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.

Hiring is difficult, but you shouldn't compromise on team members. Or it may suggest you need to look beyond years in a similar role/function.

Every hire should be someone we'd want as one of our first ten employees.

If you hire such people, your team will adapt, initiate, and problem-solve, and your company will grow. You'll stay nimble even as you scale, and you'll learn from your colleagues.

If you only hire for a specific role or someone who can execute the job, you'll become a cluster of optimizers, and talent will depart for a more fascinating company. A startup is continually changing, therefore you want individuals that embrace it.

As a leader, establishing ideal conditions for talent and having a real ideology should be high on your agenda. You can't eliminate attrition, nor would you want to, but you can hire people who will become your company's leaders.

In my last four jobs I was employee 2, 5, 3, and 5. So while this is all a bit self serving, you’re the one reading my writing — and I have some experience with who works out in the first ten!

First, we'll examine what they do well (and why they're beneficial for startups), then what they don't, and how to hire them.

First 10 are:

• Business partners: Because it's their company, they take care of whatever has to be done and have ideas about how to do it. You can rely on them to always put the success of the firm first because it is their top priority (company success is strongly connected with success for early workers). This approach will eventually take someone to leadership positions.
  

• High Speed Learners: They process knowledge quickly and can reach 80%+ competency in a new subject matter rather quickly. A growing business that is successful tries new things frequently. We have all lost a lot of money and time on employees who follow the wrong playbook or who wait for someone else within the company to take care of them.
  

• Autodidacts learn by trial and error, osmosis, networking with others, applying first principles, and reading voraciously (articles, newsletters, books, and even social media). Although teaching is wonderful, you won't have time.
  

• Self-scaling: They figure out a means to deal with issues and avoid doing the grunt labor over the long haul, increasing their leverage. Great people don't keep doing the same thing forever; as they expand, they use automation and delegation to fill in their lower branches. This is a crucial one; even though you'll still adore them, you'll have to manage their scope or help them learn how to scale on their own.
  

• Free Range: You can direct them toward objectives rather than specific chores. Check-ins can be used to keep them generally on course without stifling invention instead of giving them precise instructions because doing so will obscure their light.
  

• When people are inspired, they bring their own ideas about what a firm can be and become animated during discussions about how to get there.
  

• Novelty Seeking: They look for business and personal growth chances. Give them fresh assignments and new directions to follow around once every three months.

Here’s what the First Ten types may not be:

• Domain specialists. When you look at their resumes, you'll almost certainly think they're unqualified. Fortunately, a few strategically positioned experts may empower a number of First Ten types by serving on a leadership team or in advising capacities.
  

• Balanced. These people become very invested, and they may be vulnerable to many types of stress. You may need to assist them in managing their own stress and coaching them through obstacles. If you are reading this and work at Banza, I apologize for not doing a better job of supporting this. I need to be better at it.
  

• Able to handle micromanagement with ease. People who like to be in charge will suppress these people. Good decision-making should be delegated to competent individuals. Generally speaking, if you wish to scale.

Great startup team members have versatility, learning, innovation, and energy. When we hire for the function, not the person, we become dull and staid. Could this person go to another department if needed? Could they expand two levels in a few years?

First Ten qualities and experience level may have a weak inverse association. People with 20+ years of experience who had worked at larger organizations wanted to try something new and had a growth mentality. College graduates may want to be told what to do and how to accomplish it so they can stay in their lane and do what their management asks.

Does the First Ten archetype sound right for your org? Cool, let’s go hiring. How will you know when you’ve found one?

• They exhibit adaptive excellence, excelling at a variety of unrelated tasks. It could be hobbies or professional talents. This suggests that they will succeed in the next several endeavors they pursue.
  

• Successful risk-taking is doing something that wasn't certain to succeed, sometimes more than once, and making it do so. It's an attitude.
  

• Rapid Rise: They regularly change roles and get promoted. However, they don't leave companies when the going gets tough. Look for promotions at every stop and at least one position with three or more years of experience.

You can ask them:

• Tell me about a time when you started from scratch or achieved success. What occurred en route? You might request a variety of tales from various occupations or even aspects of life. They ought to be energized by this.
  

• What new skills have you just acquired? It is not required to be work-related. They must be able to describe it and unintentionally become enthusiastic about it.
  

• Tell me about a moment when you encountered a challenge and had to alter your strategy. The core of a startup is reinventing itself when faced with obstacles.
  

• Tell me about a moment when you eliminated yourself from a position at work. They've demonstrated they can permanently solve one issue and develop into a new one, as stated above.
  

• Why do you want to leave X position or Y duty? These people ought to be moving forward, not backward, all the time. Instead, they will discuss what they are looking forward to visiting your location.
  

• Any questions? Due to their inherent curiosity and desire to learn new things, they should practically never run out of questions. You can really tell if they are sufficiently curious at this point.

People who see their success as being the same as the success of the organization are the best-case team members, in any market. They’ll grow and change with the company, and always try to prioritize what matters. You’ll find yourself more energized by your work because you’re surrounded by others who are as well. Happy teambuilding!

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.