No wonder brands use Twitter to reach their audience. 53% of Twitter users buy new products first. 

Twitter growth does more than make your brand look popular. It helps clients trust your business. It boosts your industry standing. It shows clients, prospects, and even competitors you mean business.

How can you naturally gain Twitter followers?

• Share useful information

• Post visual content

• Tweet consistently

• Socialize

• Spread your @name everywhere.

• Use existing customers

• Promote followers

Share useful information

Twitter users join conversations and consume material. To build your followers, make sure your material appeals to them and gives value, whether it's sales, product lessons, or current events.

Use Twitter Analytics to learn what your audience likes.

Explore popular topics by utilizing relevant keywords and hashtags. Check out this post on how to use Twitter trends.

Post visual content

97% of Twitter users focus on images, so incorporating media can help your Tweets stand out. Visuals and videos make content more engaging and memorable.

Tweet often

Your audience should expect regular content updates. Plan your ideas and tweet during crucial seasons and events with a content calendar.

Socialize

Twitter connects people. Do more than tweet. Follow industry leaders. Retweet influencers, engage with thought leaders, and reply to mentions and customers to boost engagement.

Micro-influencers can promote your brand or items. They can help you gain new audiences' trust.

Spread your @name everywhere.

Maximize brand exposure. Add a follow button on your website, link to it in your email signature and newsletters, and promote it on business cards or menus.

Use existing customers

Emails can be used to find existing Twitter clients. Upload your email contacts and follow your customers on Twitter to start a dialogue.

Promote followers

Run a followers campaign to boost your organic growth. Followers campaigns promote your account to a particular demographic, and you only pay when someone follows you.

Consider short campaigns to enhance momentum or an always-on campaign to gain new followers.

Increasing your brand's Twitter followers takes effort and experimentation, but the payback is huge.

👋 Follow me on twitter

Start now.

When it comes to building my business, I’m passionate about a lot of things. I love creating user experiences that simplify branding essentials. I love creating new typefaces and color combinations to inspire logo designers. I love fixing problems to improve my product.

Business marketing isn't my thing.

This is shared by many. Many solopreneurs, like me, struggle to advertise their business and drive themselves to work on it.

Without a lot of promotion, no company will succeed. Marketing is 80% of developing a firm, and when you're starting out, it's even more. Some believe that you shouldn't build anything until you've begun marketing your idea and found enough buyers.

Marketing your business without marketing experience is difficult. There are various outlets and techniques to learn. Instead of figuring out where to start, it's easier to return to your area of expertise, whether that's writing, designing product features, or improving your site's back end. Right?

First, realize that your role as a founder is to market your firm. Being a founder focused on product, I rarely work on it.

Secondly, use these basic methods that have helped me dedicate adequate time and focus to marketing. They're all simple to apply, and they've increased my business's visibility and success.

1. Establish buckets for every task.

You've probably heard to schedule tasks you don't like. As simple as it sounds, blocking a substantial piece of my workday for marketing duties like LinkedIn or Twitter outreach, AppSumo customer support, or SEO has forced me to spend time on them.

Giving me lots of room to focus on product development has helped even more. Sure, this means scheduling time to work on product enhancements after my four-hour marketing sprint.

It also involves making space to store product inspiration and ideas throughout the day so I don't get distracted. This is like the advice to keep a notebook beside your bed to write down your insomniac ideas. I keep fonts, color palettes, and product ideas in folders on my desktop. Knowing these concepts won't be lost lets me focus on marketing in the moment. When I have limited time to work on something, I don't have to conduct the research I've been collecting, so I can get more done faster.

2. Look for various accountability systems

Accountability is essential for self-discipline. To keep focused on my marketing tasks, I've needed various streams of accountability, big and little.

Accountability groups are great for bigger things. SaaS Camp, a sales outreach coaching program, is mine. We discuss marketing duties and results every week. This motivates me to do enough each week to be proud of my accomplishments. Yet hearing what works (or doesn't) for others gives me benchmarks for my own marketing outcomes and plenty of fresh techniques to attempt.

… say, I want to DM 50 people on Twitter about my product — I get that many Q-tips and place them in one pen holder on my desk.

The best accountability group can't watch you 24/7. I use a friend's simple method that shouldn't work (but it does). When I have a lot of marketing chores, like DMing 50 Twitter users about my product, That many Q-tips go in my desk pen holder. After each task, I relocate one Q-tip to an empty pen holder. When you have a lot of minor jobs to perform, it helps to see your progress. You might use toothpicks, M&Ms, or anything else you have a lot of.

