A few days ago, I was discussing dall-e with two art and tech pals. One artist acquaintance said she knew a frightened illustrator. Would the ability to create anything with a click derail her career? The artist feared this. My curator friend smiled and said this has always been a dread among artists. When the camera was invented, didn't painters say this? Even in the Instagram era, painting exists.

When art and technology collide, there's room for innovation, experimentation, and fear — especially if the technology replicates or replaces art making. What is art's future with dall-e? How does technology affect music, beyond visual art? Recently, I saw "ABBA Voyage," a holographic ABBA concert in London.

"Abba voyage?" my phone asked in early March. A Gen X friend I met through a fashion blogging ring texted me.

"What's abba Voyage?" I asked while opening my front door with keys and coffee.

We're going! Marti, visiting London, took me to a show.

"Absolutely no ABBA songs here." I responded.

My parents didn't play ABBA much, so I don't know much about them. Dad liked Jimi Hendrix, Cream, Deep Purple, and New Orleans jazz. Marti told me ABBA Voyage was a holographic ABBA show with a live band.

The show was fun, extraordinary fun. Nearly everyone on the dance floor wore wigs, ankle-breaking platforms, sequins, and bellbottoms. I saw some millennials and Zoomers among the boomers.

I was intoxicated by the experience.

Automatons date back to the 18th-century mechanical turk. The mechanical turk was a chess automaton operated by a person. The mechanical turk seemed to perform like a human without human intervention, but it required a human in the loop to work properly.

Humans have used non-humans in entertainment for centuries, such as puppets, shadow play, and smoke and mirrors. A show can have animatronic, technological, and non-technological elements, and a live show can blur real and illusion. From medieval puppet shows to mechanical turks to AI filters, bots, and holograms, entertainment has evolved over time.

I'm not a hologram skeptic, but I'm skeptical of technology, especially since I work with it. I love live performances, I love hearing singers breathe, forget lines, and make jokes. Live shows are my favorite because I love watching performers make mistakes or interact with the audience. ABBA Voyage was different.

Marti and I traveled to Manchester after ABBA Voyage to see Liam Gallagher. Similar but different vibe. Similar in that thousands dressed up for the show. ABBA's energy was dizzying. 90s chic replaced sequins in the crowd. Doc Martens, nylon jackets, bucket hats, shaggy hair. The Charlatans and Liam Gallagher opened and closed, respectively. Fireworks. Incredible. People went crazy. Yelling exhausted my voice.

This week in music featured AI-enabled holograms and a decades-old rocker. Both are warm and gooey in our memories.

After seeing both, I'm wondering if we need AI hologram shows. Why? Is it good?

Like everything tech-related, my answer is "maybe." Because context and performance matter. Liam Gallagher and ABBA both had great, different shows.

For a hologram to work, it must be impossible and big. It must be big, showy, and improbable to justify a hologram. It must feel...expensive, like a stadium pop show. According to a quick search, ABBA broke up on bad terms. Reuniting is unlikely. This is also why Prince or Tupac hologram shows work. We can only engage with their legacy through covers or...holograms.

I drove around listening to the radio a few weeks ago. "Dreaming of You" by Selena played. Selena's music defined my childhood. I sang along and turned up the volume (or as loud as my husband would allow me while driving on the highway).

I discovered Selena's music six months after her death, so I never saw her perform live. My babysitter Melissa played me her album after I moved to Houston. Melissa took me to see the Selena movie five times when it came out. I quickly wore out my VHS copy. I constantly sang "Bibi Bibi Bom Bom" and "Como la Flor." I love Selena. A Selena hologram? Yes, probably.

Instagram advertised a cellist's Arthur Russell tribute show. Russell is another deceased artist I love. I almost walked down the aisle to "This is How We Walk on the Moon," but our cellist couldn't find it. Instead, I walked to Magnetic Fields' "The Book of Love." I "discovered" Russell after a friend introduced me to his music a few years ago.

