes per-user pricing. SaaS organizations often default to per-user analytics. About 80% of companies utilizing per-user pricing should use an alternative value metric because their goods don't give more value with more users, so charging for them doesn't make sense.

At least 3:1 LTV/CAC. Break even on the customer within 2 years, and LTV to CAC is greater than 3:1. Because customer acquisition costs are paid upfront but SaaS revenues accrue over time, SaaS companies face an early financial shortfall while paying back the CAC.

ROI should be >20:1. Indeed. Ensure the customer's ROI is 20x the product's cost. Microsoft Office costs $80 a year, but consumers would pay much more to maintain it.

A/B Testing. A/B testing is guessing. When your pricing page varies based on assumptions, you'll upset customers. You don't have enough customers anyway. A/B testing optimizes landing pages, design decisions, and other site features when you know the problem but not pricing.

Don't discount. It cheapens the product, makes it permanent, and increases churn. By discounting, you're ruining your pricing analysis.

In 8 months, I doubled my audience with them.

LinkedIn's buzz isn't over.

People dream of social proof every day. They want clients, interesting jobs, and field recognition.

LinkedIn coaches will benefit greatly. Sell learning? Probably. Can you use it?

Consistency has been key in my eight-month study of LinkedIn. However, I'll share seven of my tips. 700 to 4500 people followed me.

1. Communication, communication, communication

LinkedIn is a social network. I like to think of it as a cafe. Here, you can share your thoughts, meet friends, and discuss life and work.

Do not treat LinkedIn as if it were a board for your post-its.

More socializing improves relationships. It's about people, like any network.

Consider interactions. Three main areas:

• Respond to criticism left on your posts.

• Comment on other people's posts

• Start and maintain conversations through direct messages.

Engage people. You spend too much time on Facebook if you only read your wall. Keeping in touch and having meaningful conversations helps build your network.

Every day, start a new conversation to make new friends.

2. Stick with those you admire

Interact thoughtfully.

Choose your contacts. Build your tribe is a term. Respectful networking.

I only had past colleagues, family, and friends in my network at the start of this year. Not business-friendly. Since then, I've sought out people I admire or can learn from.

Finding a few will help you. As they connect you to their networks. Friendships can lead to clients.

Don't underestimate network power. Cafe-style. Meet people at each table. But avoid people who sell SEO, web redesign, VAs, mysterious job opportunities, etc.

3. Share eye-catching infographics

Daily infographics flood LinkedIn. Visuals are popular. Use Canva's free templates if you can't draw them.

Last week's:

It's a fun way to visualize your topic.

You can repost and comment on infographics. Involve your network. I prefer making my own because I build my brand around certain designs.

My friend posted infographics consistently for four months and grew his network to 30,000.

If you start, credit the authors. As you steal someone's work.

4. Invite some friends over.

LinkedIn alone can be lonely. Having a few friends who support your work daily will boost your growth.

I was lucky to be invited to a group of networkers. We share knowledge and advice.

Having a few regulars who can discuss your posts is helpful. It's artificial, but it works and engages others.

Consider who you'd support if they were in your shoes.

You can pay for an engagement group, but you risk supporting unrelated people with rubbish posts.

Help each other out.

5. Don't let your feed or algorithm divert you.

LinkedIn's algorithm is magical.

Which time is best? How fast do you need to comment? Which days are best?

Overemphasize algorithms. Consider the user. No need to worry about the best time.

Remember to spend time on LinkedIn actively. Not passively. That is what Facebook is for.

Surely someone would find a LinkedIn recipe. Don't beat the algorithm yet. Consider your audience.

6. The more personal, the better

Personalization isn't limited to selfies. Share your successes and failures.

The more personality you show, the better.

People relate to others, not theories or quotes. Why should they follow you? Everyone posts the same content?

Consider your friends. What's their appeal?

Because they show their work and identity. It's simple. Medium and Linkedin are your platforms. Find out what works.

You can copy others' hooks and structures. You decide how simple to make it, though.

7. Have fun with those who have various post structures.

I like writing, infographics, videos, and carousels. Because you can:

Repurpose your content!

Out of one blog post I make:

• Newsletter

• Infographics (positive and negative points of view)

• Carousel

• Personal stories

• Listicle

Create less but more variety. Since LinkedIn posts last 24 hours, you can rotate the same topics for weeks without anyone noticing.

Effective!

The final LI snippet to think about

LinkedIn is about consistency. Some say 15 minutes. If you're serious about networking, spend more time there.

