More retail traders means faster, more sophisticated, and more successful methods.

Tech specifications

Only requires a laptop and an internet connection.

We'll use OpenBB's research platform for data/analysis.

Pricing and execution on Options-Quant

Background

You don't need to know the arithmetic details to use this method.

Black-Scholes is a popular option pricing model. It's best for pricing European options. European options are only exercisable at expiration, unlike American options. American options are always exercisable.

American options carry a premium to cover for the risk of early exercise. The Black-Scholes model doesn't account for this premium, hence it can't price genuine, traded American options.

Barone-Adesi-Whaley (BAW) model. BAW modifies Black-Scholes. It accounts for exercise risk premium and stock dividends. It adds the option's early exercise value to the Black-Scholes value.

The trader need not know the formulaic derivations of this model.

https://ir.nctu.edu.tw/bitstream/11536/14182/1/000264318900005.pdf

Strategy

This strategy targets implied volatility. First, we'll locate liquid options that expire within 30 days and have minimal implied volatility.

After selecting the option that meets the requirements, we price it to get the BAW implied volatility (we choose BAW because it's a more accurate Black-Scholes model). If estimated implied volatility is larger than market volatility, we'll capture the spread.

(Calculated IV — Market IV) = (Profit)

Some approaches to target implied volatility are pricey and inaccessible to individual investors. The best and most cost-effective alternative is to acquire a straddle and delta hedge. This may sound terrifying and pricey, but as shown below, it's much less so.

The Trade

First, we want to find our ideal option, so we use OpenBB terminal to screen for options that:

• Have an IV at least 5% lower than the 20-day historical IV

• Are no more than 5% out-of-the-money

• Expire in less than 30 days

We query:

stocks/options/screen/set low_IV/scr --export Output.csv

This uses the screener function to screen for options that satisfy the above criteria, which we specify in the low IV preset (more on custom presets here). It then saves the matching results to a csv(Excel) file for viewing and analysis.

Stick to liquid names like SPY, AAPL, and QQQ since getting out of a position is just as crucial as getting in. Smaller, illiquid names have higher inefficiencies, which could restrict total profits.

We calculate IV using the BAWbisection model (the bisection is a method of calculating IV, more can be found here.) We price the IV first.

According to the BAW model, implied volatility at this level should be priced at 26.90%. When re-pricing the put, IV is 24.34%, up 3%.

Now it's evident. We must purchase the straddle (long the call and long the put) assuming the computed implied volatility is more appropriate and efficient than the market's. We just want to speculate on volatility, not price fluctuations, thus we delta hedge.

The Fun Starts

We buy both options for $7.65. (x100 multiplier). Initial delta is 2. For every dollar the stock price swings up or down, our position value moves $2.

We want delta to be 0 to avoid price vulnerability. A delta of 0 suggests our position's value won't change from underlying price changes. Being delta-hedged allows us to profit/lose from implied volatility. Shorting 2 shares makes us delta-neutral.

That's delta hedging. (Share price * shares traded) = $330.7 to become delta-neutral. You may have noted that delta is not truly 0.00. This is common since delta-hedging means getting as near to 0 as feasible, since it is rare for deltas to align at 0.00.

Now we're vulnerable to changes in Vega (and Gamma, but given we're dynamically hedging, it's not a big risk), or implied volatility. We wanted to gamble that the position's IV would climb by at least 2%, so we'll maintain it delta-hedged and watch IV.

Because the underlying moves continually, the option's delta moves continuously. A trader can short/long 5 AAPL shares at most. Paper trading lets you practice delta-hedging. Being quick-footed will help with this tactic.

Profit-Closing

As expected, implied volatility rose. By 10 minutes before market closure, the call's implied vol rose to 27% and the put's to 24%. This allowed us to sell the call for $4.95 and the put for $4.35, creating a profit of $165.

You may pull historical data to see how this trade performed. Note the implied volatility and pricing in the final options chain for August 5, 2022 (the position date).

Final Thoughts

Congratulations, that was a doozy. To reiterate, we identified tickers prone to increased implied volatility by screening OpenBB's low IV setting. We double-checked the IV by plugging the price into Options-BAW Quant's model. When volatility was off, we bought a straddle and delta-hedged it. Finally, implied volatility returned to a normal level, and we profited on the spread.

The retail trading space is very quickly catching up to that of institutions.  Commissions and fees used to kill this method, but now they cost less than $5. Watching momentum, technical analysis, and now quantitative strategies evolve is intriguing.

