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

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

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

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

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

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

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

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

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

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

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

Could this happen?

Medium isn't like other social media giants. It wasn't a dot-com startup that became a multi-trillion-dollar social media firm. It launched in 2012 but didn't gain popularity until later. Now, it's one of the largest sites by web traffic, but it's still little compared to most. Most of Medium's traffic is external, but they don't run advertisements, so it's all about memberships.

Medium isn't profitable, but they don't disclose how terrible the problem is. Most of the $163 million they raised has been spent or used for acquisitions. If the money turns off, Medium can't stop paying its writers since the site dies. Writers must be paid, but they can't substantially slash payment without hurting the platform. The existing model needs scale to be viable and has a low ceiling. Facebook and other free social media platforms are struggling to retain users. Here, you must pay to appreciate it, and it's bad for writers AND readers. If I had the same Medium stats on YouTube, I'd make thousands of dollars a month.

Then what? Medium has tried to monetize by offering writers a cut of new members, but that's unsustainable. People-based growth is limited. Imagine recruiting non-Facebook users and getting them to pay to join. Some may, but I'd rather write.

Alternatives:

• Donation buttons

• Tiered subscriptions ($5, $10, $25, etc.)

• Expanding content

and these may be short-term fixes, but they're not as profitable as allowing ads. Advertisements can pay several dollars per click and cents every view. If you get 40,000 views a month like me, that's several thousand instead of a few hundred. Also, Medium would have enough money to split ad revenue with writers, who would make more. I'm among the top 6% of Medium writers. Only 6% of Medium writers make more than $100, and I made $500 with 35,000 views last month. Compared to YouTube, the top 1% of Medium authors make a lot. Mr. Beast and PewDiePie make MILLIONS a month, yet top Medium writers make tens of thousands. Sure, paying 3 or 4 people a few grand, or perhaps tens of thousands, will keep them around. What if great authors leveraged their following to go huge on YouTube and abandoned Medium? If people use Medium to get successful on other platforms, Medium will be continuously cycling through authors and paying them to stay.

Ads might make writing on Medium more profitable than making videos on YouTube because they could preserve the present freemium model and pay users based on internal views. The $5 might be ad-free.

Consider: Would you accept Medium ads? A $5 ad-free version + pay-as-you-go, etc. What are your thoughts on this?

Original post available here

How did his money blind me?

Like most fledgling entrepreneurs, I wanted a mentor. I met as many nearby folks with "entrepreneur" in their LinkedIn biographies for coffee.

These meetings taught me a lot, and I'd suggest them to any new creator. Attention! Meeting with many experienced entrepreneurs means getting contradictory advice. One entrepreneur will tell you to do X, then the next one you talk to may tell you to do Y, which are sometimes opposites. You'll have to chose which suggestion to take after the chats.

I experienced this. Same afternoon, I had two coffee meetings with experienced entrepreneurs. The first meeting was with a billionaire entrepreneur who took his company public.

I met him in a swanky hotel lobby and ordered a drink I didn't pay for. As a fledgling entrepreneur, money was scarce.

During the meeting, I demoed the software I'd built, he liked it, and we spent the hour discussing what features would make it a success. By the end of the meeting, he requested I include a killer feature we both agreed would attract buyers. The feature was complex and would require some time. The billionaire I was sipping coffee with in a beautiful hotel lobby insisted people would love it, and that got me enthusiastic.

The second meeting was with a young entrepreneur who had recently raised a small amount of investment and looked as eager to pitch me as I was to pitch him. I forgot his name. I mostly recall meeting him in a filthy coffee shop in a bad section of town and buying his pricey cappuccino. Water for me.

After his pitch, I demoed my app. When I was done, he barely noticed. He questioned my customer acquisition plan. Who was my client? What did they offer? What was my plan? Etc. No decent answers.

After our meeting, he insisted I spend more time learning my market and selling. He ignored my questions about features. Don't worry about features, he said. Customers will request features. First, find them.

Putting your faith in results over relevance

Problems plagued my afternoon. I met with two entrepreneurs who gave me differing advice about how to proceed, and I had to decide which to pursue. I couldn't decide.

Ultimately, I followed the advice of the billionaire.

Obviously.

Who wouldn’t? That was the guy who clearly knew more.

A few months later, I constructed the feature the billionaire said people would line up for.

The new feature was unpopular. I couldn't even get the billionaire to answer an email showing him what I'd done. He disappeared.