The good news is that it is worth it. The bad news is that it takes time.

900K impressions, 8K clicks, and $$$ orders…

I recently started dropshipping. Now that I own my business and can charge it as a business expense, it feels less like money wasted if it doesn't work. I also made t-shirts to sell. I intended to open a t-shirt store and had many designs on a hard drive. I read that Tiktok advertising had a high conversion rate and low cost because they were new. According to many, the advertising' cost/efficiency ratio would plummet and become as bad as Google or Facebook Ads. Now felt like the moment to try Tiktok marketing and dropshipping. I work in marketing for a SaaS firm and have seen how poorly ads perform. I wanted to try it alone.

I set up $250 and ran advertising for a week. Before that, I made my own products, store, and marketing. In this post, I'll show you my process and results.

Setting up the store

Dropshipping is a sort of retail business in which the manufacturer ships the product directly to the client through an online platform maintained by a seller. The seller takes orders but has no stock. The manufacturer handles all orders. This no-stock concept increases profitability and flexibility.

In my situation, I used previous t-shirt designs to make my own product. I didn't want to handle order fulfillment logistics, so I looked for a way to print my designs on demand, ship them, and handle order tracking/returns automatically. So I found Printful.

I needed to connect my backend and supplier to a storefront so visitors could buy. 99% of dropshippers use Shopify, but I didn't want to master the difficult application. I wanted a one-day project. I'd previously worked with Big Cartel, so I chose them.

Big Cartel doesn't collect commissions on sales, simply a monthly flat price ($9.99 to $19.99 depending on your plan).

After opening a Big Cartel account, I uploaded 21 designs and product shots, then synced each product with Printful.

Developing the ads

I mocked up my designs on cool people photographs from placeit.net, a great tool for creating product visuals when you don't have a studio, camera gear, or models to wear your t-shirts.

I opened an account on the website and had advertising visuals within 2 hours.

Because my designs are simple (black design on white t-shirt), I chose happy, stylish people on plain-colored backdrops. After that, I had to develop an animated slideshow.

Because I'm a graphic designer, I chose to use Adobe Premiere to create animated Tiktok advertising.

Premiere is a fancy video editing application used for more than advertisements. Premiere is used to edit movies, not social media marketing. I wanted this experiment to be quick, so I got 3 social media ad templates from motionarray.com and threw my visuals in. All the transitions and animations were pre-made in the files, so it only took a few hours to compile. The result:

I downloaded 3 different soundtracks for the videos to determine which would convert best.

After that, I opened a Tiktok business account, uploaded my films, and inserted ad info. They went live within one hour.

The (poor) outcomes

As a European company, I couldn't deliver ads in the US. All of my advertisements' material (title, description, and call to action) was in English, hence they continued getting rejected in Europe for countries that didn't speak English. There are a lot of them:

I lost a lot of quality traffic, but I felt that if the images were engaging, people would check out the store and buy my t-shirts. I was wrong.

• 51,071 impressions on Day 1. 0 orders after 411 clicks

• 114,053 impressions on Day 2. 1.004 clicks and no orders

• Day 3: 987 clicks, 103,685 impressions, and 0 orders

• 101,437 impressions on Day 4. 0 orders after 963 clicks

• 115,053 impressions on Day 5. 1,050 clicks and no purchases

• 125,799 impressions on day 6. 1,184 clicks, no purchases

• 115,547 impressions on Day 7. 1,050 clicks and no purchases

• 121,456 impressions on day 8. 1,083 clicks, no purchases

• 47,586 impressions on Day 9. 419 Clicks. No orders

My overall conversion rate for video advertisements was 0.9%. TikTok's paid ad formats all result in strong engagement rates (ads average 3% to 12% CTR to site), therefore a 1 to 2% CTR should have been doable.

My one-week experiment yielded 8,151 ad clicks but no sales. Even if 0.1% of those clicks converted, I should have made 8 sales. Even companies with horrible web marketing would get one download or trial sign-up for every 8,151 clicks. I knew that because my advertising were in English, I had no impressions in the main EU markets (France, Spain, Italy, Germany), and that this impacted my conversion potential. I still couldn't believe my numbers.

I dug into the statistics and found that Tiktok's stats didn't match my store traffic data.

Looking more closely at the numbers

My ads were approved on April 26 but didn't appear until April 27. My store dashboard showed 440 visitors but 1,004 clicks on Tiktok. This happens often while tracking campaign results since different platforms handle comparable user activities (click, view) differently. In online marketing, residual data won't always match across tools.