I'm not linked with these sites and receive no financial benefit from my writing.

Tell me how your experience goes and how I helped; I love success tales.

Three options exist. The third one is the quickest and most fruitful.

You've mastered crypto trading and want to become a broker.

So you may wonder: Where to begin?

If so, keep reading.

Today I'll compare three different approaches to becoming a cryptocurrency trader.

What are cryptocurrency brokers, and how do they vary from stockbrokers?

A stockbroker implements clients' market orders (retail or institutional ones).

Brokerage firms are regulated, insured, and subject to regulatory monitoring.

Stockbrokers are required between buyers and sellers. They can't trade without a broker. To trade, a trader must open a broker account and deposit money. When a trader shops, he tells his broker what orders to place.

Crypto brokerage is trade intermediation with cryptocurrency.

In crypto trading, however, brokers are optional.

Crypto exchanges offer direct transactions. Open an exchange account (no broker needed) and make a deposit.

Question:

Since crypto allows DIY trading, why use a broker?

Let's compare cryptocurrency exchanges vs. brokers.

Broker versus cryptocurrency exchange

Most existing crypto exchanges are basically brokers.

Examine their primary services:

• connecting purchasers and suppliers

• having custody of clients' money (with the exception of decentralized cryptocurrency exchanges),

• clearance of transactions.

Brokerage is comparable, don't you think?

There are exceptions. I mean a few large crypto exchanges that follow the stock exchange paradigm. They outsource brokerage, custody, and clearing operations. Classic exchange setups are rare in today's bitcoin industry.

Back to our favorite “standard” crypto exchanges. All-in-one exchanges and brokers. And usually, they operate under a broker or a broker-dealer license, save for the exchanges registered somewhere in a free-trade offshore paradise. Those don’t bother with any licensing.

What’s the sense of having two brokers at a time?

Better liquidity and trading convenience.

The crypto business is compartmentalized.

We have CEXs, DEXs, hybrid exchanges, and semi-exchanges (those that aggregate liquidity but do not execute orders on their sides). All have unique regulations and act as sovereign states.

There are about 18k coins and hundreds of blockchain protocols, most of which are heterogeneous (i.e., different in design and not interoperable).

A trader must register many accounts on different exchanges, deposit funds, and manage them all concurrently to access global crypto liquidity.

It’s extremely inconvenient.

Crypto liquidity fragmentation is the largest obstacle and bottleneck blocking crypto from mass adoption.

Crypto brokers help clients solve this challenge by providing one-gate access to deep and diverse crypto liquidity from numerous exchanges and suppliers. Professionals and institutions need it.

Another killer feature of a brokerage may be allowing clients to trade crypto with fiat funds exclusively, without fiat/crypto conversion. It is essential for professional and institutional traders.

Who may work as a cryptocurrency broker?

Apparently, not anyone. Brokerage requires high-powered specialists because it involves other people's money.

Here's the essentials:

• excellent knowledge, skills, and years of trading experience

• high-quality, quick, and secure infrastructure

• highly developed team

• outstanding trading capital

• High-ROI network: long-standing, trustworthy connections with customers, exchanges, liquidity providers, payment gates, and similar entities

• outstanding marketing and commercial development skills.

What about a license for a cryptocurrency broker? Is it necessary?

Complex question.

If you plan to play in white-glove jurisdictions, you may need a license. For example, in the US, as a “money transmitter” or as a CASSP (crypto asset secondary services provider) in Australia.

Even in these jurisdictions, there are no clear, holistic crypto brokerage and licensing policies.

Your lawyer will help you decide if your crypto brokerage needs a license.

Getting a license isn't quick. Two years of patience are needed.

How can you turn into a cryptocurrency broker?

Finally, we got there! 🎉

Three actionable ways exist:

1. To kickstart a regulated stand-alone crypto broker

2. To get a crypto broker franchise, and

3. To become a liquidity network broker.

Let's examine each.

1. Opening a regulated cryptocurrency broker

It's difficult. Especially If you're targeting first-world users.

You must comply with many regulatory, technical, financial, HR, and reporting obligations to keep your organization running. Some are mentioned above.

The licensing process depends on the products you want to offer (spots or derivatives) and the geographic areas you plan to service. There are no general rules for that.

In an overgeneralized way, here are the boxes you will have to check:

• capital availability (usually a large amount of capital c is required)

• You will have to move some of your team members to the nation providing the license in order to establish an office presence there.