3. Continue to monitor your feedback loops

Knowing which marketing methods work best requires monitoring results. As an entrepreneur with little go-to-market expertise, every tactic I pursue is an experiment. I need to know how each trial is doing to maximize my time.

I placed Google and Facebook advertisements on hold since they took too much time and money to obtain Return. LinkedIn outreach has been invaluable to me. I feel that talking to potential consumers one-on-one is the fastest method to grasp their problem areas, figure out my messaging, and find product market fit.

Data proximity offers another benefit. Seeing positive results makes it simpler to maintain doing a work you don't like. Why every fitness program tracks progress.

Marketing's goal is to increase customers and revenues, therefore I've found it helpful to track those metrics and celebrate monthly advances. I provide these updates for extra accountability.

Finding faster feedback loops is also motivating. Marketing brings more clients and feedback, in my opinion. Product-focused founders love that feedback. Positive reviews make me proud that my product is benefitting others, while negative ones provide me with suggestions for product changes that can improve my business.

The best advice I can give a lone creator who's afraid of marketing is to just start. Start early to learn by doing and reduce marketing stress. Start early to develop habits and successes that will keep you going. The sooner you start, the sooner you'll have enough consumers to return to your favorite work.

Digital influences that mimic humans are rising.

Lil Miquela has 3M Instagram followers, 3.6M TikTok followers, and 30K Twitter followers. She's been on the covers of Prada, Dior, and Calvin Klein magazines. Miquela released Not Mine in 2017 and launched Hard Feelings at Lollapazoolas this year. This isn't surprising, given the rise of influencer marketing.

This may be unexpected. Miquela's fake. Brud, a Los Angeles startup, produced her in 2016.

Lil Miquela is one of many rising virtual influencers in the new era of social media marketing. She acts like a real person and performs the same tasks as sports stars and models.

The emergence of online influencers

Before 2018, computer-generated characters were rare. Since the virtual human industry boomed, they've appeared in marketing efforts worldwide.

In 2020, the WHO partnered up with Atlanta-based virtual influencer Knox Frost (@knoxfrost) to gather contributions for the COVID-19 Solidarity Response Fund.

Lu do Magalu (@magazineluiza) has been the virtual spokeswoman for Magalu since 2009, using social media to promote reviews, product recommendations, unboxing videos, and brand updates. Magalu's 10-year profit was $552M.

In 2020, PUMA partnered with Southeast Asia's first virtual model, Maya (@mayaaa.gram). She joined Singaporean actor Tosh Zhang in the PUMA campaign. Local virtual influencer Ava Lee-Graham (@avagram.ai) partnered with retail firm BHG to promote their in-house labels.

In Japan, Imma (@imma.gram) is the face of Nike, PUMA, Dior, Salvatore Ferragamo SpA, and Valentino. Imma's bubblegum pink bob and ultra-fine fashion landed her on the cover of Grazia magazine.

Lotte Home Shopping created Lucy (@here.me.lucy) in September 2020. She made her TV debut as a Christmas show host in 2021. Since then, she has 100K Instagram followers and 13K TikTok followers.

Liu Yiexi gained 3 million fans in five days on Douyin, China's TikTok, in 2021. Her two-minute video went viral overnight. She's posted 6 videos and has 830 million Douyin followers.

China's virtual human industry was worth $487 million in 2020, up 70% year over year, and is expected to reach $875.9 million in 2021.

Investors worldwide are interested. Immas creator Aww Inc. raised $1 million from Coral Capital in September 2020, according to Bloomberg. Superplastic Inc., the Vermont-based startup behind influencers Janky and Guggimon, raised $16 million by 2020. Craft Ventures, SV Angels, and Scooter Braun invested. Crunchbase shows the company has raised $47 million.

The industries they represent, including Augmented and Virtual reality, were worth $14.84 billion in 2020 and are projected to reach $454.73 billion by 2030, a CAGR of 40.7%, according to PR Newswire.

Advantages for brands

Forbes suggests brands embrace computer-generated influencers. Examples:

1. Unlimited creative opportunities: Because brands can personalize everything—from a person's look and activities to the style of their content—virtual influencers may be suited to a brand's needs and personalities.

2. 100% brand control: Brand managers now have more influence over virtual influencers, so they no longer have to give up and rely on content creators to include brands into their storytelling and style. Virtual influencers can constantly produce social media content to promote a brand's identity and ideals because they are completely scandal-free.