I use these as analogies for the Liam Gallagher and ABBA concerts.

You have no idea how much I'd pay to see a hologram of Selena's 1995 Houston Livestock Show and Rodeo concert. Arthur Russell's hologram is unnecessary. Russell's work was intimate and performance-based. We can't separate his life from his legacy; popular audiences overlooked his genius. He died of AIDS broke. Like Selena, he died prematurely. Given his music and history, another performer would be a better choice than a hologram. He's no Selena. Selena could have rivaled Beyonce.

Pop shows' size works for holograms. Along with ABBA holograms, there was an anime movie and a light show that would put Tron to shame. ABBA created a tourable stadium show. The event was lavish, expensive, and well-planned. Pop, unlike rock, isn't gritty. Liam Gallagher hologram? No longer impossible, it wouldn't work. He's touring. I'm not sure if a rockstar alone should be rendered as a hologram; it was the show that made ABBA a hologram.

Holograms, like AI, are part of the future of entertainment, but not all of it. Because only modern interpretations of Arthur Russell's work reveal his legacy. That's his legacy.

Large-scale arena performers may use holograms in the future, but the experience must be impossible. A teacher once said that the only way to convey emotion in opera is through song, and I feel the same way about holograms, AR, VR, and mixed reality. A story's impossibility must make sense, like in opera. Impossibility and bombastic performance must be present for an immersive element to "work." ABBA was an impossible and improbable experience, which made it magical. It helped the holographic show work.

Marti told me about ABBA Voyage. She said it was a great concert. Marti has worked in music since the 1990s. She's a music expert; she's seen many shows.

Ai isn't a god or sentient, and the ABBA holograms aren't real. The renderings were glassy-eyed, flat, and robotic, like the Polar Express or the Jaws shark. Even today, the uncanny valley is insurmountable. We know it's not real because it's not about reality. It was about a suspended moment and performance feelings.

I knew this was impossible, an 'unreal' experience, but the emotions I felt were real, like watching a movie or tv show. Perhaps this is one of the better uses of AI, like CGI and special effects, like the beauty of entertainment- we were enraptured and entertained for hours. I've been playing ABBA since then.

Unleash the power of the Option key ⌥

#1 Open a link in the Private tab first.

Previously, if I needed to open a Safari link in a private window, I would:

• copied the URL with the right click command,

• choose File > New Private Window to open a private window, and

• clicked return after pasting the URL.

I've found a more straightforward way.

Right-clicking a link shows this, right?

Hold option (⌥) for:

Click Open Link in New Private Window while holding.

Finished!

#2. Instead of searching for specific characters, try this

You may use unicode for business or school. Most people Google them when they need them.

That is lengthy!

You can type some special characters just by pressing ⌥ and a key.

For instance

• ⌥+2 -> ™ (Trademark)
• ⌥+0 -> ° (Degree)
• ⌥+G -> © (Copyright)
• ⌥+= -> ≠ (Not equal to)
• ⌥+< -> ≤ (Less than or equal to)
• ⌥+> -> ≥ (Greater then or equal to)
• ⌥+/ -> ÷ (Different symbol for division)

#3 Activate Do Not Disturb silently.

Do Not Disturb when sharing my screen is awkward for me (because people may think Im trying to hide some secret notifications).

Here's another method.

Hold ⌥ and click on Time (at the extreme right on the menu-bar).

Now, DND is activated (secretly!). To turn it off, do it again.

Note: This works only for DND focus.

#4. Resize a window starting from its center

Although this is rarely useful, it is still a hidden trick.

When you resize a window, the opposite edge or corner is used as the pivot, right?

However, if you want to resize it with its center as the pivot, hold while doing so.

#5. Yes, Cut-Paste is available on Macs as well (though it is slightly different).

I call it copy-move rather than cut-paste. This is how it works.

Carry it out.

