Calmness is a vital life skill.

It aids communication. It boosts creativity and performance.

I've studied calm people's habits for years. Commonalities:

Have learned to laugh at themselves.

Those who have something to protect can’t help but make it a very serious business, which drains the energy out of the room.

They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.

Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.

Discover ways to take pleasure in life's challenges.

Since perspective is malleable, they change their view.

Set your own needs first.

Stressed people neglect themselves and wonder why they struggle.

Prioritize self-care.

Don't ruin your life to please others.

Make something.

Calm people create more than react.

They love creating beautiful things—paintings, children, relationships, and projects.

Hold your breath, please.

If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.

Release, breathe, and relax to find calm.

Stopped rushing.

Rushing is disadvantageous.

Calm people handle life better.

Are attuned to their personal dietary needs.

They avoid junk food and eat foods that keep them healthy, happy, and calm.

Don’t take anything personally.

Stressed people control everything.

Self-conscious.

Calm people put others and their work first.

Keep their surroundings neat.

Maintaining an uplifting and clutter-free environment daily calms the mind.

Minimise negative people.

Calm people are ruthless with their boundaries and avoid negative and drama-prone people.

A must-read for everyone

Jobs is well-known. You probably know the tall, thin guy who wore the same clothing every day. His influence is unavoidable. In fewer than 40 years, Jobs' innovations have impacted computers, movies, cellphones, music, and communication.

Steve Jobs may be more imaginative than the typical person, but if we can use some of his ingenuity, ambition, and good traits, we'll be successful. This essay explains how to follow his guidance and success secrets.

1. Repetition is necessary for success.

Be patient and diligent to master something. Practice makes perfect. This is why older workers are often more skilled.

When should you repeat a task? When you're confident and excited to share your product. It's when to stop tweaking and repeating.

Jobs stated he'd make the crowd sh** their pants with an iChat demo.

Use this in your daily life.

• Start with the end in mind. You can put it in writing and be as detailed as you like with your plan's schedule and metrics. For instance, you have a goal of selling three coffee makers in a week.

• Break it down, break the goal down into particular tasks you must complete, and then repeat those tasks. To sell your coffee maker, you might need to make 50 phone calls.

• Be mindful of the amount of work necessary to produce the desired results. Continue doing this until you are happy with your product.

2. Acquire the ability to add and subtract.

How did Picasso invent cubism? Pablo Picasso was influenced by stylised, non-naturalistic African masks that depict a human figure.

Artists create. Constantly seeking inspiration. They think creatively about random objects. Jobs said creativity is linking things. Creative people feel terrible when asked how they achieved something unique because they didn't do it all. They saw innovation. They had mastered connecting and synthesizing experiences.

Use this in your daily life.

• On your phone, there is a note-taking app. Ideas for what you desire to learn should be written down. It may be learning a new language, calligraphy, or anything else that inspires or intrigues you.

• Note any ideas you have, quotations, or any information that strikes you as important.

• Spend time with smart individuals, that is the most important thing. Jim Rohn, a well-known motivational speaker, has observed that we are the average of the five people with whom we spend the most time.

• Learning alone won't get you very far. You need to put what you've learnt into practice. If you don't use your knowledge and skills, they are useless.

3. Develop the ability to refuse.

Steve Jobs deleted thousands of items when he created Apple's design ethic. Saying no to distractions meant upsetting customers and partners.

John Sculley, the former CEO of Apple, said something like this. According to Sculley, Steve’s methodology differs from others as he always believed that the most critical decisions are things you choose not to do.

Use this in your daily life.

• Never be afraid to say "no," "I won't," or "I don't want to." Keep it simple. This method works well in some situations.

• Give a different option. For instance, X might be interested even if I won't be able to achieve it.

• Control your top priority. Before saying yes to anything, make sure your work schedule and priority list are up to date.

4. Follow your passion

“Follow your passion” is the worst advice people can give you. Steve Jobs didn't start Apple because he suddenly loved computers. He wanted to help others attain their maximum potential.

Great things take a lot of work, so quitting makes sense if you're not passionate. Jobs learned from history that successful people were passionate about their work and persisted through challenges.

Use this in your daily life.

• Stay away from your passion. Allow it to develop daily. Keep working at your 9-5-hour job while carefully gauging your level of desire and endurance. Less risk exists.