3. Long-term cost savings: Because virtual influencers are made of pixels, they may be reused endlessly and never lose their beauty. Additionally, they can move anywhere around the world and even into space to fit a brand notion. They are also always available. Additionally, the expense of creating their content will not rise in step with their expanding fan base.

4. Introduction to the metaverse: Statista reports that 75% of American consumers between the ages of 18 and 25 follow at least one virtual influencer. As a result, marketers that support virtual celebrities may now interact with younger audiences that are more tech-savvy and accustomed to the digital world. Virtual influencers can be included into any digital space, including the metaverse, as they are entirely computer-generated 3D personas. Virtual influencers can provide brands with a smooth transition into this new digital universe to increase brand trust and develop emotional ties, in addition to the young generations' rapid adoption of the metaverse.

5. Better engagement than in-person influencers: A Hype Auditor study found that online influencers have roughly three times the engagement of their conventional counterparts. Virtual influencers should be used to boost brand engagement even though the data might not accurately reflect the entire sector.

Concerns about influencers created by computers

Virtual influencers could encourage excessive beauty standards in South Korea, which has a $10.7 billion plastic surgery industry.

A classic Korean beauty has a small face, huge eyes, and pale, immaculate skin. Virtual influencers like Lucy have these traits. According to Lee Eun-hee, a professor at Inha University's Department of Consumer Science, this could make national beauty standards more unrealistic, increasing demand for plastic surgery or cosmetic items.

Other parts of the world raise issues regarding selling items to consumers who don't recognize the models aren't human and the potential of cultural appropriation when generating influencers of other ethnicities, called digital blackface by some.

Meta, Facebook and Instagram's parent corporation, acknowledges this risk.

“Like any disruptive technology, synthetic media has the potential for both good and harm. Issues of representation, cultural appropriation and expressive liberty are already a growing concern,” the company stated in a blog post. “To help brands navigate the ethical quandaries of this emerging medium and avoid potential hazards, (Meta) is working with partners to develop an ethical framework to guide the use of (virtual influencers).”

Despite theoretical controversies, the industry will likely survive. Companies think virtual influencers are the next frontier in the digital world, which includes the metaverse, virtual reality, and digital currency.

In conclusion

Virtual influencers may garner millions of followers online and help marketers reach youthful audiences. According to a YouGov survey, the real impact of computer-generated influencers is yet unknown because people prefer genuine connections. Virtual characters can supplement brand marketing methods. When brands are metaverse-ready, the author predicts virtual influencer endorsement will continue to expand.

Many of us have struggled for years to master a second language (in my case, English). Because (at least in my situation) we've always used an input-based system or method.

I'll explain in detail, but briefly: We can understand some conversations or sentences (since we've trained), but we can't give sophisticated answers or speak fluently (because we have NOT trained at all).

What exactly is input-based learning?

Reading, listening, writing, and speaking are key language abilities (if you look closely at that list, it seems that people tend to order them in this way: inadvertently giving more priority to the first ones than to the last ones).

These talents fall under two learning styles:

• Reading and listening are input-based activities (sometimes referred to as receptive skills or passive learning).

• Writing and speaking are output-based tasks (also known as the productive skills and/or active learning).

What's the best learning style? To learn a language, we must master four interconnected skills. The difficulty is how much time and effort we give each.

According to Shion Kabasawa's books The Power of Input: How to Maximize Learning and The Power of Output: How to Change Learning to Outcome (available only in Japanese), we spend 7:3 more time on Input Based skills than Output Based skills when we should be doing the opposite, leaning more towards Output (Input: Output->3:7).

I can't tell you how he got those numbers, but I think he's not far off because, for example, think of how many people say they're learning a second language and are satisfied bragging about it by only watching TV, series, or movies in VO (and/or reading a book or whatever) their Input is: 7:0 output!

You can't be good at a sport by watching TikTok videos about it; you must play.

“being pushed to produce language puts learners in a better position to notice the ‘gaps’ in their language knowledge”, encouraging them to ‘upgrade’ their existing interlanguage system. And, as they are pushed to produce language in real time and thereby forced to automate low-level operations by incorporating them into higher-level routines, it may also contribute to the development of fluency. — Scott Thornbury (P is for Push)

How may I practice output-based learning more?