Choose a file (by clicking on it), then copy it (⌘+C).

Go to a new location on your Mac. Do you use ⌘+V to paste it? However, to move it, press ⌘+⌥+V.

This removes the file from its original location and copies it here. And it works exactly like cut-and-paste on Windows.

#6. Instantly expand all folders

Set your Mac's folders to List view.

Assume you have one folder with multiple subfolders, each of which contains multiple files. And you wanted to look at every single file that was over there.

How would you do?

You're used to clicking the ⌄ glyph near the folder and each subfolder to expand them all, right? Instead, hold down ⌥ while clicking ⌄ on the parent folder.

This is what happens next.

Everything expands.

View/Copy a file's path as an added bonus

If you want to see the path of a file in Finder, select it and hold ⌥, and you'll see it at the bottom for a moment.

To copy its path, right-click on the folder and hold down ⌥ to see this

Click on Copy <"folder name"> as Pathname to do it.

#7 "Save As"

I was irritated by the lack of "Save As" in Pages when I first got a Mac (after 15 years of being a Windows guy).

It was necessary for me to save the file as a new file, in a different location, with a different name, or both.

Unfortunately, I couldn't do it on a Mac.

However, I recently discovered that it appears when you hold ⌥ when in the File menu.

Yay!

Apocodes helps entrepreneurs create SaaS products without writing code. This post introduces micro-SaaS and outlines its basic strategy.

Strategy

Vision and strategy differ when starting a startup.

• The company's long-term future state is outlined in the vision. It establishes the overarching objectives the organization aims to achieve while also justifying its existence. The company's future is outlined in the vision.

• The strategy consists of a collection of short- to mid-term objectives, the accomplishment of which will move the business closer to its vision. The company gets there through its strategy.

The vision should be stable, but the strategy must be adjusted based on customer input, market conditions, or previous experiments.

Begin modestly and aim high.

Be truthful. It's impossible to automate SaaS product creation from scratch. It's like climbing Everest without running a 5K. Physical rules don't prohibit it, but it would be suicide.

Apocodes 5K equivalent? Two options:

• (A) Create a feature that includes every setting option conceivable. then query potential clients “Would you choose us to build your SaaS solution if we offered 99 additional features of the same caliber?” After that, decide which major feature to implement next.

• (B) Build a few straightforward features with just one or two configuration options. Then query potential clients “Will this suffice to make your product?” What's missing if not? Finally, tweak the final result a bit before starting over.

(A) is an all-or-nothing approach. It's like training your left arm to climb Mount Everest. My right foot is next.

(B) is a better method because it's iterative and provides value to customers throughout.

Focus on a small market sector, meet its needs, and expand gradually. Micro-SaaS is Apocode's first market.

What is micro-SaaS.

Micro-SaaS enterprises have these characteristics:

• A limited range: They address a specific problem with a small number of features.

• A small group of one to five individuals.

• Low external funding: The majority of micro-SaaS companies have Total Addressable Markets (TAM) under $100 million. Investors find them unattractive as a result. As a result, the majority of micro-SaaS companies are self-funded or bootstrapped.

• Low competition: Because they solve problems that larger firms would rather not spend time on, micro-SaaS enterprises have little rivalry.

• Low upkeep: Because of their simplicity, they require little care.

• Huge profitability: Because providing more clients incurs such a small incremental cost, high profit margins are possible.

Micro-SaaS enterprises created with no-code are Apocode's ideal first market niche.

We'll create our own micro-SaaS solutions to better understand their needs. Although not required, we believe this will improve community discussions.

The challenge

In 100 days (September 12–December 20, 2022), we plan to build 10 micro-SaaS enterprises using Apocode.

They will be:

• Self-serve: Customers will be able to use the entire product experience without our manual assistance.

• Real: They'll deal with actual issues. They won't be isolated proofs of concept because we'll keep up with them after the challenge.

