Unlimited everything for $19 monthly!?

Even with pretty words, no one wants to read an ugly email.

• Not Gen Z

• Not Millennials

• Not Gen X

• Not Boomers

I am a minimalist.

I like Mozart. I like avos. I love Apple.

When I hear seamlessly, effortlessly, or Apple's new adverb fluidly, my toes curl.

No email marketing tool gave me that feeling.

As a marketing consultant helping high-growth brands create marketing that doesn't feel like marketing, I've worked with every email marketing platform imaginable, including that naughty monkey and the expensive platform whose sales teams don't stop calling.

Most email marketing platforms are flawed.

1. They are overpriced.

2. They use dreadful templates.

3. They employ a poor visual designer.

4. The user experience there is awful.

5. Too many useless buttons are present. (Similar to the TV remote!)

I may have finally found the perfect email marketing tool. It creates strong flows. It helps me focus on storytelling.

It’s called Flodesk.

It’s effortless. It’s seamless. It’s fluid.

Here’s why it excites me.

Unlimited everything for $19 per month

Sends unlimited. Emails unlimited. Signups unlimited.

Most email platforms penalize success.

Pay for performance?

• $87 for 10k contacts

• $605 for 100K contacts

• $1,300+ for 200K contacts

In the 1990s, this made sense, but not now. It reminds me of when ISPs capped internet usage at 5 GB per month.

Flodesk made unlimited email for a low price a reality. Affordable, attractive email marketing isn't just for big companies.

Flodesk doesn't penalize you for growing your list. Price stays the same as lists grow.

Flodesk plans cost $38 per month, but I'll give you a 30-day trial for $19.

Amazingly strong flows

Foster different people's flows.

Email marketing isn't one-size-fits-all.

Different times require different emails.

People don't open emails because they're irrelevant, in my experience. A colder audience needs a nurturing sequence.

Flodesk automates your email funnels so top-funnel prospects fall in love with your brand and values before mid- and bottom-funnel email flows nudge them to take action.

I wish I could save more custom audience fields to further customize the experience.

Dynamic editor

Easy. Effortless.

Flodesk's editor is Apple-like.

You understand how it works almost instantly.

Like many Apple products, it's intentionally limited. No distractions. You can focus on emotional email writing.

Flodesk's inability to add inline HTML to emails is my biggest issue with larger projects. I wish I could upload HTML emails.

Simple sign-up procedures

Dream up joining.

I like how easy it is to create conversion-focused landing pages. Linkly lets you easily create 5 landing pages and A/B test messaging.

I like that you can use signup forms to ask people what they're interested in so they get relevant emails instead of mindless mass emails nobody opens.

I love how easy it is to embed in-line on a website.

Wonderful designer templates

Beautiful, connecting emails.

Flodesk has calm email templates. My designer's eye felt at rest when I received plain text emails with big impacts.

As a typography nerd, I love Flodesk's handpicked designer fonts. It gives emails a designer feel that is hard to replicate on other platforms without coding and custom font licenses.

Small adjustments can have a big impact

Details matter.

Flodesk remembers your brand colors. Flodesk automatically adds your logo and social handles to emails after signup.

Flodesk uses Zapier. This lets you send emails based on a user's action.

A bad live chat can trigger a series of emails to win back a customer.

Flodesk isn't for everyone.

Flodesk is great for Apple users like me.

If you waste time every day, even though you're ambitious, you're not alone.

Many of us could use some new time-management strategies, like these:

Focus on the following three.

You're thinking about everything at once.

You're overpowered.

It's mental. We just have what's in front of us. So savor the moment's beauty.

Prioritize 1-3 things.

To be one of the most productive people you and I know, follow these steps.

Get along with boredom.

Many of us grow bored, sweat, and turn on Netflix.

We shout, "I'm rarely bored!" Look at me! I'm happy.

Shut it, Sally.

You're not making wonderful things for the world. Boredom matters.

If you can sit with it for a second, you'll get insight. Boredom? Breathe.

Go blank.

Then watch your creativity grow.

Check your MacroVision once more.

We don't know what to do with our time, which contributes to time-wasting.

Nobody does, either. Jeff Bezos won't hand-deliver that crap to you.

Daily vision checks are required.

Also:

What are 5 things you'd love to create in the next 5 years?

You're soul-searching. It's food.

Return here regularly, and you'll adore the high you get from doing valuable work.

