Yes, salary details ought to be mentioned in job postings. Recruiters and candidates both agree, so why doesn't it happen?

The short answer is “Unfortunately, it’s not the Recruiter’s decision”. The longer answer is well… A LOT.

Starting in November 2022, NYC employers must include salary ranges in job postings. It should have started in May, but companies balked.

I'm thrilled about salary transparency. This decision will promote fair, inclusive, and equitable hiring practices, and I'm sure other states will follow suit. Good news!

Candidates, recruiters, and ED&I practitioners have advocated for pay transparency for years. Why the opposition?

Let's quickly review why companies have trouble sharing salary bands.

💰 Pay Parity

Many companies and leaders still oppose pay parity. Yes, even in 2022.

💰 Pay Equity

Many companies believe in pay parity and have reviewed their internal processes and systems to ensure equality.

However, Pay Equity affects who gets roles/promotions/salary raises/bonuses and when. Enter the pay gap!

💰Pay Transparency and its impact on Talent Retention

Sharing salary bands with external candidates (and the world) means current employees will have access to that information, which is one of the main reasons companies don't share salary data.

If a company has Pay Parity and Pay Equity issues, they probably have a Pay Transparency policy as well.

Sharing salary information with external candidates without ensuring current employees understand their own salary bands and how promotions/raises are decided could impact talent retention strategies.

This information should help clarify recent conversations.

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 recently wrote about getting VCs excited about Marketplace start-ups. SaaS founders became envious!

Understanding how people wire tens of millions is the only Series A hack I recommend.

Few people understand the intellectual process behind investing.

VC is risk management.

Series A-focused VCs must cover two risks.

1. Market risk

You need a large market to cross a threshold beyond which you can build defensibilities. Series A VCs underwrite market risk.

They must see you have reached product-market fit (PMF) in a large total addressable market (TAM).

2. Execution risk

When evaluating your growth engine's blitzscaling ability, execution risk arises.

When investors remove operational uncertainty, they profit.

Series A VCs like businesses with derisked revenue streams. Don't raise unless you have a predictable model, pipeline, and growth.

Please beat these 3 metrics before Series A:

Achieve $1.5m ARR in 12-24 months (Market risk)

Above 100% Net Dollar Retention. (Market danger)

Lead Velocity Rate supporting $10m ARR in 2–4 years (Execution risk)

Hit the 3 and you'll raise $10M in 4 months. Discussing 2/3 may take 6–7 months.

If none, don't bother raising and focus on becoming a capital-efficient business (Topics for other posts).

Let's examine these 3 metrics for the brave ones.

1. Lead Velocity Rate supporting €$10m ARR in 2 to 4 years

Last because it's the least discussed. LVR is the most reliable data when evaluating a growth engine, in my opinion.

SaaS allows you to see the future.

Monthly Sales and Sales Pipelines, two predictive KPIs, have poor data quality. Both are lagging indicators, and minor changes can cause huge modeling differences.

Analysts and Associates will trash your forecasts if they're based only on Monthly Sales and Sales Pipeline.

LVR, defined as month-over-month growth in qualified leads, is rock-solid. There's no lag. You can See The Future if you use Qualified Leads and a consistent formula and process to qualify them.

With this metric in your hand, scaling your company turns into an execution play on which VCs are able to perform calculations risk.

2. Above-100% Net Dollar Retention.

Net Dollar Retention is a better-known SaaS health metric than LVR.

Net Dollar Retention measures a SaaS company's ability to retain and upsell customers. Ask what $1 of net new customer spend will be worth in years n+1, n+2, etc.

Depending on the business model, SaaS businesses can increase their share of customers' wallets by increasing users, selling them more products in SaaS-enabled marketplaces, other add-ons, and renewing them at higher price tiers.

If a SaaS company's annualized Net Dollar Retention is less than 75%, there's a problem with the business.

Slack's ARR chart (below) shows how powerful Net Retention is. Layer chart shows how existing customer revenue grows. Slack's S1 shows 171% Net Dollar Retention for 2017–2019.

Slack S-1

3. $1.5m ARR in the last 12-24 months.

According to Point 9, $0.5m-4m in ARR is needed to raise a $5–12m Series A round.

Target at least what you raised in Pre-Seed/Seed. If you've raised $1.5m since launch, don't raise before $1.5m ARR.

Capital efficiency has returned since Covid19. After raising $2m since inception, it's harder to raise $1m in ARR.

P9's 2016-2021 SaaS Funding Napkin

In summary, less than 1% of companies VCs meet get funded. These metrics can help you win.

If there’s demand for it, I’ll do one on direct-to-consumer.

Cheers!

A completely operating application requires many processes and technical challenges. Implementing coding standards can make apps right, work, and faster.

With years of experience working in software houses. Many client apps are scarcely maintained.

Why are these programs "barely maintainable"? If we're used to coding concepts, we can probably tell if an app is awful or good from its codebase.

This is how I coded much of my app.

