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.

ERC165 (or EIP-165) is a standard utilized by various open-source smart contracts like Open Zeppelin or Aavegotchi.

What's it? You must implement? Why do we need it? I'll describe the standard and answer any queries.

What is ERC165

ERC165 detects and publishes smart contract interfaces. Meaning? It standardizes how interfaces are recognized, how to detect if they implement ERC165, and how a contract publishes the interfaces it implements. How does it work?

Why use ERC165? Sometimes it's useful to know which interfaces a contract implements, and which version.

Identifying interfaces

An interface function's selector. This verifies an ABI function. XORing all function selectors defines an interface in this standard. The following code demonstrates.

// SPDX-License-Identifier: UNLICENCED
pragma solidity >=0.8.0 <0.9.0;

interface Solidity101 {
    function hello() external pure;
    function world(int) external pure;
}

contract Selector {
    function calculateSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.hello.selector ^ i.world.selector;
        // Returns 0xc6be8b58
    }

    function getHelloSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.hello.selector;
        // Returns 0x19ff1d21
    }

    function getWorldSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.world.selector;
        // Returns 0xdf419679
    }
}

This code isn't necessary to understand function selectors and how an interface's selector can be determined from the functions it implements.

Run that sample in Remix to see how interface function modifications affect contract function output.

Contracts publish their implemented interfaces.

We can identify interfaces. Now we must disclose the interfaces we're implementing. First, import IERC165 like so.

pragma solidity ^0.4.20;

interface ERC165 {
    /// @notice Query if a contract implements an interface
    /// @param interfaceID The interface identifier, as specified in ERC-165
    /// @dev Interface identification is specified in ERC-165. 
    /// @return `true` if the contract implements `interfaceID` and
    ///  `interfaceID` is not 0xffffffff, `false` otherwise
    function supportsInterface(bytes4 interfaceID) external view returns (bool);
}

We still need to build this interface in our smart contract. ERC721 from OpenZeppelin is a good example.

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/ERC721.sol)

pragma solidity ^0.8.0;

import "./IERC721.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/introspection/ERC165.sol";
// ...

contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
  // ...

  function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
    return
      interfaceId == type(IERC721).interfaceId ||
      interfaceId == type(IERC721Metadata).interfaceId ||
      super.supportsInterface(interfaceId);
  }
  
  // ...
}

I deleted unnecessary code. The smart contract imports ERC165, IERC721 and IERC721Metadata. The is keyword at smart contract declaration implements all three.

Kind (interface).

Note that type(interface).interfaceId returns the same as the interface selector.

We override supportsInterface in the smart contract to return a boolean that checks if interfaceId is the same as one of the implemented contracts.

Super.supportsInterface() calls ERC165 code. Checks if interfaceId is IERC165.

function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
    return interfaceId == type(IERC165).interfaceId;
}

So, if we run supportsInterface with an interfaceId, our contract function returns true if it's implemented and false otherwise. True for IERC721, IERC721Metadata, andIERC165.

Conclusion

I hope this post has helped you understand and use ERC165 and why it's employed.

Have a great day, thanks for reading!

Here's me. Perfectionism is unnecessary.

This post isn't for people who gag at the prospect of eating french fries. I've been ridiculed for stating you can lose weight eating carbs and six-pack abs aren't good.

My family eats frozen processed meals and quick food most weeks (sometimes more). Clean eaters may think I'm unqualified to give fitness advice. I get it.

Hear me out, though. I’m a 44-year-old raising two busy kids with a weekly-traveling husband. Tutoring, dance, and guitar classes fill weeknights. I'm also juggling my job and freelancing.

I'm as worried and tired as my clients. I wish I ate only kale smoothies and salads. I can’t. Despite my mistakes, I'm fit. I won't promise you something just because it worked for me. But here’s a look at how I manage.

What I largely get right about eating

I have a flexible diet and track my daily intake. I count protein, fat, and carbs. Only on vacation or exceptional occasions do I not track.

My protein goal is 1 g per lb. I consume a lot of chicken breasts, eggs, turkey, and lean ground beef. I also occasionally drink protein shakes.

I eat 220–240 grams of carbs daily. My carb count depends on training volume and goals. I'm trying to lose weight slowly. If I want to lose weight faster, I cut carbs to 150-180.

My carbs include white rice, Daves Killer Bread, fruit, pasta, and veggies. I don't eat enough vegetables, so I take Athletic Greens. Also, V8.

Fat grams over 50 help me control my hormones. Recently, I've reached 70-80 grams. Cooking with olive oil. I eat daily dark chocolate. Eggs, butter, milk, and cheese contribute to the rest.

Those frozen meals? What can I say? Stouffer’s lasagna is sometimes needed. I order the healthiest fast food I can find (although I can never bring myself to order the salad). That's a chicken sandwich or a kid's hamburger. I rarely order fries. I eat slowly and savor each bite to feel full.

Potato chips and sugary cereals are in the pantry, but I'm not tempted. My kids eat them because I'd rather teach them moderation than total avoidance. If I eat them, I only eat one portion.

If you're not hungry and eating enough protein and fat, you won't want to eat everything in sight.

I drink once or twice a week. As a result, I rarely overdo it.

Food tracking is tedious and frustrating for many. Taking breaks and using estimates when eating out help. Not perfect, but realistic.

I practice a prolonged fast to enhance metabolic adaptability

Metabolic flexibility is the ability to switch between fuel sources (fat and carbs) based on activity intensity and time since eating. At rest or during low to moderate exertion, your body burns fat. Your body burns carbs after eating and during intense exercise.