Improve your thinking.

What's Alex's latest nonsense?

I'm talking about overcoming our own thoughts. Worrying wastes so much time.

Too many of us are assaulted by lies, myths, and insecurity.

Stop letting your worries massage you into a worried coma like a Thai woman.

Optimizing your thoughts requires accepting what you can't control.

It means letting go of unhelpful thoughts and returning to the moment.

Keep your blood sugar level.

I gave up gluten, donuts, and sweets.

This has really boosted my energy.

Blood-sugar-spiking carbs make us irritable and tired.

These day-to-day ups and downs aren't productive. It's crucial.

Know how your diet affects insulin levels. Now I have more energy and can do more without clenching my teeth.

Reduce harmful carbs to boost energy.

Create a focused setting for yourself.

When we optimize the mind, we have more energy and use our time better because we're not tense.

Changing our environment can also help us focus. Disabling alerts is one example.

Too hot makes me procrastinate and irritable.

List five items that hinder your productivity.

You may be amazed at how much you may improve by removing distractions.

Be responsible.

Accountability is a time-saver.

Creating an emotional pull to finish things.

Writing down our goals makes us accountable.

We can engage a coach or work with an accountability partner to feel horrible if we don't show up and finish on time.

‘Hey Jake, I’m going to write 1000 words every day for 30 days — you need to make sure I do.’ ‘Sure thing, Nathan, I’ll be making sure you check in daily with me.’

Tick.

You might also blog about your ambitions to show your dedication.

Now you can't hide when you promised to appear.

Acquire a liking for bravery.

Boldness changes everything.

I sometimes feel lazy and wonder why. If my food and sleep are in order, I should assess my footing.

Most of us live backward. Doubtful. Uncertain. Feelings govern us.

Backfooting isn't living. It's lame, and you'll soon melt. Live boldly now.

Be assertive.

Get disgustingly into everything. Expand.

Even if it's hard, stop being a b*tch.

Those that make Mr. Bold Bear their spirit animal benefit. Save time to maximize your effect.

Sundar Pichai unveiled Simplicity Sprint at Google's latest all-hands conference.

To boost employee efficiency.

Not surprising. Few envisioned Google declaring a productivity drive.

Sunder Pichai's speech:

“There are real concerns that our productivity as a whole is not where it needs to be for the head count we have. Help me create a culture that is more mission-focused, more focused on our products, more customer focused. We should think about how we can minimize distractions and really raise the bar on both product excellence and productivity.”

The primary driver driving Google's efficiency push is:

Google's efficiency push follows 13% quarterly revenue increase. Last year in the same quarter, it was 62%.

Market newcomers may argue that the previous year's figure was fuelled by post-Covid reopening and growing consumer spending. Investors aren't convinced. A promising company like Google can't afford to drop so quickly.

Google’s quarterly revenue growth stood at 13%, against 62% in last year same quarter.

Google isn't alone. In my recent essay regarding 2025 programmers, I warned about the economic downturn's effects on FAAMG's workforce. Facebook had suspended hiring, and Microsoft had promised hefty bonuses for loyal staff.

In the same article, I predicted Google's troubles. Online advertising, especially the way Google and Facebook sell it using user data, is over.

FAAMG and 2nd rung IT companies could be the first to fall without Post-COVID revival and uncertain global geopolitics.

Google has hardly ever discussed effectiveness:

Apparently openly.

Amazon treats its employees like robots, even in software positions. It has significant turnover and a terrible reputation as a result. Because of this, it rarely loses money due to staff productivity.

Amazon trumps Google. In reality, it treats its employees poorly.

Google was the founding father of the modern-day open culture.

Larry and Sergey Google founded the IT industry's Open Culture. Silicon Valley called Google's internal democracy and transparency near anarchy. Management rarely slammed decisions on employees. Surveys and internal polls ensured everyone knew the company's direction and had a vote.

20% project allotment (weekly free time to build own project) was Google's open-secret innovation component.

After Larry and Sergey's exit in 2019, this is Google's first profitability hurdle. Only Google insiders can answer these questions.

• Would Google's investors compel the company's management to adopt an Amazon-style culture where the developers are treated like circus performers?

• If so, would Google follow suit?

• If so, how does Google go about doing it?

Before discussing Google's likely plan, let's examine programming productivity.