My data gap was too large. Even if half of the 1,004 persons who clicked closed their browser or left before the store site loaded, I would have gained 502 visitors. The significant difference between Tiktok clicks and Big Cartel store visits made me suspicious. It happened all week:

• Day 1: 440 store visits and 1004 ad clicks

• Day 2: 482 store visits, 987 ad clicks

• 3rd day: 963 hits on ads, 452 store visits

• 443 store visits and 1,050 ad clicks on day 4.

• Day 5: 459 store visits and 1,184 ad clicks

• Day 6: 430 store visits and 1,050 ad clicks

• Day 7: 409 store visits and 1,031 ad clicks

• Day 8: 166 store visits and 418 ad clicks

The disparity wasn't related to residual data or data processing. The disparity between visits and clicks looked regular, but I couldn't explain it.

After the campaign concluded, I discovered all my creative assets (the videos) had a 0% CTR and a $0 expenditure in a separate dashboard. Whether it's a dashboard reporting issue or a budget allocation bug, online marketers shouldn't see this.

Tiktok can present any stats they want on their dashboard, just like any other platform that runs advertisements to promote content to its users. I can't verify that 895,687 individuals saw and clicked on my ad. I invested $200 for what appears to be around 900K impressions, which is an excellent ROI. No one bought a t-shirt, even an unattractive one, out of 900K people?

Would I do it again?

Nope. Whether I didn't make sales because Tiktok inflated the dashboard numbers or because I'm horrible at producing advertising and items that sell, I’ll stick to writing content and making videos. If setting up a business and ads in a few days was all it took to make money online, everyone would do it.

Video advertisements and dropshipping aren't dead. As long as the internet exists, people will click ads and buy stuff. Converting ads and selling stuff takes a lot of work, and I want to focus on other things.

I had always wanted to try dropshipping and I’m happy I did, I just won’t stick to it because that’s not something I’m interested in getting better at.

If I want to sell t-shirts again, I'll avoid Tiktok advertisements and find another route.

It's free now.

Most content writers—including me—write about side hustles because they do well.

I wrote several articles on a profitable programming side hustle.

Later, I learnt about AI content-generating platforms like Jasper.ai and Copy.ai, which I thought were terrible because they required subscriptions and had bad content. Even I dislike automatic online posting.

Since ChatGPT is becoming more popular, I tried it. It's free now.

Note: I wasn’t compensated to write this piece by this tool. In other words, I don’t receive any payment from their founders. There is no affiliate link, and right now it is free to use. Also, ChatGPT can do a lot more than what I ever did.

Begin.

OpenAI account registration requires visiting the website (if you don’t have one). Just write anything into the chatbot and get a response.

First, I wrote about the top 10 2023 side businesses.

This came in seconds.

2023 is shaping up to be a year of growth and opportunity for entrepreneurs and side hustlers. With the rise of remote work and the growing gig economy, there are many income streams to consider launching in the coming year. Here are the top 10 income streams to launch in 2023:

1. Virtual Assistant — The demand for virtual assistants is on the rise as more businesses move online. As a virtual assistant, you can offer administrative, technical, or creative services to clients remotely.

2. Online Tutoring — If you have expertise in a particular subject, consider becoming an online tutor. There are many platforms that connect tutors with students looking for help with their studies.

3. Freelance Writing — If you have a knack for writing, consider becoming a freelance writer. You can offer your services to businesses, bloggers, and individuals looking for content for their websites or social media platforms.

4. Graphic Design — If you have a talent for design, consider starting a graphic design side hustle. You can create logos, banners, and other visual content for businesses and individuals.

5. Social Media Management — Many businesses are looking for help with managing their social media accounts. As a social media manager, you can help businesses create and execute social media strategies to reach their target audience.

6. Dropshipping — Dropshipping is a business model where you sell products without actually holding any inventory. You can partner with suppliers and ship the products directly to the customer on behalf of the business.

7. Pet Sitting — If you love animals, consider starting a pet-sitting side hustle. You can offer your services to pet owners who need someone to take care of their pets while they are away.

8. Home Cleaning — With busy schedules, many people are looking for help with cleaning their homes. As a home cleaning service provider, you can offer your services to help keep homes tidy and organized.

9. Event Planning — If you have a talent for organization and planning, consider starting an event planning side hustle. You can offer your services to help plan and execute events for businesses and individuals.

10. Online Teaching — With the rise of online education, there is a growing demand for online teachers. If you have expertise in a particular subject, consider becoming an online teacher and offer your services to students looking for personalized instruction.