Our metabolic flexibility can be hampered by lack of exercise, overeating, and stress. Our bodies become lousy fat burners, making weight loss difficult.

Once a week, I skip dinner (usually around 24 hours). Long-term fasting teaches my body to burn fat. It provides me one low-calorie day a week (I break the fast with a normal-sized dinner).

Fasting day helps me maintain my weight on weekends, when I typically overeat and drink.

Try an extended fast slowly. Delay breakfast by two hours. Next week, add two hours, etc. It takes practice to go that long without biting off your arm. I also suggest consulting your doctor.

I stay active.

I've always been active. As a child, I danced many nights a week, was on the high school dance team, and ran marathons in my 20s.

Often, I feel driven by an internal engine. Working from home makes it easy to exercise. If that’s not you, I get it. Everyone can benefit from raising their baseline.

After taking the kids to school, I walk two miles around the neighborhood. When I need to think, I switch off podcasts. First thing in the morning, I go for a walk.

I lift weights Monday, Wednesday, and Friday. 45 minutes is typical. I run 45-90 minutes on Tuesday and Thursday. I'm slow but reliable. On Saturdays and Sundays, I walk and add a short spin class if I'm not too tired.

I almost never forgo sleep.

I rarely stay up past 10 p.m., much to my night-owl husband's dismay. My 7-8-hour nights help me recover from workouts and handle stress. Without it, I'm grumpy.

I suppose sleep duration matters more than bedtime. Some people just can't fall asleep early. Internal clock and genetics determine sleep and wake hours.

Prioritize sleep.

Last thoughts

Fitness and diet advice is often useless. Some of the advice is inaccurate, dangerous, or difficult to follow if you have a life. I want to throw a shoe at my screen when I see headlines promising to speed up my metabolism or help me lose fat.

I studied exercise physiology for years. No shortcuts exist. No medications or cleanses reset metabolism. I play the hand I'm dealt. I realize that just because something works for me, it won't for you.

If I wanted 15% body fat and ripped abs, I'd have to be stricter. I occasionally think I’d like to get there. But then I remember I’m happy with my life. I like fast food and beer. Pizza and margaritas are favorites (not every day).

You can get it mostly right and live a healthy life.

Reddit's NFT market is alive and well.

NFT owners outnumber OpenSea on Reddit.

Reddit NFTs flip in OpenSea in days:

Fast-selling.

NFT sales will make Reddit's current communities more engaged.

I don't think NFTs will affect existing groups, but they will build hype for people to acquire them.

The first season of Collectibles is unique, but many missed the first season.

Second-season NFTs are less likely to be sold for a higher price than first-season ones.

If you use Reddit, it's fun to own NFTs.

You do not want to miss these

Stop! Stop it! Two things to avoid when starting a YouTube channel. Critical. Possible channel-killers Its future revenue.

I'll tell you now, so don't say "I wish I knew."

The Notorious Copyright Allegation

My YouTube channel received a copyright claim before I sold it. This claim was on a one-minute video I thought I'd changed enough to make mine, but the original owner disagreed.

It cost me thousands in ad revenue. Original owner got the profits.

Well, it wasn't your video, you say.

Touché.

I've learned. Sorta

I couldn't stop looking at the video's views. The video got 1,000,000 views without any revenue. I made 4 more similar videos.

If they didn't get copyrighted, I'd be rolling in dough.

You've spent a week editing and are uploading to YouTube. You're thrilled as you stand and stretch your back. You see the video just before publishing.

No way!

The red exclamation point on checks.

Copyright claim!

YouTube lets you publish, but you won't make money.

Sounds fair? Well, it is.

Copyright claims mean you stole someone's work. Song, image, or video clip.

We wouldn't want our content used for money.

The only problem with this is that almost everything belongs to someone else. I doubt some of the biggest creators are sitting down and making their music for their videos. That just seems really excessive when you could make a quick search on YouTube and download a song (I definitely don’t do this because that would be stealing).

So how do you defeat a copyright defense?

Even copyright-free songs on YouTube aren't guaranteed. Some copyrighted songs claim to be free.

Use YouTube's free music library or pay for a subscription to adobe stock, epidemic sound, or artlist.io.

Most of my videos have Nintendo music. Almost all game soundtracks are copyright-free and offer a variety of songs.

Restriction on age

Age restrictions are a must-avoid. A channel dies.

YouTube never suggests age-restricted videos.

Shadow banning means YouTube hides your content from subscribers and non-subscribers.

Keeping your channel family-friendly can help.

I hear you complaining that your channel isn't for kids. I agree. Not everyone has a clean mouth or creates content for minors.

YouTube has changed rapidly in recent years. Focusing on kids. Fewer big creators are using profanity or explicit content in videos. Not YouTube-worthy.

Youtube wants to be family-friendly. A family-friendly movie. It won't promote illegal content. Yes, it allows profanity.

Do I recommend avoiding no-no words in videos? Never. Okay. YouTube's policies are shaky. YouTube uses video content to determine ad suitability.

No joke. If you're serious about becoming a content creator, avoid profanity and inappropriate topics.

If your channel covers 18+ topics, like crime or commentary, censor as much as possible.

YouTube can be like walking on eggshells. You never know what is gonna upset the boss. So play it safe and try to avoid getting on their bad side.

Mr. Beast, Dream, Markplier, Faze Rug, and PewDewPie are popular creators. They maintain it family-friendly while entertaining fans.

You got this.