I know that listening or reading is easy and convenient because we can do it on our own in a wide range of situations, even during another activity (although, as you know, it's not ideal), writing can be tedious/boring (it's funny that we almost always excuse ourselves in the lack of ideas), and speaking requires an interlocutor. But we must leave our comfort zone and modify our thinking to go from 3:7 to 7:3. (or at least balance it better to something closer). Gradually.

“You don’t have to do a lot every day, but you have to do something. Something. Every day.” — Callie Oettinger (Do this every day)

We can practice speaking like boxers shadow box.

Speaking out loud strengthens the mind-mouth link (otherwise, you will still speak fluently in your mind but you will choke when speaking out loud). This doesn't mean we should talk to ourselves on the way to work, while strolling, or on public transportation. We should try to do it without disturbing others, such as explaining what we've heard, read, or seen (the list is endless: you can TALK about what happened yesterday, your bedtime book, stories you heard at the office, that new kitten video you saw on Instagram, an experience you had, some new fact, that new boring episode you watched on Netflix, what you ate, what you're going to do next, your upcoming vacation, what’s trending, the news of the day)

Who will correct my grammar, vocabulary, or pronunciation with an imagined friend? We can't have everything, but tools and services can help [1].

Lack of bravery

Fear of speaking a language different than one's mother tongue in front of native speakers is global. It's easier said than done, because strangers, not your friends, will always make fun of your accent or faults. Accept it and try again. Karma will prevail.

Perfectionism is a trap. Stop self-sabotaging. Communication is key (and for that you have to practice the Output too ).

“Don’t forget to have fun and enjoy the process.” — Ruri Ohama

[1] Grammarly, Deepl, Google Translate, etc.

Never design a product without explicit metrics and tracking tools.

Imagine driving cross-country without a dashboard. How do you know your school zone speed? Low gas? Without a dashboard, you can't monitor your car. You can't improve what you don't measure, as Peter Drucker said. Product managers must constantly enhance their understanding of their users, how they use their product, and how to improve it for optimum value. Customers will only pay if they consistently acquire value from your product.

I’m Solomon Ayanlakin. I’m a product manager at CredPal, a financial business that offers credit cards and Buy Now Pay Later services. Before falling into product management (like most PMs lol), I self-trained as a data analyst, using Alex the Analyst's YouTube playlists and DannyMas' virtual data internship. This article aims to help product managers, owners, and CXOs understand product metrics, give a methodology for creating them, and execute product experiments to enhance them.

☝🏽Introduction

Product metrics assist companies track product performance from the user's perspective. Metrics help firms decide what to construct (feature priority), how to build it, and the outcome's success or failure. To give the best value to new and existing users, track product metrics.

Why should a product manager monitor metrics?

• to assist your users in having a "aha" moment

• To inform you of which features are frequently used by users and which are not

• To assess the effectiveness of a product feature

• To aid in enhancing client onboarding and retention

• To assist you in identifying areas throughout the user journey where customers are satisfied or dissatisfied

• to determine the percentage of returning users and determine the reasons for their return

📈 What Metrics Ought a Product Manager to Monitor?

What indicators should a product manager watch to monitor product health? The metrics to follow change based on the industry, business stage (early, growth, late), consumer needs, and company goals. A startup should focus more on conversion, activation, and active user engagement than revenue growth and retention. The company hasn't found product-market fit or discovered what features drive customer value.

Depending on your use case, company goals, or business stage, here are some important product metric buckets:

All measurements shouldn't be used simultaneously. It depends on your business goals and what value means for your users, then selecting what metrics to track to see if they get it.

Some KPIs are more beneficial to track, independent of industry or customer type. To prevent recording vanity metrics, product managers must clearly specify the types of metrics they should track. Here's how to segment metrics:

1. The North Star Metric, also known as the Focus Metric, is the indicator and aid in keeping track of the top value you provide to users.

2. Primary/Level 1 Metrics: These metrics should either add to the north star metric or be used to determine whether it is moving in the appropriate direction. They are metrics that support the north star metric.

3. These measures serve as leading indications for your north star and Level 2 metrics. You ought to have been aware of certain problems with your L2 measurements prior to the North star metric modifications.

North Star Metric

This is the key metric. A good north star metric measures customer value. It emphasizes your product's longevity. Many organizations fail to grow because they confuse north star measures with other indicators. A good focus metric should touch all company teams and be tracked forever. If a company gives its customers outstanding value, growth and success are inevitable. How do we measure this value?

A north star metric has these benefits:

• Customer Obsession: It promotes a culture of customer value throughout the entire organization.