What determines a programmer's productivity is simple:

How would we answer Google's questions?

As a programmer, I'm more concerned about Simplicity Sprint's aftermath than its economic catalysts.

Large organizations don't care much about quarterly and annual productivity metrics. They have 10-year product-launch plans. If something seems horrible today, it's likely due to someone's lousy judgment 5 years ago who is no longer in the blame game.

Deconstruct our main question.

• How exactly do you change the culture of the firm so that productivity increases?

• How can you accomplish that without affecting your capacity to profit? There are countless ways to increase output without decreasing profit.

• How can you accomplish this with little to no effect on employee motivation? (While not all employers care about it, in this case we are discussing the father of the open company culture.)

• How do you do it for a 10-developer IT firm that is losing money versus a 1,70,000-developer organization with a trillion-dollar valuation?

When implementing a large-scale organizational change, success must be carefully measured.

The fastest way to do something is to do it right, no matter how long it takes.

You require clearly-defined group/team/role segregation and solid pass/fail matrices to:

• You can give performers rewards.

• Ones that are average can be inspired to improve

• Underachievers may receive assistance or, in the worst-case scenario, rehabilitation

As a 20-year programmer, I associate productivity with greatness.

Doing something well, no matter how long it takes, is the fastest way to do it.

Let's discuss a programmer's productivity.

Why productivity is a strange term in programming:

Productivity is work per unit of time.

Money=time This is an economic proverb. More hours worked, more pay. Longer projects cost more.

As a buyer, you desire a quick supply. As a business owner, you want employees who perform at full capacity, creating more products to transport and boosting your profits.

All economic matrices encourage production because of our obsession with it. Productivity is the only organic way a nation may increase its GDP.

Time is money — is not just a proverb, but an economical fact.

Applying the same productivity theory to programming gets problematic. An automating computer. Its capacity depends on the software its master writes.

Today, a sophisticated program can process a billion records in a few hours. Creating one takes a competent coder and the necessary infrastructure. Learning, designing, coding, testing, and iterations take time.

Programming productivity isn't linear, unlike manufacturing and maintenance.

Average programmers produce code every day yet miss deadlines. Expert programmers go days without coding. End of sprint, they often surprise themselves by delivering fully working solutions.

Reversing the programming duties has no effect. Experts aren't needed for productivity.

These patterns remind me of an XKCD comic.

Programming productivity depends on two factors:

• The capacity of the programmer and his or her command of the principles of computer science

• His or her productive bursts, how often they occur, and how long they last as they engineer the answer

At some point, productivity measurement becomes Schrödinger’s cat.

Product companies measure productivity using use cases, classes, functions, or LOCs (lines of code). In days of data-rich source control systems, programmers' merge requests and/or commits are the most preferred yardstick. Companies assess productivity by tickets closed.

Every organization eventually has trouble measuring productivity. Finer measurements create more chaos. Every measure compares apples to oranges (or worse, apples with aircraft.) On top of the measuring overhead, the endeavor causes tremendous and unnecessary stress on teams, lowering their productivity and defeating its purpose.

Macro productivity measurements make sense. Amazon's factory-era management has done it, but at great cost.

Google can pull it off if it wants to.

What Google meant in reality when it said that employee productivity has decreased:

When Google considers its employees unproductive, it doesn't mean they don't complete enough work in the allotted period.

They can't multiply their work's influence over time.

• Programmers who produce excellent modules or products are unsure on how to use them.

• The best data scientists are unable to add the proper parameters in their models.

• Despite having a great product backlog, managers struggle to recruit resources with the necessary skills.

• Product designers who frequently develop and A/B test newer designs are unaware of why measures are inaccurate or whether they have already reached the saturation point.

• Most ignorant: All of the aforementioned positions are aware of what to do with their deliverables, but neither their supervisors nor Google itself have given them sufficient authority.

So, Google employees aren't productive.

How to fix it?

• Business analysis: White suits introducing novel items can interact with customers from all regions. Track analytics events proactively, especially the infrequent ones.

• SOLID, DRY, TEST, and AUTOMATION: Do less + reuse. Use boilerplate code creation. If something already exists, don't implement it yourself.

• Build features-building capabilities: N features are created by average programmers in N hours. An endless number of features can be built by average programmers thanks to the fact that expert programmers can produce 1 capability in N hours.

• Work on projects that will have a positive impact: Use the same algorithm to search for images on YouTube rather than the Mars surface.