• Both free and paid options: including a free plan and a free trial period. Although financial success would be a good result, the challenge's stated objective is not financial success.

This will let us design Apocodes features, showcase them, and talk to customers.

(Edit: The first micro-SaaS was launched!)

Follow along

If you want to follow the story of Apocode or our progress in this challenge, you can subscribe here.

If you are interested in using Apocode, sign up here.

If you want to provide feedback, discuss the idea further or get involved, email me at nicolas.tresegnie@gmail.com

Discover How We Used Facebook Ads to Grow a New Mobile App from $0 to $15K MRR in Just 6 Months and Our Strategy to Hit $100K a Month.

Our client introduced a mobile app for Poshmark resellers in December and wanted as many to experience it and subscribe to the monthly plan.

An Error We Committed

We initiated a Facebook ad campaign with a "awareness" goal, not "installs." This sent them to a landing page that linked to the iPhone App Store and Android Play Store. Smart, right?

We got some installs, but we couldn't tell how many came from the ad versus organic/other channels because the objective we chose only reported landing page clicks, not app installs.

We didn't know which interest groups/audiences had the best cost per install (CPI) to optimize and scale our budget.

After spending $700 without adequate data (installs and trials report), we stopped the campaign and worked with our client's app developer to set up app events tracking.

This allowed us to create an installs campaign and track installs, trials, and purchases (in some cases).

Finding a Successful Audience

Once we knew what ad sets brought in what installs at what cost, we began optimizing and testing other interest groups and audiences, growing the profitable low CPI ones and eliminating the high CPI ones.

We did all our audience testing using an ABO campaign (Ad Set Budget Optimization), spending $10 to $30 on each ad set for three days and optimizing afterward. All ad sets under $30 were moved to a CBO campaign (Campaign Budget Optimization).

We let Facebook's AI decide how much to spend on each ad set, usually the one most likely to convert at the lowest cost.

If the CBO campaign maintains a nice CPI, we keep increasing the budget by $50 every few days or duplicating it sometimes in order to double the budget. This is how we've scaled to $400/day profitably.

Finding Successful Creatives

Per campaign, we tested 2-6 images/videos. Same ad copy and CTA. There was no clear winner because some images did better with some interest groups.

The image above with mail packages, for example, got us a cheap CPI of $9.71 from our Goodwill Stores interest group but, a high $48 CPI from our lookalike audience. Once we had statistically significant data, we turned off the high-cost ad.

New marketers who are just discovering A/B testing may assume it's black and white — winner and loser. However, Facebook ads' machine learning and reporting has gotten so sophisticated that it's hard to call a creative a flat-out loser, but rather a 'bad fit' for some audiences, and perfect for others.

You can see how each creative performs across age groups and optimize.

How Many Installs Did It Take Us to Earn $15K Per Month?

Six months after paying $25K, we got 1,940 app installs, 681 free trials, and 522 $30 monthly subscriptions. 522 * $30 gives us $15,660 in monthly recurring revenue (MRR).

Next, what? $100K per month

The conversation above is with the app's owner. We got on a 30-minute call where I shared how I plan to get the app to be making $100K a month like I’ve done for other businesses.

Reverse Engineering $100K

Formula:

For $100K/month, we need 3,334 people to pay $30/month. 522 people pay that. We need 2,812 more paid users.

522 paid users from 1,940 installs is a 27% conversion rate. To hit $100K/month, we need 10,415 more installs. Assuming...

With a $400 daily ad spend, we average 40 installs per day. This means that if everything stays the same, it would take us 260 days (around 9 months) to get to $100K a month (MRR).

Conclusion

You must market your goods to reach your income objective (without waiting forever). Paid ads is the way to go if you hate knocking on doors or irritating friends and family (who aren’t scalable anyways).

You must also test and optimize different angles, audiences, interest groups, and creatives.

Don't promote it.

