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!

Traditional sales organizations used the concept of a sales “funnel” to describe the process through which potential customers move, ending up with sales at the end. Winners today have abandoned that way of thinking in favor of building flywheels — business models in which every element reinforces every other.

Ah, the marketing funnel…

Prospective clients go through a predictable set of experiences, students learn in business school marketing classes. It looks like this:

Understanding the funnel helps evaluate sales success indicators. Gail Goodwin, former CEO of small business direct mail provider Constant Contact, said managing the pipeline was key to escaping the sluggish SaaS ramp of death.

Like the funnel concept. To predict how well your business will do, measure how many potential clients are aware of it (awareness) and how many take the next step. If 1,000 people heard about your offering and 10% showed interest, you'd have 100 at that point. If 50% of these people made buyer-like noises, you'd know how many were, etc. It helped model buying trends.

TV, magazine, and radio advertising are pricey for B2C enterprises. Traditional B2B marketing involved armies of sales reps, which was expensive and a barrier to entry.

Cracks in the funnel model

Digital has exposed the funnel's limitations. Hubspot was born at a time when buyers and sellers had huge knowledge asymmetries, according to co-founder Brian Halligan. Those selling a product could use the buyer's lack of information to become a trusted partner.

As the world went digital, getting information and comparing offerings became faster, easier, and cheaper. Buyers didn't need a seller to move through a funnel. Interactions replaced transactions, and the relationship didn't end with a sale.

Instead, buyers and sellers interacted in a constant flow. In many modern models, the sale is midway through the process (particularly true with subscription and software-as-a-service models). Example:

You're creating a winding journey with many touch points, not a funnel (and lots of opportunities for customers to get lost).

From winding journey to flywheel

Beyond this revised view of an interactive customer journey, a company can create what Jim Collins famously called a flywheel. Imagine rolling a heavy disc on its axis. The first few times you roll it, you put in a lot of effort for a small response. The same effort yields faster turns as it gains speed. Over time, the flywheel gains momentum and turns without your help.

Modern digital organizations have created flywheel business models, in which any additional force multiplies throughout the business. The flywheel becomes a force multiplier, according to Collins.

Amazon is a famous flywheel example. Collins explained the concept to Amazon CEO Jeff Bezos at a corporate retreat in 2001. In The Everything Store, Brad Stone describes in his book The Everything Store how he immediately understood Amazon's levers.

The result (drawn on a napkin):

Low prices and a large selection of products attracted customers, while a focus on customer service kept them coming back, increasing traffic. Third-party sellers then increased selection. Low-cost structure supports low-price commitment. It's brilliant! Every wheel turn creates acceleration.

Where from here?

Flywheel over sales funnel! Consider these business terms.

The holy grail of plain text task management is finally within reach

Plain text task management? Are you serious?? Dedicated task managers exist for a reason, you know. Sheesh.

—Oh, I know. Believe me, I know! But hear me out.

I've managed projects and tasks in plain text for more than four years. Since reorganizing my to-do list, plain text task management is within reach.

Data completely yours? One billion percent. Beef it up with coding? Be my guest.

Enter: The List

The answer? A list. That’s it!

Write down tasks. Obsidian, Notenik, Drafts, or iA Writer are good plain text note-taking apps.

List too long? Of course, it is! A large list tells you what to do. Feel the itch and friction. Then fix it.

• But I want to be able to distinguish between work and personal life! List two things.

• However, I need to know what should be completed first. Put those items at the top.

• However, some things keep coming up, and I need to be reminded of them! Put those in your calendar and make an alarm for them.

• But since individual X hasn't completed task Y, I can't proceed with this. Create a Waiting section on your list by dividing it.

• But I must know what I'm supposed to be doing right now! Read your list(s). Check your calendar. Think critically.

Before I begin a new one, I remind myself that "Listory Never Repeats."

There’s no such thing as too many lists if all are needed. There is such a thing as too many lists if you make them before they’re needed. Before they complain that their previous room was small or too crowded or needed a new light.

A list that feels too long has a voice; it’s telling you what to do next.

I use one Master List. It's a control panel that tells me what to focus on short-term. If something doesn't need semi-immediate attention, it goes on my Backlog list.

Todd Lewandowski's DWTS (Done, Waiting, Top 3, Soon) performance deserves praise. His DWTS to-do list structure has transformed my plain-text task management. I didn't realize it was upside down.

This is my take on it:

D = Done

Move finished items here. If they pile up, clear them out every week or month. I have a Done Archive folder.

W = Waiting

Things seething in the background, awaiting action. Stir them occasionally so they don't burn.

T = Top 3

Three priorities. Personal comes first, then work. There will always be a top 3 (no more than 5) in every category. Projects, not chores, usually.

S = Soon

This part is action-oriented. It's for anything you can accomplish to finish one of the Top 3. This collection includes thoughts and project lists. The sole requirement is that they should be short-term goals.

Some of you have probably concluded this isn't for you. Please read Todd's piece before throwing out the baby. Often. You shouldn't miss a newborn.

As much as Dancing With The Stars helps me recall this method, I may try switching their order. TSWD; Drilling Tunnel Seismic? Serenity After Task?

Master List Showcase

My Master List lives alone in its own file, but sometimes appears in other places.  It's included in my Weekly List template. Here's a (soon-to-be-updated) demo vault of my Obsidian planning setup to download for free.

Here's the code behind my weekly screenshot:

## [[Master List - 2022|✓]]  TO DO

![[Master List - 2022]]

FYI, I use the Minimal Theme in Obsidian, with a few tweaks.

You may note I'm utilizing a checkmark as a link. For me, that's easier than locating the proper spot to click on the embed.

Blue headings for Done and Waiting are links. Done links to the Done Archive page and Waiting to a general waiting page.

Read my full article here.