Make It Work

Before adopting any concept, make sure the apps are completely functional. Why have a fully maintained codebase if the app can't be used?

The user doesn't care if the app is created on a super server or uses the greatest coding practices. The user just cares if the program helps them.

After the application is working, we may implement coding principles.

You Aren’t Gonna Need It

As a junior software engineer, I kept unneeded code, components, comments, etc., thinking I'd need them later.

In reality, I never use that code for weeks or months.

First, we must remove useless code from our primary codebase. If you insist on keeping it because "you'll need it later," employ version control.

If we remove code from our codebase, we can quickly roll back or copy-paste the previous code without preserving it permanently.

The larger the codebase, the more maintenance required.

Keep It Simple Stupid

Indeed. Keep things simple.

Why complicate something if we can make it simpler?

Our code improvements should lessen the server load and be manageable by others.

If our code didn't pass those benchmarks, it's too convoluted and needs restructuring. Using an open-source code critic or code smell library, we can quickly rewrite the code.

Simpler codebases and processes utilize fewer server resources.

Don't Repeat Yourself

Have you ever needed an action or process before every action, such as ensuring the user is logged in before accessing user pages?

As you can see from the above code, I try to call is user login? in every controller action, and it should be optimized, because if we need to rename the method or change the logic, etc. We can improve this method's efficiency.

We can write a constructor/middleware/before action that calls is_user_login?

The code is more maintainable and readable after refactoring.

Each programming language or framework handles this issue differently, so be adaptable.

Clean Code

Clean code is a broad notion that you've probably heard of before.

When creating a function, method, module, or variable name, the first rule of clean code is to be precise and simple.

The name should express its value or logic as a whole, and follow code rules because every programming language is distinct.

If you want to learn more about this topic, I recommend reading https://www.amazon.com/Clean-Code-Handbook-Software-Craftsmanship/dp/0132350882.

Standing On The Shoulder of Giants

Use industry standards and mature technologies, not your own(s).

There are several resources that explain how to build boilerplate code with tools, how to code with best practices, etc.

I propose following current conventions, best practices, and standardization since we shouldn't innovate on top of them until it gives us a competitive edge.

Boy Scout Rule

What reduces programmers' productivity?

When we have to maintain or build a project with messy code, our productivity decreases.

Having to cope with sloppy code will slow us down (shame of us).

How to cope? Uncle Bob's book says, "Always leave the campground cleaner than you found it."

When developing new features or maintaining current ones, we must improve our codebase. We can fix minor issues too. Renaming variables, deleting whitespace, standardizing indentation, etc.

Make It Fast

After making our code more maintainable, efficient, and understandable, we can speed up our app.

Whether it's database indexing, architecture, caching, etc.

A smart craftsman understands that refactoring takes time and it's preferable to balance all the principles simultaneously. Don't YAGNI phase 1.

Using these ideas in each iteration/milestone, while giving the bottom items less time/care.

You can check one of my articles for further information. https://medium.com/life-at-mekari/why-does-my-website-run-very-slowly-and-how-do-i-optimize-it-for-free-b21f8a2f0162

https://medium.com/life-at-mekari/what-you-need-to-make-your-app-a-high-availability-system-tackling-the-technical-challenges-8896abec363f

Skip this if you don't want to discover why your lively, no-brainer pitch isn't making $10k a month.

You don't want to be repulsive as an entrepreneur or anyone else. Making friends, influencing people, and converting strangers into customers will be difficult if your words evoke disgust, distrust, or disrespect. You may be one of many entrepreneurs who do this obliviously and involuntarily.

I've had to master selling my skills to recruiters (to land 6-figure jobs on Wall Street), selling companies to buyers in M&A transactions, and selling my own companies' products to strangers-turned-customers. I probably committed every cardinal sin of sales repulsion before realizing it was me or my poor salesmanship strategy.

If you're launching a new business, frustrated by low conversion rates, or just curious if you're repelling customers, read on to identify (and avoid) the 6 fatal errors that can kill any sales pitch.

1. The first indication

So many people fumble before they even speak because they assume their role is to convince the buyer. In other words, they expect to pressure, arm-twist, and combat objections until they convert the buyer. Actuality, the approach stinks of disgust, and emotionally-aware buyers would feel "gross" immediately.

Instead of trying to persuade a customer to buy, ask questions that will lead them to do so on their own. When a customer discovers your product or service on their own, they need less outside persuasion. Why not position your offer in a way that leads customers to sell themselves on it?

2. A flawless performance

Are you memorizing a sales script, tweaking video testimonials, and expunging historical blemishes before hitting "publish" on your new campaign? If so, you may be hurting your conversion rate.

Perfection may be a step too far and cause prospects to mistrust your sincerity. Become a great conversationalist to boost your sales. Seriously. Being charismatic is hard without being genuine and showing a little vulnerability.

People like vulnerability, even if it dents your perfect facade. Show the customer's stuttering testimonial. Open up about your or your company's past mistakes (and how you've since improved). Make your sales pitch a two-way conversation. Let the customer talk about themselves to build rapport. Real people sell, not canned scripts and movie-trailer testimonials.