I rarely read a post on how Rich Dad, Poor Dad motivated someone to grow rich or change their investing/finance attitude. Rich Dad, Poor Dad is a sham, though. This book isn't worth anyone's attention.

Robert Kiyosaki, the author of this garbage, doesn't deserve recognition or attention. This first finance guru wanted to build his own wealth at your expense. These charlatans only care about themselves.

The reason why Rich Dad, Poor Dad is a huge steaming piece of trash

The book's ideas are superficial, apparent, and unsurprising to entrepreneurs and investors. The book's themes may seem profound to first-time readers.

Apparently, starting a business will make you rich.

The book supports founding or buying a business, making it self-sufficient, and being rich through it. Starting a business is time-consuming, tough, and expensive. Entrepreneurship isn't for everyone. Rarely do enterprises succeed.

Robert says we should think like his mentor, a rich parent. Robert never said who or if this guy existed. He was apparently his own father. Robert proposes investing someone else's money in several enterprises and properties. The book proposes investing in:

“have returns of 100 percent to infinity. Investments that for $5,000 are soon turned into $1 million or more.”

In rare cases, a business may provide 200x returns, but 65% of US businesses fail within 10 years. Australia's first-year business failure rate is 60%. A business that lasts 10 years doesn't mean its owner is rich. These statistics only include businesses that survive and pay their owners.

Employees are depressed and broke.

The novel portrays employees as broke and sad. The author degrades workers.

I've owned and worked for a business. I was broke and miserable as a business owner, working 80 hours a week for absolutely little salary. I work 50 hours a week and make over $200,000 a year. My work is hard, intriguing, and I'm surrounded by educated individuals. Self-employed or employee?

Don't listen to a charlatan's tax advice.

From a bad advise perspective, Robert's tax methods were funny. Robert suggests forming a corporation to write off holidays as board meetings or health club costs as business expenses. These actions can land you in serious tax trouble.

Robert dismisses college and traditional schooling. Rich individuals learn by doing or living, while educated people are agitated and destitute, says Robert.

Rich dad says:

“All too often business schools train employees to become sophisticated bean-counters. Heaven forbid a bean counter takes over a business. All they do is look at the numbers, fire people, and kill the business.”

And then says:

“Accounting is possibly the most confusing, boring subject in the world, but if you want to be rich long-term, it could be the most important subject.”

Get rich by avoiding paying your debts to others.

While this book has plenty of bad advice, I'll end with this: Robert advocates paying yourself first. This man's work with Trump isn't surprising.

Rich Dad's book says:

“So you see, after paying myself, the pressure to pay my taxes and the other creditors is so great that it forces me to seek other forms of income. The pressure to pay becomes my motivation. I’ve worked extra jobs, started other companies, traded in the stock market, anything just to make sure those guys don’t start yelling at me […] If I had paid myself last, I would have felt no pressure, but I’d be broke.“

Paying yourself first shouldn't mean ignoring debt, damaging your credit score and reputation, or paying unneeded fees and interest. Good business owners pay employees, creditors, and other costs first. You can pay yourself after everyone else.

If you follow Robert Kiyosaki's financial and business advice, you might as well follow Donald Trump's, the most notoriously ineffective businessman and swindle artist.

This book's popularity is unfortunate. Robert utilized the book's fame to promote paid seminars. At these seminars, he sold more expensive seminars to the gullible. This strategy was utilized by several conmen and Trump University.

It's reasonable that many believed him. It sounded appealing because he was pushing to get rich by thinking like a rich person. Anyway. At a time when most persons addressing wealth development advised early sacrifices (such as eschewing luxury or buying expensive properties), Robert told people to act affluent now and utilize other people's money to construct their fantasy lifestyle. It's exciting and fast.

I often voice my skepticism and scorn for internet gurus now that social media and platforms like Medium make it easier to promote them. Robert Kiyosaki was a guru. Many people still preach his stuff because he was so good at pushing it.

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.