• The truth is that if you decide to work on a project by yourself rather than in a group, it will take you years to complete it instead of a week. Instead, network with others who have interests in common.

• Prepare a fallback strategy in case things go wrong.

Success, this small two-syllable word eventually gives your life meaning, a perspective. What is success?  For most, it's achieving their ambitions. However, there's a catch. Successful people aren't always happy.

Furthermore, where do people’s goals and achievements end? It’s a never-ending process. Success is a journey, not a destination. We wish you not to lose your way on this journey.

Ready to quit full-time? No worries.

Baby Boomer retirement has accelerated since COVID-19 began. In 2020, 29 million boomers retire. Over 3 million more than in 2019. 75 million Baby Boomers will retire by 2030.

First, quit your work to enjoy retirement. Leave a professional legacy. Your retirement will start well. It all starts with a retirement letter.

Retirement Letter

Retirement letters are formal resignation letters. Different from other resignation letters, these don't tell your employer you're leaving. Instead, you're quitting.

Since you're not departing over grievances or for a better position or higher income, you may usually terminate the relationship amicably. Consulting opportunities are possible.

Thank your employer for their support and give them transition information.

Resignation letters aren't merely a formality. This method handles wages, insurance, and retirement benefits.

Retirement letters often accompany verbal notices to managers. Schedule a meeting before submitting your retirement letter to discuss your plans. The letter will be stored alongside your start date, salary, and benefits in your employee file.

Retirement is typically well-planned. Employers want 6-12 months' notice.

Summary

• Guidelines for Giving Retirement Notice

• Components of a Successful Retirement Letter

• Template for Retirement Letter

• Ideas for Samples of Retirement Letters

• First Example of Retirement Letter

• Second Example of Retirement Letter

• Third Example of Retirement Letter

• Fourth Example of Retirement Letter

• Fifth Example of Retirement Letter

• Sixth Example of Retirement Letter

• Seventh Example of Retirement Letter

• Eighth Example of Retirement Letter

• Ninth Example of Retirement Letter

• Tenth Example of Retirement Letter

• Frequently Asked Questions

• 1. What is a letter of retirement?

• 2. Why should you include a letter of retirement?

• 3. What information ought to be in your retirement letter?

• 4. Must I provide notice?

• 5. What is the ideal retirement age?

Guidelines for Giving Retirement Notice

While starting a new phase, you're also leaving a job you were qualified for. You have years of experience. So, it may not be easy to fill a retirement-related vacancy.

Talk to your boss in person before sending a letter. Notice is always appreciated. Properly announcing your retirement helps you and your organization transition.

How to announce retirement:

• Learn about the retirement perks and policies offered by the company. The first step in figuring out whether you're eligible for retirement benefits is to research your company's retirement policy.

• Don't depart without providing adequate notice. You should give the business plenty of time to replace you if you want to retire in a few months.

• Help the transition by offering aid. You could be a useful resource if your replacement needs training.

• Contact the appropriate parties. The original copy should go to your boss. Give a copy to HR because they will manage your 401(k), pension, and health insurance.

• Investigate the option of working as a consultant or part-time. If you desire, you can continue doing some limited work for the business.

• Be nice to others. Describe your achievements and appreciation. Additionally, express your gratitude for giving you the chance to work with such excellent coworkers.

• Make a plan for your future move. Simply updating your employer on your goals will help you maintain a good working relationship.

• Use a formal letter or email to formalize your plans. The initial step is to speak with your supervisor and HR in person, but you must also give written notice.

Components of a Successful Retirement Letter

To write a good retirement letter, keep in mind the following:

• A formal salutation. Here, the voice should be deliberate, succinct, and authoritative.

• Be specific about your intentions. The key idea of your retirement letter is resignation. Your decision to depart at this time should be reflected in your letter. Remember that your intention must be clear-cut.

• Your deadline. This information must be in resignation letters. Laws and corporate policies may both stipulate a minimum amount of notice.

• A kind voice. Your retirement letter shouldn't contain any resentments, insults, or other unpleasantness. Your letter should be a model of professionalism and grace. A straightforward thank you is a terrific approach to accomplish that.

• Your ultimate goal. Chaos may start to happen as soon as you turn in your resignation letter. Your position will need to be filled. Additionally, you will have to perform your obligations up until a successor is found. Your availability during the interim period should be stated in your resignation letter.