• Consensus: Everyone can quickly understand where the business is at and can promptly make improvements, according to consensus.

• Growth: It provides a tool to measure the company's long-term success. Do you think your company will last for a long time?

How can I pick a reliable North Star Metric?

Some fear a single metric. Ensure product leaders can objectively determine a north star metric. Your company's focus metric should meet certain conditions. Here are a few:

1. A good focus metric should reflect value and, as such, should be closely related to the point at which customers obtain the desired value from your product. For instance, the quick delivery to your home is a value proposition of UberEats. The value received from a delivery would be a suitable focal metric to use. While counting orders is alluring, the quantity of successfully completed positive review orders would make a superior north star statistic. This is due to the fact that a client who placed an order but received a defective or erratic delivery is not benefiting from Uber Eats. By tracking core value gain, which is the number of purchases that resulted in satisfied customers, we are able to track not only the total number of orders placed during a specific time period but also the core value proposition.
   

2. Focus metrics need to be quantifiable; they shouldn't only be feelings or states; they need to be actionable. A smart place to start is by counting how many times an activity has been completed.
   

3. A great focus metric is one that can be measured within predetermined time limits; otherwise, you are not measuring at all. The company can improve that measure more quickly by having time-bound focus metrics. Measuring and accounting for progress over set time periods is the only method to determine whether or not you are moving in the right path. You can then evaluate your metrics for today and yesterday. It's generally not a good idea to use a year as a time frame. Ideally, depending on the nature of your organization and the measure you are focusing on, you want to take into account on a daily, weekly, or monthly basis.
   

4. Everyone in the firm has the potential to affect it: A short glance at the well-known AAARRR funnel, also known as the Pirate Metrics, reveals that various teams inside the organization have an impact on the funnel. Ideally, the NSM should be impacted if changes are made to one portion of the funnel. Consider how the growth team in your firm is enhancing customer retention. This would have a good effect on the north star indicator because at this stage, a repeat client is probably being satisfied on a regular basis. Additionally, if the opposite were true and a client churned, it would have a negative effect on the focus metric.
   

5. It ought to be connected to the business's long-term success: The direction of sustainability would be indicated by a good north star metric. A company's lifeblood is product demand and revenue, so it's critical that your NSM points in the direction of sustainability. If UberEats can effectively increase the monthly total of happy client orders, it will remain in operation indefinitely.

Many product teams make the mistake of focusing on revenue. When the bottom line is emphasized, a company's goal moves from giving value to extracting money from customers. A happy consumer will stay and pay for your service. Customer lifetime value always exceeds initial daily, monthly, or weekly revenue.

Great North Star Metrics Examples

🥇 Basic/L1 Metrics:

The NSM is broad and focuses on providing value for users, while the primary metric is product/feature focused and utilized to drive the focus metric or signal its health. The primary statistic is team-specific, whereas the north star metric is company-wide. For UberEats' NSM, the marketing team may measure the amount of quality food vendors who sign up using email marketing. With quality vendors, more orders will be satisfied. Shorter feedback loops and unambiguous team assignments make L1 metrics more actionable and significant in the immediate term.

🥈 Supporting L2 metrics:

These are supporting metrics to the L1 and focus metrics. Location, demographics, or features are examples of L1 metrics. UberEats' supporting metrics might be the number of sales emails sent to food vendors, the number of opens, and the click-through rate. Secondary metrics are low-level and evident, and they relate into primary and north star measurements. UberEats needs a high email open rate to attract high-quality food vendors. L2 is a leading sign for L1.

Where can I find product metrics?

How can I measure in-app usage and activity now that I know what metrics to track? Enter product analytics. Product analytics tools evaluate and improve product management parameters that indicate a product's health from a user's perspective.

Various analytics tools on the market supply product insight. From page views and user flows through A/B testing, in-app walkthroughs, and surveys. Depending on your use case and necessity, you may combine tools to see how users engage with your product. Gainsight, MixPanel, Amplitude, Google Analytics, FullStory, Heap, and Pendo are product tools.

This article isn't sponsored and doesn't market product analytics tools. When choosing an analytics tool, consider the following:

• Tools for tracking your Focus, L1, and L2 measurements

• Pricing

• Adaptations to include external data sources and other products

• Usability and the interface

• Scalability

• Security

An investment in the appropriate tool pays off. To choose the correct metrics to track, you must first understand your business need and what value means to your users. Metrics and analytics are crucial for any tech product's growth. It shows how your business is doing and how to best serve users.

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.