In conclusion, 2023 is shaping up to be a great year for launching new income streams. Whether you are looking to start a virtual assistant business, become an online tutor, or offer home cleaning services, there are many opportunities to turn your skills and expertise into a profitable side hustle.

Better than most online side hustle posts, right?

Write about the top 10 programming side hustles to start in 2023.

I got this.

If you are a programmer looking to start a side hustle, 2023 is the perfect time to launch your own business. With the growing demand for software and app development, there are many opportunities for programmers to turn their skills into a profitable side hustle. Here are the top 10 programming side hustles to start in 2023:

1. App Development — With the rise of smartphones and tablets, there is a growing demand for app development. You can offer your services to businesses and individuals looking to create custom apps for their needs.

2. Website Development — Many businesses and individuals are looking for help with creating and maintaining their websites. As a website developer, you can offer your services to help design, build, and manage websites for your clients.

3. Software Development — If you have expertise in a particular programming language, consider starting a software development side hustle. You can offer your services to businesses and individuals looking to create custom software solutions for their needs.

4. Game Development — The gaming industry is thriving, and there is a growing demand for game development. If you have experience in game development, you can offer your services to businesses and individuals looking to create custom games.

5. Data Analysis — With the rise of big data, there is a growing demand for data analysts. As a data analyst, you can offer your services to businesses and individuals looking to make sense of their data and gain insights from it.

6. Machine Learning — Machine learning is a rapidly growing field, and there is a growing demand for machine learning experts. If you have experience in machine learning, you can offer your services to businesses and individuals looking to develop custom machine learning solutions.

7. Cloud Computing — With the rise of cloud computing, there is a growing demand for cloud experts. If you have experience in cloud computing, you can offer your services to businesses and individuals looking to migrate their applications and data to the cloud.

8. Blockchain Development — Blockchain technology is gaining popularity, and there is a growing demand for blockchain developers. If you have experience in blockchain development, you can offer your services to businesses and individuals looking to develop custom blockchain solutions.

9. Artificial Intelligence — Artificial intelligence is a rapidly growing field, and there is a growing demand for AI experts. If you have experience in artificial intelligence, you can offer your services to businesses and individuals looking to develop custom AI solutions.

10. Virtual Reality — Virtual reality is an exciting and emerging technology, and there is a growing demand for VR developers. If you have experience in VR development, you can offer your services to businesses and individuals looking to create custom VR experiences.

In conclusion, 2023 is a great time to start a programming side hustle. Whether you are interested in app development, website development, or machine learning, there are many opportunities for programmers to turn their skills into a profitable business.

These two blogs show that AI can simplify blog authoring.

I asked some tough programming questions, and most were suitable.

The content may occasionally not be what we want, but it will almost always be very helpful to you.

Enjoy.

The web adds millions or billions of pages per day.

How much Google traffic does this content get?

In 2017, we studied 2 million randomly-published pages to answer this question. Only 5.7% of them ranked in Google's top 10 search results within a year of being published.

94.3 percent of roughly two million pages got no Google traffic.

Two million pages is a small sample compared to the entire web. We did another study.

We analyzed over a billion pages to see how many get organic search traffic and why.

How many pages get search traffic?

90% of pages in our index get no Google traffic, and 5.2% get ten visits or less.

90% of google pages get no organic traffic

How can you join the minority that gets Google organic search traffic?

There are hundreds of SEO problems that can hurt your Google rankings. If we only consider common scenarios, there are only four.

Reason #1: No backlinks

I hate to repeat what most SEO articles say, but it's true:

Backlinks boost Google rankings.

Google's "top 3 ranking factors" include them.

Why don't we divide our studied pages by the number of referring domains?

66.31 percent of pages have no backlinks, and 26.29 percent have three or fewer.

Did you notice the trend already?

Most pages lack search traffic and backlinks.

But are these the same pages?

Let's compare monthly organic search traffic to backlinks from unique websites (referring domains):

More backlinks equals more Google organic traffic.

Referring domains and keyword rankings are correlated.

It's important to note that correlation does not imply causation, and none of these graphs prove backlinks boost Google rankings. Most SEO professionals agree that it's nearly impossible to rank on the first page without backlinks.

You'll need high-quality backlinks to rank in Google and get search traffic. 

Is organic traffic possible without links?

Here are the numbers:

Four million pages get organic search traffic without backlinks. Only one in 20 pages without backlinks has traffic, which is 5% of our sample.