• Give us a way to reach you. Even if you aren't consulting, your company will probably get in touch with you at some point. They might send you tax documents and details on perks. By giving your contact information, you can make this process easier.

Template for Retirement Letter

Identify

Title you held

Address

Supervisor's name

Supervisor’s position

Company name

HQ address

Date

[SUPERVISOR],

1.

Inform that you're retiring. Include your last day worked.

2.

Employer thanks. Mention what you're thankful for. Describe your accomplishments and successes.

3.

Helping moves things ahead. Plan your retirement. Mention your consultancy interest.

Sincerely,

[Signature]

First and last name

Phone number

Personal Email

Ideas for Samples of Retirement Letters

First Example of Retirement Letter

Martin D. Carey

123 Fleming St

Bloomfield, New Jersey 07003

(555) 555-1234

June 6th, 2022

Willie E. Coyote

President

Acme Co

321 Anvil Ave

Fairfield, New Jersey 07004

Dear Mr. Coyote,

This letter notifies Acme Co. of my retirement on August 31, 2022.

There has been no other organization that has given me that sense of belonging and purpose.

My fifteen years at the helm of the Structural Design Division have given me‌ ‌a‌ ‌strong sense‌ ‌of‌ ‌purpose. I’ve been fortunate to have your support, and I’ll be always grateful for the opportunity you offered me.

I had a difficult time making this decision. ‌As a result of finding a small property in Arizona where we will be able to spend our remaining days together, my wife and I have decided to officially retire.

In spite of my regret at being unable to contribute to the firm we’ve built, I believe it is wise to move on.

My heart will always belong to Acme Co. ‌Thank you for the opportunity and best of luck in the years to come.

Sincerely,

Martin D. Carey

Second Example of Retirement Letter

Gustavo Fring

Los Pollas Hermanos

12000–12100 Coors Rd SW,

Albuquerque, New Mexico 87045

Dear Mr. Fring,

I write this letter to announce my formal retirement from Los Pollas Hermanos as manager, effective October 15.

As an employee at Los Pollas Hermanos, I appreciate all the great opportunities you have given me. ‌It has been a pleasure to work with and learn from my colleagues for the past 10 years, and I am looking forward to my next challenge.

If there is anything I can do to assist during this time, please let me know.

Sincerely,

Linda T. Crespo

Third Example of Retirement Letter

William M. Arviso

4387 Parkview Drive

Tustin, CA 92680

May 2, 2023

Tony Stark

Owner

Stark Industries

200 Industrial Avenue

Long Beach, CA 90803

Dear Tony:

I’m writing to inform you that my final day of work at Stark Industries will be May14, 2023. ‌When that time comes, I intend‌ ‌to‌ ‌retire.

As I embark on this new chapter in my life, I would like to thank you and the entire Stark Industries team for providing me with so many opportunities. ‌You have all been a pleasure to work with and I will miss you all when I retire.

I am glad to assist you with the transition in any way I can to ensure your new hire has a seamless experience. ‌All ongoing projects will be completed until my retirement date, and all key information will be handed over‌ ‌to‌ ‌the‌ ‌team.

Once again, thank you for the opportunity to be part of the Stark Industries team. ‌All the best to you and the team in the days to come.

Please do not hesitate to contact me if you require any additional information. ‌In order to finalize my retirement plans, I’ll meet with HR and can provide any details that may be necessary.

Sincerely,

(Signature)

William M. Arviso

Fourth Example of Retirement Letter

Garcia, Barbara

First Street, 5432

New York City, NY 10001

(1234) (555) 123–1234

1 October 2022

Gunther

Owner

Central Perk

199 Lafayette St.

New York City, NY 10001

Mr. Gunther,

The day has finally arrived. ‌As I never imagined, I will be formally retiring from Central Perk on November 1st, 2022.

Considering how satisfied I am with my current position, this may surprise you. ‌It would be best if I retired now since my health has deteriorated, so I think this is a good time to do so.

There is no doubt that the past‌ ‌two‌ ‌decades‌ ‌have‌ ‌been‌ ‌wonderful. ‌Over the years, I have seen a small coffee shop grow into one of the city’s top‌ ‌destinations.

It will be hard for me to leave this firm without wondering what more success we could have achieved. But I’m confident that you and the rest of the Central Perk team will achieve great things.