Within a few months, I shut down the company, wasting all the time and effort I'd invested into constructing the killer feature the billionaire said I required.

Would follow the struggling entrepreneur's advice have saved my company? It would have saved me time in retrospect. Potential consumers would have told me they didn't want what I was producing, and I could have shut down the company sooner or built something they did want. Both outcomes would have been better.

Now I know, but not then. I favored achievement above relevance.

Success vs. relevance

The millionaire gave me advice on building a large, successful public firm. A successful public firm is different from a startup. Priorities change in the last phase of business building, which few entrepreneurs reach. He gave wonderful advice to founders trying to double their stock values in two years, but it wasn't beneficial for me.

The other failing entrepreneur had relevant, recent experience. He'd recently been in my shoes. We still had lots of problems. He may not have achieved huge success, but he had valuable advice on how to pass the closest hurdle.

The money blinded me at the moment. Not alone So much of company success is defined by money valuations, fundraising, exits, etc., so entrepreneurs easily fall into this trap. Money chatter obscures the value of knowledge.

Don't base startup advice on a person's income. Focus on what and when the person has learned. Relevance to you and your goals is more important than a person's accomplishments when considering advice.

Great technology opens up an universe of possibilities.

Need a friend? WhatsApp, Telegram, Slack, etc.

Traveling? AirBnB, Expedia, Google Flights, etc.

Money transfer? Use digital banking, e-wallet, or crypto applications

Products inspire us. How do we become great?

I asked product managers in my network:

What does it take to be a great product manager?

52 product managers from 40+ prominent IT businesses in Southeast Asia responded passionately. Many of the PMs I've worked with have built fantastic products, from unicorns (Lazada, Tokopedia, Ovo) to incumbents (Google, PayPal, Experian, WarnerMedia) to growing (etaily, Nium, Shipper).

TL;DR:

• Soft talents are more important than hard skills. Technical expertise was hardly ever stressed by product managers, and empathy was mentioned more than ten times. Janani from Xendit expertly recorded the moment. A superb PM must comprehend that their empathy for the feelings of their users must surpass all logic and data.

• Constant attention to the needs of the user. Many people concur that the closer a PM gets to their customer/user, the more likely it is that the conclusion will be better. There were almost 30 references to customers and users. Focusing on customers has the advantage because it is hard to overshoot, as Rajesh from Lazada puts it best.

• Setting priorities is invaluable. Prioritization is essential because there are so many problems that a PM must deal with every day. My favorite quotation on this is from Rakuten user Yee Jie. Viki, A competent product manager extinguishes fires. A good product manager lets things burn and then prioritizes.

This summary isn't enough to capture what excellent PMs claim it requires. Read below!

What qualities make a successful product manager?

Themed quotes are alphabetized by author.

Embrace your user/customer

Aeriel Dela Paz, Rainmaking Venture Architect, ex-GCash Product Head

Great PMs know what customers need even when they don’t say it directly. It’s about reading between the lines and going through the numbers to address that need.

Anders Nordahl, OrkestraSCS's Product Manager

Understanding the vision of your customer is as important as to get the customer to buy your vision

Angel Mendoza, MetaverseGo's Product Head

Most people think that to be a great product manager, you must have technical know-how. It’s textbook and I do think it is helpful to some extent, but for me the secret sauce is EMPATHY — the ability to see and feel things from someone else’s perspective. You can’t create a solution without deeply understanding the problem.

Senior Product Manager, Tokopedia

Focus on delivering value and helping people (consumer as well as colleague) and everything else will follow

Darren Lau, Deloitte Digital's Head of Customer Experience

Start with the users, and work backwards. Don’t have a solution looking for a problem

Darryl Tan, Grab Product Manager

I would say that a great product manager is able to identify the crucial problems to solve through strong user empathy and synthesis of insights

Diego Perdana, Kitalulus Senior Product Manager

I think to be a great product manager you need to be obsessed with customer problems and most important is solve the right problem with the right solution

Senior Product Manager, AirAsia

Lot of common sense + Customer Obsession. The most important role of a Product manager is to bring clarity of a solution. Your product is good if it solves customer problems. Your product is great if it solves an eco-system problem and disrupts the business in a positive way.

Edward Xie, Mastercard Managing Consultant, ex-Shopee Product Manager

Perfect your product, but be prepared to compromise for right users

AVP Product, Shipper

For me, a great product manager need to be rational enough to find the business opportunities while obsessing the customers.