If marketing or sales calls feel like a performance, you may be doing something wrong or leaving money on the table.

3. Your greatest phobia

Three minutes into prospect talks, I'd start sweating. I was talking 100 miles per hour, covering as many bases as possible to avoid the ones I feared. I knew my then-offering was inadequate and my firm had fears I hadn't addressed. So I word-vomited facts, features, and everything else to avoid the customer's concerns.

Do my prospects know I'm insecure? Maybe not, but it added an unnecessary and unhelpful layer of paranoia that kept me stressed, rushed, and on edge instead of connecting with the prospect. Skirting around a company, product, or service's flaws or objections is a poor, temporary, lazy (and cowardly) decision.

How can you project confidence and trust if you're afraid? Before you make another sales call, face your shortcomings, weak points, and objections. Your company won't be everyone's cup of tea, but you should have answers to every question or objection. You should be your business's top spokesperson and defender.

4. The unintentional apologies

Have you ever begged for a sale? I'm going to say no, however you may be unknowingly emitting sorry, inferior, insecure energy.

Young founders, first-time entrepreneurs, and those with severe imposter syndrome may elevate their target customer. This is common when trying to get first customers for obvious reasons.

• Since you're truly new at this, you naturally lack experience.

• You don't have the self-confidence boost of thousands or hundreds of closed deals or satisfied client results to remind you that your good or service is worthwhile.

• Getting those initial few clients seems like the most difficult task, as if doing so will decide the fate of your company as a whole (it probably won't, and you shouldn't actually place that much emphasis on any one transaction).

Customers can smell fear, insecurity, and anxiety just like they can smell B.S. If you believe your product or service improves clients' lives, selling it should feel like a benevolent act of service, not a sleazy money-grab. If you're a sincere entrepreneur, prospects will believe your proposition; if you're apprehensive, they'll notice.

Approach every sale as if you're fine with or without it. This has improved my salesmanship, marketing skills, and mental health. When you put pressure on yourself to close a sale or convince a difficult prospect "or else" (your company will fail, your rent will be late, your electricity will be cut), you emit desperation and lower the quality of your pitch. There's no point.

5. The endless promises

We've all read a million times how to answer or disprove prospects' arguments and add extra incentives to speed or secure the close. Some objections shouldn't be refuted. What if I told you not to offer certain incentives, bonuses, and promises? What if I told you to walk away from some prospects, even if it means losing your sales goal?

If you market to enough people, make enough sales calls, or grow enough companies, you'll encounter prospects who can't be satisfied. These prospects have endless questions, concerns, and requests for more, more, more that you'll never satisfy. These people are a distraction, a resource drain, and a test of your ability to cut losses before they erode your sanity and profit margin.

To appease or convert these insatiably needy, greedy Nellies into customers, you may agree with or acquiesce to every request and demand — even if you can't follow through. Once you overpromise and answer every hole they poke, their trust in you may wane quickly.

Telling a prospect what you can't do takes courage and integrity. If you're honest, upfront, and willing to admit when a product or service isn't right for the customer, you'll gain respect and positive customer experiences. Sometimes honesty is the most refreshing pitch and the deal-closer.

6. No matter what

Have you ever said, "I'll do anything to close this sale"? If so, you've probably already been disqualified. If a prospective customer haggles over a price, requests a discount, or continues to wear you down after you've made three concessions too many, you have a metal hook in your mouth, not them, and it may not end well. Why?

If you're so willing to cut a deal that you cut prices, comp services, extend payment plans, waive fees, etc., you betray your own confidence that your product or service was worth the stated price. They wonder if anyone is paying those prices, if you've ever had a customer (who wasn't a blood relative), and if you're legitimate or worth your rates.

Once a prospect senses that you'll do whatever it takes to get them to buy, their suspicions rise and they wonder why.

• Why are you cutting pricing if something is wrong with you or your service?

• Why are you so desperate for their sale?

• Why aren't more customers waiting in line to pay your pricing, and if they aren't, what on earth are they doing there?

That's what a prospect thinks when you reveal your lack of conviction, desperation, and willingness to give up control. Some prospects will exploit it to drain you dry, while others will be too frightened to buy from you even if you paid them.

Walking down a two-way street. Be casual.

If we track each act of repulsion to an uneasiness, fear, misperception, or impulse, it's evident that these sales and marketing disasters were forced communications. Stiff, imbalanced, divisive, combative, bravado-filled, and desperate. They were unnatural and accepted a power struggle between two sparring, suspicious, unequal warriors, rather than a harmonious oneness of two natural, but opposite parties shaking hands.

Sales should be natural, harmonious. Sales should feel good for both parties, not like one party is having their arm twisted.

You may be doing sales wrong if it feels repulsive, icky, or degrading. If you're thinking cringe-worthy thoughts about yourself, your product, service, or sales pitch, imagine what you're projecting to prospects. Don't make it unpleasant, repulsive, or cringeworthy.

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.