My family and I will never forget what you’ve done for us, and I am grateful for the chance you’ve given me. My house is always open to you.

Sincerely Yours

Garcia, Barbara

Fifth Example of Retirement Letter

Pat Williams

618 Spooky Place

Monstropolis, 23221

123–555–0031

pwilliams@email.com

Feb. 16, 2022

Mike Wazowski

Co-CEO

Monters, Inc.

324 Scare Road

Monstropolis

Dear Mr. Wazowski,

As a formal notice of my upcoming retirement, I am submitting this letter. ‌I will be leaving Monters, Inc. on‌ ‌April‌ ‌13.

These past 10 years as a marketing associate have provided me with many opportunities. ‌Since we started our company a decade ago, we have seen the face of harnessing screams change dramatically into harnessing laughter. ‌During my time working with this dynamic marketing team, I learned a lot about customer behavior and marketing strategies. ‌Working closely with some of our long-standing clients, such as Boo, was a particular pleasure.

I would be happy to‌ ‌assist‌ ‌with‌ ‌the‌ ‌transition‌ ‌following‌ ‌my‌ ‌retirement. ‌It would be my pleasure to assist in the hiring or training of‌ ‌my‌ ‌replacement. ‌In order to spend more time with my family, I will also be able to offer part-time consulting services.

After I retire, I plan to cash out the eight unused vacation days I’ve accumulated and take my pension as a lump sum.

Thank you for the opportunity to work with Monters, Inc. ‌In the years to come, I wish you all the best!

Sincerely,

Paul Williams

Sixth Example of Retirement Letter

Dear Micheal,

As In my tenure at Dunder Mifflin Paper Company, I have given everything I had. It has been an honor to work here. But‌ ‌I‌ ‌have‌ ‌decided‌ ‌to‌ ‌move on to new challenges and retire from my position — mainly bears, beets, and Battlestar Galactia.

I appreciate the opportunity to work here and learn so much. During my time at this company, I will always remember the good times and memories we shared. Wishing you all the best in the future.

Sincerely,

Dwight K. Shrute

Your signature

May 16

Seventh Example of Retirement Letter

Greetings, Bill

I am announcing my retirement from Initech, effective March 15, 2023.

Over the course of my career here, I’ve had the privilege of working with so many talented and inspiring people.

In 1999, when I began working as a customer service representative, we were a small organization located in a remote office park.

The fact that we now occupy a floor of the Main Street office building with over 150 employees continues to amaze me.

I am looking forward to spending more time with family and traveling the country in our RV. Although I will be sad to leave.

Please let me know if there are any extra steps I can take to facilitate this transfer.

Sincerely,

Frankin, RenitaEighth Example of Retirement Letter

Height Example of Retirement Letter

Bruce,

Please accept my resignation from Wayne Enterprises as Marketing Communications Director. My last day will be August 1, 2022.

The decision to retire has been made after much deliberation. Now that I have worked in the field for forty years, I believe it is a good time to begin completing my bucket list.

It was not easy for me to decide to leave the company. Having worked at Wayne Enterprises has been rewarding both professionally and personally. There are still a lot of memories associated with my first day as a college intern.

My intention was not to remain with such an innovative company, as you know. I was able to see the big picture with your help, however. Today, we are a force that is recognized both nationally and internationally.

In addition to your guidance, the bold, visionary leadership of our company contributed to the growth of our company.

My departure from the company coincides with a particularly hectic time. Despite my best efforts, I am unable to postpone my exit.

My position would be well served by an internal solution. I have a more than qualified marketing manager in Caroline Crown. It would be a pleasure to speak with you about this.

In case I can be of assistance during the switchover, please let me know. Contact us at (555)555–5555. As part of my responsibilities, I am responsible for making sure all work is completed to Wayne Enterprise’s stringent requirements. Having the opportunity to work with you has been a pleasure. I wish you continued success with your thriving business.

Sincerely,

Cash, Cole

Marketing/Communications

Ninth Example of Retirement Letter

Norman, Jamie

2366 Hanover Street

Whitestone, NY 11357

555–555–5555

jamie.norman@email.com

15 October 2022

Mr. Lippman

Head of Pendant Publishing

600 Madison Ave.

New York, New York

Respected Mr. Lippman,

Please accept my resignation effective‌ ‌November‌ ‌1,‌ ‌2022.