Janani Gopalakrishnan is a senior product manager of a stealth firm.

While as a good PM it’s important to be data-driven, to be a great PM one needs to understand that their empathy for their users’ emotions must exceed all logic and data. Great PMs also make these product discussions thrive within the team by intently listening to all the members thoughts and influence the team’s skin in the game positively.

Director, Product Management, Indeed

Great product managers put their users first. They discover problems that matter most to their users and inspire their team to find creative solutions.

Grab's Senior Product Manager Lakshay Kalra

Product management is all about finding and solving most important user problems

Quipper's Mega Puji Saraswati

First of all, always remember the value of “user first” to solve what user really needs (the main problem) for guidance to arrange the task priority and develop new ideas. Second, ownership. Treat the product as your “2nd baby”, and the team as your “2nd family”. Third, maintain a good communication, both horizontally and vertically. But on top of those, always remember to have a work — life balance, and know exactly the priority in life :)

Senior Product Manager, Prosa.AI Miswanto Miswanto

A great Product Manager is someone who can be the link between customer needs with the readiness and flexibility of the team. So that it can provide, build, and produce a product that is useful and helps the community to carry out their daily activities. And He/She can improve product quality ongoing basis or continuous to help provide solutions for users or our customer.

Lead Product Manager, Tokopedia, Oriza Wahyu Utami

Be a great listener, be curious and be determined. every great product manager have the ability to listen the pain points and understand the problems, they are always curious on the users feedback, and they also very determined to look for the solutions that benefited users and the business.

99 Group CPO Rajesh Sangati

The advantage of focusing on customers: it’s impossible to overshoot

Ray Jang, founder of Scenius, formerly of ByteDance

The difference between good and great product managers is that great product managers are willing to go the unsexy and unglamorous extra mile by rolling up their sleeves and ironing out all minutiae details of the product such that when the user uses the product, they can’t help but say “This was made for me.”

BCG Digital Ventures' Sid Narayanan

Great product managers ensure that what gets built and shipped is at the intersection of what creates value for the customer and for the business that’s building the product…often times, especially in today’s highly liquid funding environment, the unit economics, aka ensuring that what gets shipped creates value for the business and is sustainable, gets overlooked

Stephanie Brownlee, BCG Digital Ventures Product Manager

There is software in the world that does more harm than good to people and society. Great Product Managers build products that solve problems not create problems

Experiment constantly

Delivery Hero's Abhishek Muralidharan

Embracing your failure is the key to become a great Product Manager

DeliveryHero's Anuraag Burman

Product Managers should be thick skinned to deal with criticism and the stomach to take risk and face failures.

DataSpark Product Head Apurva Lawale

Great product managers enjoy the creative process with their team to deliver intuitive user experiences to benefit users.

Dexter Zhuang, Xendit Product Manager

The key to creating winning products is building what customers want as quickly as you can — testing and learning along the way.

PayPal's Jay Ko

To me, great product managers always remain relentlessly curious. They are empathetic leaders and problem solvers that glean customer insights into building impactful products

Home Credit Philippines' Jedd Flores

Great Product Managers are the best dreamers; they think of what can be possible for the customers, for the company and the positive impact that it will have in the industry that they’re part of

Set priorities first, foremost, foremost.

HBO Go Product Manager Akshay Ishwar

Good product managers strive to balance the signal to noise ratio, Great product managers know when to turn the dials for each up exactly

Zuellig Pharma's Guojie Su

Have the courage to say no. Managing egos and request is never easy and rejecting them makes it harder but necessary to deliver the best value for the customers.

Ninja Van's John Prawira

(1) PMs should be able to ruthlessly prioritize. In order to be effective, PMs should anchor their product development process with their north stars (success metrics) and always communicate with a purpose. (2) User-first when validating assumptions. PMs should validate assumptions early and often to manage risk when leading initiatives with a focus on generating the highest impact to solving a particular user pain-point. We can’t expect a product/feature launch to be perfect (there might be bugs or we might not achieve our success metric — which is where iteration comes in), but we should try our best to optimize on user-experience earlier on.

Nium Product Manager Keika Sugiyama

I’d say a great PM holds the ability to balance ruthlessness and empathy at the same time. It’s easier said than done for sure!

ShopBack product manager Li Cai

Great product managers are like great Directors of movies. They do not create great products/movies by themselves. They deliver it by Defining, Prioritising, Energising the team to deliver what customers love.