• Avoid tasks that can only be measured in terms of time linearity at all costs (if a task can be completed in N minutes, then M copies of the same task would cost M*N minutes).

In conclusion:

Software development isn't linear. Why should the makers be measured?

Notation for The Big O

I'm discussing a new way to quantify programmer productivity. (It applies to other professions, but that's another subject)

The Big O notation expresses the paradigm (the algorithmic performance concept programmers rot to ace their Google interview)

Google (or any large corporation) can do this.

1. Sort organizational roles into categories and specify their impact vs. time objectives. A CXO role's time vs. effect function, for instance, has a complexity of O(log N), meaning that if a CEO raises his or her work time by 8x, the result only increases by 3x.

2. Plot the influence of each employee over time using the X and Y axes, respectively.

3. Add a multiplier for Y-axis values to the productivity equation to make business objectives matter. (Example values: Support = 5, Utility = 7, and Innovation = 10).

4. Compare employee scores in comparable categories (developers vs. devs, CXOs vs. CXOs, etc.) and reward or help employees based on whether they are ahead of or behind the pack.

After measuring every employee's inventiveness, it's straightforward to help underachievers and praise achievers.

Example of a Big(O) Category:

If I ran Google (God forbid, its worst days are far off), here's how I'd classify it. You can categorize Google employees whichever you choose.

The Google interview truth:

O(1) < O(log n) < O(n) < O(n log n) < O(n^x) where all logarithmic bases are < n.

O(1): Customer service workers' hours have no impact on firm profitability or customer pleasure.

CXOs Most of their time is spent on travel, strategic meetings, parties, and/or meetings with minimal floor-level influence. They're good at launching new products but bad at pivoting without disaster. Their directions are being followed.

Devops, UX designers, testers Agile projects revolve around deployment. DevOps controls the levers. Their automation secures results in subsequent cycles.

UX/UI Designers must still prototype UI elements despite improved design tools.

All test cases are proportional to use cases/functional units, hence testers' work is O(N).

Architects Their effort improves code quality. Their right/wrong interference affects product quality and rollout decisions even after the design is set.

Core Developers Only core developers can write code and own requirements. When people understand and own their labor, the output improves dramatically. A single character error can spread undetected throughout the SDLC and cost millions.

Core devs introduce/eliminate 1000x bugs, refactoring attempts, and regression. Following our earlier hypothesis.

The fastest way to do something is to do it right, no matter how long it takes.

Conclusion:

Google is at the liberal extreme of the employee-handling spectrum

Microsoft faced an existential crisis after 2000. It didn't choose Amazon's data-driven people management to revitalize itself.

Instead, it entrusted developers. It welcomed emerging technologies and opened up to open source, something it previously opposed.

Google is too lax in its employee-handling practices. With that foundation, it can only follow Amazon, no matter how carefully.

Any attempt to redefine people's measurements will affect the organization emotionally.

The more Google compares apples to apples, the higher its chances for future rebirth.

Quitting your job for a side gig isn't smart.

A few years ago, I would have laughed at the idea of starting a side business.

I never thought a side gig could earn more than my 9-to-5. My side gig pays more than my main job now.

You may then tell me to leave your job.  But I don't want to gamble, and my side gig is important. Programming and web development help me write better because of my job.

Yes, I share work-related knowledge. Web development, web3, programming, money, investment, and side hustles are key.

Let me now show you how to make one.

Create a side business based on your profession or your interests.

I'd be direct.

Most people don't know where to start or which side business to pursue.

You can make money by taking online surveys, starting a YouTube channel, or playing web3 games, according to several blogs.

You won't make enough money and will waste time.

Nitin directs our efforts. My friend, you've worked and have talent. Profit from your talent.

Example:

College taught me web development. I soon created websites, freelanced, and made money. First year was hardest for me financially and personally.

As I worked, I became more skilled. Soon after, I got more work, wrote about web development on Medium, and started selling products.

I've built multiple income streams from web development. It wasn't easy. Web development skills got me a 9-to-5 job.

Focus on a specific skill and earn money in many ways. Most people start with something they hate or are bad at; the rest is predictable.

Result? They give up, frustrated.

Quietly focus for a year.

I started my side business in college and never told anyone. My parents didn't know what I did for fun.

The only motivation is time constraints. So I focused.