Over the course of my ten years at Pendant Publishing, I’ve had a great deal of fun and I’m quite grateful for all the assistance I’ve received.

It was a pleasure to wake up and go to work every day because of our outstanding corporate culture and the opportunities for promotion and professional advancement available to me.

While‌ ‌I am excited about retiring, I am going to miss being part of our team. ‌It’s my hope that I’ll be able to maintain the friendships I’ve formed here for a long time to come.

In case I can be of assistance prior to or following my departure, please let me know. ‌If I can assist in any way to ensure a smooth transfer to my successor, I would be delighted to do so.

Sincerely,

Signed (hard copy letter)

Norman, Jamie

Tenth Example of Retirement Letter

17 January 2023

Greg S. Jackson

Cyberdyne Systems

18144 El Camino Real,

Sunnyvale, CA

Respected Mrs. Duncan,

I‌ ‌am‌ ‌writing‌ ‌to‌ ‌inform you that I will be resigning from Cyberdyne Systems as of March 1, 2023. I’m grateful to have had this opportunity, and it was a difficult decision to make.

My development as a programmer and as a more seasoned member of the organization has been greatly assisted by your coaching.

I have been proud of Cyberdyne Systems’ ethics and success throughout my 25 years at the company. Starting as a mailroom clerk and currently serving as head programmer.

The portfolios of our clients have always been handled with the greatest care by my colleagues. It is our employees and services that have made Cyberdyne Systems the success it is today.

During my tenure as head of my division, I’ve increased our overall productivity by 800 percent, and I expect that trend to continue after‌ ‌I‌ ‌retire.

In light of the fact that the process of replacing me may take some time, I would like to offer my assistance in any way I can.

The greatest contender for this job is Troy Ledford, my current assistant.

Also, before I leave, I would be willing to teach any partners how to use the programmer I developed to track and manage the development of Skynet.

Over the next few months, I’ll be enjoying vacations with my wife as well as my granddaughter moving‌ ‌to‌ ‌college.

If Cyberdyne Systems has any openings for consultants, please let me know. ‌It has been a pleasure working with you over the last 25 years. I appreciate your concern and care.

Sincerely,

Greg S, Jackson

Questions and Answers

1. What is a letter of retirement?

Retirement letters tell your supervisor you're retiring. This informs your employer that you're departing, like a letter. A resignation letter also requests retirement benefits.

Supervisors frequently receive retirement letters and verbal resignations. Before submitting your retirement letter, meet to discuss your plans. This letter will be filed with your start date, salary, and benefits.

2. Why should you include a letter of retirement?

Your retirement letter should explain why you're leaving. When you quit, your manager and HR department usually know. Regardless, a retirement letter might help you leave on a positive tone. It ensures they have the necessary papers.

In your retirement letter, you tell the firm your plans so they can find your replacement. You may need to stay in touch with your company after sending your retirement letter until a successor is identified.

3. What information ought to be in your retirement letter?

Format it like an official letter. Include your retirement plans and retirement-specific statistics. Date may be most essential.

In some circumstances, benefits depend on when you resign and retire. A date on the letter helps HR or senior management verify when you gave notice and how long.

In addition to your usual salutation, address your letter to your manager or supervisor.

The letter's body should include your retirement date and transition arrangements. Tell them whether you plan to help with the transition or train a new employee. You may have a three-month time limit.

Tell your employer your job title, how long you've worked there, and your biggest successes. Personalize your letter by expressing gratitude for your career and outlining your retirement intentions. Finally, include your contact info.

4. Must I provide notice?

Two-week notice isn't required. Your company may require it. Some state laws contain exceptions.

Check your contract, company handbook, or HR to determine your retirement notice. Resigning may change the policy.

Regardless of your company's policy, notification is standard. Entry-level or junior jobs can be let go so the corporation can replace them.

Middle managers, high-level personnel, and specialists may take months to replace. Two weeks' notice is a courtesy. Start planning months ahead.

You can finish all jobs at that period. Prepare transition documents for coworkers and your replacement.

5. What is the ideal retirement age?

Depends on finances, state, and retirement plan. The average American retires at 62. The average retirement age is 66, according to Gallup's 2021 Economy and Personal Finance Survey.