Quincus' Michael Lim

A great product manager, keeps a pulse on the company’s big picture, identifies key problems, and discerns its rightful prioritization, is able to switch between the macro perspective to micro specifics, and communicates concisely with humility that influences naturally for execution

Mathieu François-Barseghian, SVP, Citi Ventures

“You ship your org chart”. This is Conway’s Law short version (1967!): the fundamental socio-technical driver behind innovation successes (Netflix) and failures (your typical bank). The hype behind micro-services is just another reflection of Conway’s Law

Mastercard's Regional Product Manager Nikhil Moorthy

A great PM should always look to build products which are scalable & viable , always keep the end consumer journey in mind. Keeping things simple & having a MVP based approach helps roll out products faster. One has to test & learn & then accordingly enhance / adapt, these are key to success

Rendy Andi, Tokopedia Product Manager

Articulate a clear vision and the path to get there, Create a process that delivers the best results and Be serious about customers.

Senior Product Manager, DANA Indonesia

Own the problem, not the solution — Great PMs are outstanding problem preventers. Great PMs are discerning about which problems to prevent, which problems to solve, and which problems not to solve

Tat Leong Seah, LionsBot International Senior UX Engineer, ex-ViSenze Product Manager

Prioritize outcomes for your users, not outputs of your system” or more succinctly “be agile in delivering value; not features”

Senior Product Manager, Rakuten Viki

A good product manager puts out fires. A great product manager lets fires burn and prioritize from there

acquire fundamental soft skills

Oracle NetSuite's Astrid April Dominguez

Personally, i believe that it takes grit, empathy, and optimistic mindset to become a great PM

Ovo Lead Product Manager Boy Al Idrus

Contrary to popular beliefs, being a great product manager doesn’t have anything to do with technicals, it sure plays a part but most important weapons are: understanding pain points of users, project management, sympathy in leadership and business critical skills; these 4 aspects would definitely help you to become a great product manager.

PwC Product Manager Eric Koh

Product managers need to be courageous to be successful. Courage is required to dive deep, solving big problems at its root and also to think far and dream big to achieve bold visions for your product

Ninja Van's Product Director

In my opinion the two most important ingredients to become a successful product manager is: 1. Strong critical thinking 2. Strong passion for the work. As product managers, we typically need to solve very complex problems where the answers are often very ambiguous. The work is tough and at times can be really frustrating. The 2 ingredients I mentioned earlier will be critical towards helping you to slowly discover the solution that may become a game changer.

PayPal's Lead Product Manager

A great PM has an eye of a designer, the brain of an engineer and the tongue of a diplomat

Product Manager Irene Chan

A great Product Manager is able to think like a CEO of the company. Visionary with Agile Execution in mind

Isabella Yamin, Rakuten Viki Product Manager

There is no one model of being a great product person but what I’ve observed from people I’ve had the privilege working with is an overflowing passion for the user problem, sprinkled with a knack for data and negotiation

Google product manager Jachin Cheng

Great product managers start with abundant intellectual curiosity and grow into a classic T-shape. Horizontally: generalists who range widely, communicate fluidly and collaborate easily cross-functionally, connect unexpected dots, and have the pulse both internally and externally across users, stakeholders, and ecosystem players. Vertically: deep product craftsmanship comes from connecting relentless user obsession with storytelling, business strategy with detailed features and execution, inspiring leadership with risk mitigation, and applying the most relevant tools to solving the right problems.

Jene Lim, Experian's Product Manager

3 Cs and 3 Rs. Critical thinking , Customer empathy, Creativity. Resourcefulness, Resilience, Results orientation.

Nirenj George, Envision Digital's Security Product Manager

A great product manager is someone who can lead, collaborate and influence different stakeholders around the product vision, and should be able to execute the product strategy based on customer insights, as well as take ownership of the product roadmap to create a greater impact on customers.

Grab's Lead Product Manager

Product Management is a multi-dimensional role that looks very different across each product team so each product manager has different challenges to deal with but what I have found common among great product managers is ability to create leverage through their efforts to drive outsized impacts for their products. This leverage is built using data with intuition, building consensus with stakeholders, empowering their teams and focussed efforts on needle moving work.

NCS Product Manager Umar Masagos

To be a great product manager, one must master both the science and art of Product Management. On one hand, you need have a strong understanding of the tools, metrics and data you need to drive your product. On the other hand, you need an in-depth understanding of your organization, your target market and target users, which is often the more challenging aspect to master.