As I've said, I focused on my strengths (learned skills) and made money. Yes, I was among Medium's top 500 authors in a year and got a bonus.

How did I succeed? Since I know success takes time, I never imagined making enough money in a month. I spent a year concentrating.

I became wealthy. Now that I have multiple income sources, some businesses pay me based on my skill.

I recommend learning skills and working quietly for a year. You can do anything with this.

The hardest part will always be the beginning.

When someone says you can make more money working four hours a week. Leave that, it's bad advice.

If someone recommends a paid course to help you succeed, think twice.

The beginning is always the hardest.

I made many mistakes learning web development. When I started my technical content side gig, it was tough. I made mistakes and changed how I create content, which helped.

And it’s applicable everywhere.

Don't worry if you face problems at first. Time and effort heal all wounds.

Quitting your job to work a side job is not a good idea.

Some honest opinions.

Most online gurus encourage side businesses. It takes time to start and grow a side business.

Suppose you quit and started a side business.

After six months, what happens? Your side business won't provide enough money to survive.

Indeed. Later, you'll become demotivated and tense and look for work.

Instead, work 9-5, and start a side business. You decide. Stop watching Netflix and focus on your side business.

I know you're busy, but do it.

Next? It'll succeed or fail in six months. You can continue your side gig for another six months because you have a job and have tried it.

You'll probably make money, but you may need to change your side gig.

That’s it.

You've created a new revenue stream.

Remember.

Starting a side business, a company, or finding work is difficult. There's no free money in a competitive world. You'll only succeed with skill.

Read it again.

Focusing silently for a year can help you succeed.

I studied web development and wrote about it. First year was tough. I went viral, hit the top 500, and other firms asked me to write for them. So, my life changed.

Yours can too. One year of silence is required.

Enjoy!

Learn these subtle cues to gain influence.

Hate being ignored?

As a 24-year-old, I struggled at work. Attention-getting tips How to avoid being judged by my size, gender, and lack of wrinkles or gray hair?

I've learned seniority hacks. Influence. Within two years as a product manager, I led a team. I'm a Stanford MBA student.

These communication hacks can make you look senior and influential.

1. Slowly speak

We speak quickly because we're afraid of being interrupted.

When I doubt my ideas, I speak quickly. How can we slow down? Jamie Chapman says speaking slowly saps our energy.

Chapman suggests emphasizing certain words and pausing.

2. Interrupted? Stop the stopper

Someone interrupt your speech?

Don't wait. "May I finish?" No pause needed. Stop interrupting. I first tried this in Leadership Laboratory at Stanford. How quickly I gained influence amazed me.

Next time, try “May I finish?” If that’s not enough, try these other tips from Wendy R.S. O’Connor.

3. Context

Others don't always see what's obvious to you.

Through explanation, you help others see the big picture. If a senior knows it, you help them see where your work fits.

4. Don't ask questions in statements

“Your statement lost its effect when you ended it on a high pitch,” a group member told me. Upspeak, it’s called. I do it when I feel uncertain.

Upspeak loses influence and credibility. Unneeded. When unsure, we can say "I think." We can even ask a proper question.

Someone else's boasting is no reason to be dismissive. As leaders and colleagues, we should listen to our colleagues even if they use this speech pattern.

Give your words impact.

5. Signpost structure

Signposts improve clarity by providing structure and transitions.

Communication coach Alexander Lyon explains how to use "first," "second," and "third" He explains classic and summary transitions to help the listener switch topics.

Signs clarify. Clarity matters.

6. Eliminate email fluff

“Fine. When will the report be ready? — Jeff.”

Notice how senior leaders write short, direct emails? I often use formalities like "dear," "hope you're well," and "kind regards"

Formality is (usually) unnecessary.

7. Replace exclamation marks with periods

See how junior an exclamation-filled email looks:

Hi, all!
Hope you’re as excited as I am for tomorrow! We’re celebrating our accomplishments with cake! Join us tomorrow at 2 pm!
See you soon!

Why the exclamation points? Why not just one?

Hi, all.
Hope you’re as excited as I am for tomorrow. We’re celebrating our accomplishments with cake. Join us tomorrow at 2 pm!
See you soon.

8. Take space

"Playing high" means having an open, relaxed body, says Stanford professor and author Deborah Gruenfield.

Crossed legs or looking small? Relax. Get bigger.

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.