Remember:

• Before the age of 59 1/2, withdrawals from pre-tax retirement accounts, such as 401(k)s and IRAs, are subject to a penalty.

• Benefits from Social Security can be accessed as early as age 62.

• Medicare isn't available to you till you're 65,

• Depending on the year of your birth, your Full Retirement Age (FRA) will be between 66 and 67 years old.

• If you haven't taken them already, your Social Security benefits increase by 8% annually between ages 6 and 77.

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.

He explained everything.

A drinking buddy confessed. Alexander. He says he works at a startup based on a scam, which appears too clever to be a lie.

Alexander (assuming he developed the story) or the startup's creator must have been a genius.

This is the story of an Internet scam that targets older individuals and generates tens of millions of dollars annually.

The business sells authentic things at 10% of their market value. This firm cannot be lucrative, but the entrepreneur has a plan: monthly subscriptions to a worthless service.

The firm can then charge the customer's credit card to settle the gap. The buyer must subscribe without knowing it. What's their strategy?

How does the con operate?

Imagine a website with a split homepage. On one page, the site offers an attractive goods at a ridiculous price (from 1 euro to 10% of the product's market worth).

Same product, but with a stupid monthly subscription. Business is unsustainable. They buy overpriced products and resell them too cheaply, hoping customers will subscribe to a useless service.

No customer will want this service. So they create another illegal homepage that hides the monthly subscription offer. After an endless scroll, a box says Yes, I want to subscribe to a service that costs x dollars per month.

Unchecking the checkbox bugs. When a customer buys a product on this page, he's enrolled in a monthly subscription. Not everyone should see it because it's illegal. So what does the startup do?

A page that varies based on the sort of website visitor, a possible consumer or someone who might be watching the startup's business

Startup technicians make sure the legal page is displayed when the site is accessed normally. Typing the web address in the browser, using Google, etc. The page crashes when buying a goods, preventing the purchase.

This avoids the startup from selling a product at a loss because the buyer won't subscribe to the worthless service and charge their credit card each month.

The illegal page only appears if a customer clicks on a Google ad, indicating interest in the offer.

Alexander says that a banker, police officer, or anyone else who visits the site (maybe for control) will only see a valid and buggy site as purchases won't be possible.

The latter will go to the site in the regular method (by typing the address in the browser, using Google, etc.) and not via an online ad.

Those who visit from ads are likely already lured by the site's price. They'll be sent to an illegal page that requires a subscription.

Laziness is humanity's secret weapon. The ordinary person ignores tiny monthly credit card charges. The subscription lasts around a year before the customer sees an unexpected deduction.

After-sales service (ASS) is useful in this situation.

After-sales assistance begins when a customer notices slight changes on his credit card, usually a year later.

The customer will search Google for the direct debit reference. How he'll complain to after-sales service.

It's crucial that ASS appears in the top 4/5 Google search results. This site must be clear, and offer chat, phone, etc., he argues.

The pigeon must be comforted after waking up. The customer learns via after-sales service that he subscribed to a service while buying the product, which justifies the debits on his card.

The customer will then clarify that he didn't intend to make the direct debits. The after-sales care professional will pretend to listen to the customer's arguments and complaints, then offer to unsubscribe him for free because his predicament has affected him.

In 99% of cases, the consumer is satisfied since the after-sales support unsubscribed him for free, and he forgets the debited amounts.

The remaining 1% is split between 0.99% who are delighted to be reimbursed and 0.01%. We'll pay until they're done. The customer should be delighted, not object or complain, and keep us beneath the radar (their situation is resolved, the rest, they don’t care).

It works, so we expand our thinking.

Startup has considered industrialization. Since this fraud is working, try another. Automate! So they used a site generator (only for product modifications), underpaid phone operators for after-sales service, and interns for fresh product ideas.

The company employed a data scientist. This has allowed the startup to recognize that specific customer profiles can be re-registered in the database and that it will take X months before they realize they're subscribing to a worthless service. Customers are re-subscribed to another service, then unsubscribed before realizing it.

Alexander took months to realize the deception and leave. Lawyers and others apparently threatened him and former colleagues who tried to talk about it.

The startup would have earned prizes and competed in contests. He adds they can provide evidence to any consumer group, media, police/gendarmerie, or relevant body. When I submitted my information to the FBI, I was told, "We know, we can't do much.", he says.