Most get 300 or fewer organic visits per month.

What happens if we exclude high-Domain-Rating pages?

The numbers worsen. Less than 4% of our sample (1.4 million pages) receive organic traffic. Only 320,000 get over 300 monthly organic visits, or 0.1% of our sample.

This suggests high-authority pages without backlinks are more likely to get organic traffic than low-authority pages.

Internal links likely pass PageRank to new pages.

Two other reasons:

1. Our crawler's blocked. Most shady SEOs block backlinks from us. This prevents competitors from seeing (and reporting) PBNs.

2. They choose low-competition subjects. Low-volume queries are less competitive, requiring fewer backlinks to rank.

If the idea of getting search traffic without building backlinks excites you, learn about Keyword Difficulty and how to find keywords/topics with decent traffic potential and low competition.

Reason #2: The page has no long-term traffic potential.

Some pages with many backlinks get no Google traffic.

Why? I filtered Content Explorer for pages with no organic search traffic and divided them into four buckets by linking domains.

Almost 70k pages have backlinks from over 200 domains, but no search traffic.

By manually reviewing these (and other) pages, I noticed two general trends that explain why they get no traffic:

1. They overdid "shady link building" and got penalized by Google;

2. They're not targeting a Google-searched topic.

I won't elaborate on point one because I hope you don't engage in "shady link building"

#2 is self-explanatory:

If nobody searches for what you write, you won't get search traffic.

Consider one of our blog posts' metrics:

No organic traffic despite 337 backlinks from 132 sites.

The page is about "organic traffic research," which nobody searches for.

News articles often have this. They get many links from around the web but little Google traffic.

People can't search for things they don't know about, and most don't care about old events and don't search for them.

Note:

Some news articles rank in the "Top stories" block for relevant, high-volume search queries, generating short-term organic search traffic.

The Guardian's top "Donald Trump" story:

Ahrefs caught on quickly:

"Donald Trump" gets 5.6M monthly searches, so this page got a lot of "Top stories" traffic.

I bet traffic has dropped if you check now.

One of the quickest and most effective SEO wins is:

1. Find your website's pages with the most referring domains;

2. Do keyword research to re-optimize them for relevant topics with good search traffic potential.

Bryan Harris shared this "quick SEO win" during a course interview:

He suggested using Ahrefs' Site Explorer's "Best by links" report to find your site's most-linked pages and analyzing their search traffic. This finds pages with lots of links but little organic search traffic.

We see:

The guide has 67 backlinks but no organic traffic.

We could fix this by re-optimizing the page for "SERP"

A similar guide with 26 backlinks gets 3,400 monthly organic visits, so we should easily increase our traffic.

Don't do this with all low-traffic pages with backlinks. Choose your battles wisely; some pages shouldn't be ranked.

Reason #3: Search intent isn't met

Google returns the most relevant search results.

That's why blog posts with recommendations rank highest for "best yoga mat."

Google knows that most searchers aren't buying.

It's also why this yoga mats page doesn't rank, despite having seven times more backlinks than the top 10 pages:

The page ranks for thousands of other keywords and gets tens of thousands of monthly organic visits. Not being the "best yoga mat" isn't a big deal.

If you have pages with lots of backlinks but no organic traffic, re-optimizing them for search intent can be a quick SEO win.

It was originally a boring landing page describing our product's benefits and offering a 7-day trial.

We realized the problem after analyzing search intent.

People wanted a free tool, not a landing page.

In September 2018, we published a free tool at the same URL. Organic traffic and rankings skyrocketed.

Reason #4: Unindexed page

Google can’t rank pages that aren’t indexed.

If you think this is the case, search Google for site:[url]. You should see at least one result; otherwise, it’s not indexed.

A rogue noindex meta tag is usually to blame. This tells search engines not to index a URL.

Rogue canonicals, redirects, and robots.txt blocks prevent indexing.

Check the "Excluded" tab in Google Search Console's "Coverage" report to see excluded pages.

Google doesn't index broken pages, even with backlinks.

Surprisingly common.

In Ahrefs' Site Explorer, the Best by Links report for a popular content marketing blog shows many broken pages.

One dead page has 131 backlinks:

According to the URL, the page defined content marketing. —a keyword with a monthly search volume of 5,900 in the US.

Luckily, another page ranks for this keyword. Not a huge loss.

At least redirect the dead page's backlinks to a working page on the same topic. This may increase long-tail keyword traffic.

This post is a summary. See the original post here

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.