M1 product manager Wei Jiao Keong

A great product manager is multi-faceted. First, you need to have the ability to see the bigger picture, yet have a keen eye for detail. Secondly, you are empathetic and is able to deliver products with exceptional user experience while being analytical enough to achieve business outcomes. Lastly, you are highly resourceful and independent yet comfortable working cross-functionally.

Yudha Utomo, ex-Senior Product Manager, Tokopedia

A great Product Manager is essentially an effective note-taker. In order to achieve the product goals, It is PM’s job to ensure objective has been clearly conveyed, efforts are assessed, and tasks are properly tracked and managed. PM can do this by having top-notch documentation skills.

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.

A J.Crew collaboration for fashion label Eveliina Vintage is not a paradox; it is a solution.

Eveliina Vintage's capsule collection debuted yesterday at J.Crew. This J.Crew partnership stopped me in my tracks.

Eveliina Vintage sells vintage goods. Eeva Musacchia founded the shop in Finland in the 1970s. It's recognized for its one-of-a-kind slip dresses from the 1930s and 1940s.

I wondered why a vintage brand would partner with a mass shop. Fast fashion against vintage shopping? Will Eveliina Vintages customers be turned off?

But Eveliina Vintages customers don't care about sustainability. They want Eveliina's Instagram look. Eveliina Vintage collaborated with J.Crew to give customers what they wanted: more Eveliina at a lower price.

Vintage: A Fashion Option That Is Eco-Conscious

Secondhand shopping is a trendy response to quick fashion. J.Crew releases hundreds of styles annually. Waste and environmental damage have been criticized. A pair of jeans requires 1,800 gallons of water. J.Crew's limited-time deals promote more purchases. J.Crew items are likely among those Americans wear 7 times before discarding.

Consumers and designers have emphasized sustainability in recent years. Stella McCartney and Eileen Fisher are popular eco-friendly brands. They've also flocked to ThredUp and similar sites.

Gap, Levis, and Allbirds have listened to consumer requests. They promote recycling, ethical sourcing, and secondhand shopping.

Secondhand shoppers feel good about reusing and recycling clothing that might have ended up in a landfill.

Eco-conscious fashionistas shop vintage. These shoppers enjoy the thrill of the hunt (that limited-edition Chanel bag!) and showing off a unique piece (nobody will have my look!). They also reduce their environmental impact.

Is Eveliina Vintage capitalizing on an aesthetic or is it a sustainable brand?

Eveliina Vintage emphasizes environmental responsibility. Vogue's Amanda Musacchia emphasized sustainability. Amanda, founder Eeva's daughter, is a company leader.

But Eveliina's press message doesn't address sustainability, unlike Instagram. Scarcity and fame rule.

Eveliina Vintages Instagram has see-through dresses and lace-trimmed slip dresses. Celebrities and influencers are often photographed in Eveliina's apparel, which has 53,000+ followers. Vogue appreciates Eveliina's style. Multiple publications discuss Alexa Chung's Eveliina dress.

Eveliina Vintage markets its one-of-a-kind goods. It teases future content, encouraging visitors to return. Scarcity drives demand and raises clothing prices. One dress is $1,600+, but most are $500-$1,000.

The catch: Eveliina can't monetize its expanding popularity due to exorbitant prices and limited quantity. Why?

1. Most people struggle to pay for their clothing. But Eveliina Vintage lacks those more affordable entry-level products, in contrast to other luxury labels that sell accessories or perfume.

2. Many people have trouble fitting into their clothing. The bodies of most women in the past were different from those for which vintage clothing was designed. Each Eveliina dress's specific measurements are mentioned alongside it. Be careful, you can fall in love with an ill-fitting dress.

3. No matter how many people can afford it and fit into it, there is only one item to sell. To get the item before someone else does, those people must be on the Eveliina Vintage website as soon as it becomes available.

A Way for Eveliina Vintage to Make Money (and Expand) with J.Crew Its following

Eveliina Vintages' cooperation with J.Crew makes commercial sense.

This partnership spreads Eveliina's style. Slightly better pricing The $390 outfits have multicolored slips and gauzy cotton gowns. Sizes range from 00 to 24, which is wider than vintage racks.

Eveliina Vintage customers like the combination. Excited comments flood the brand's Instagram launch post. Nobody is mocking the 50-year-old vintage brand's fast-fashion partnership.

Vintage may be a sustainable fashion trend, but that's not why Eveliina's clients love the brand. They only care about the old look.

And that is a tale as old as fashion.