• the core team with the necessary professional training (especially applies to CEO, Head of Trading, Assistant to Head of Trading, etc.)

• insurance

• infrastructure that is trustworthy and secure

• adopted proper AML/KYC/financial monitoring policies, etc.

Assuming you passed, what's next?

I bet it won’t be mind-blowing for you that the license is just a part of the deal. It won't attract clients or revenue.

To bring in high-dollar clientele, you must be a killer marketer and seller. It's not easy to convince people to give you money.

You'll need to be a great business developer to form successful, long-term agreements with exchanges (ideally for no fees), liquidity providers, banks, payment gates, etc. Persuade clients.

It's a tough job, isn't it?

I expect a Quora-type question here:

Can I start an unlicensed crypto broker?

Well, there is always a workaround with crypto!

You can register your broker in a free-trade zone like Seychelles to avoid US and other markets with strong watchdogs.

This is neither wise nor sustainable.

First, such experiments are illegal.

Second, you'll have trouble attracting clients and strategic partners.

A license equals trust. That’s it.

Even a pseudo-license from Mauritius matters.

Here are this method's benefits and downsides.

Cons first.

• As you navigate this difficult and expensive legal process, you run the risk of missing out on business prospects. It's quite simple to become excellent compliance yet unable to work. Because your competitors are already courting potential customers while you are focusing all of your effort on paperwork.

• Only God knows how long it will take you to pass the break-even point when everything with the license has been completed.

• It is a money-burning business, especially in the beginning when the majority of your expenses will go toward marketing, sales, and maintaining license requirements. Make sure you have the fortitude and resources necessary to face such a difficult challenge.

Pros

• It may eventually develop into a tool for making money. Because big guys who are professionals at trading require a white-glove regulated brokerage. You have every possibility if you work hard in the areas of sales, marketing, business development, and wealth. Simply put, everything must align.

Launching a regulated crypto broker is analogous to launching a crypto exchange. It's ROUGH. Sure you can take it?

2. Franchise for Crypto Broker (Crypto Sub-Brokerage)

A broker franchise is easier and faster than becoming a regulated crypto broker. Not a traditional brokerage.

A broker franchisee, often termed a sub-broker, joins with a broker (a franchisor) to bring them new clients. Sub-brokers market a broker's products and services to clients.

Sub-brokers are the middlemen between a broker and an investor.

Why is sub-brokering easier?

• less demanding qualifications and legal complexity. All you need to do is keep a few certificates on hand (each time depends on the jurisdiction).

• No significant investment is required

• there is no demand that you be a trading member of an exchange, etc.

As a sub-broker, you can do identical duties without as many rights and certifications.

What about the crypto broker franchise?

Sub-brokers aren't common in crypto.

In most existing examples (PayBito, PCEX, etc.), franchises are offered by crypto exchanges, not brokers. Though we remember that crypto exchanges are, in fact, brokers, do we?

Similarly:

• For a commission, a franchiser crypto broker receives new leads from a crypto sub-broker.

See above for why enrolling is easy.

Finding clients is difficult. Most crypto traders prefer to buy-sell on their own or through brokers over sub-broker franchises.

3. Broker of the Crypto Trading Network (or a Network Broker)

It's the greatest approach to execute crypto brokerage, based on effort/return.

Network broker isn't an established word. I wrote it for clarity.

Remember how we called crypto liquidity fragmentation the current crypto finance paradigm's main bottleneck?

Where there's a challenge, there's progress.

Several well-funded projects are aiming to fix crypto liquidity fragmentation. Instead of launching another crypto exchange with siloed trading, the greatest minds create trading networks that aggregate crypto liquidity from desynchronized sources and enable quick, safe, and affordable cross-blockchain transactions. Each project offers a distinct option for users.

Crypto liquidity implies:

• One-account access to cryptocurrency liquidity pooled from network participants' exchanges and other liquidity sources

• compiled price feeds

• Cross-chain transactions that are quick and inexpensive, even for HFTs

• link between participants of all kinds, and

• interoperability among diverse blockchains

Fast, diversified, and cheap global crypto trading from one account.

How does a trading network help cryptocurrency brokers?

I’ll explain it, taking Yellow Network as an example.

Yellow provides decentralized Layer-3 peer-to-peer trading.

• trade across chains globally with real-time settlement and

• Between cryptocurrency exchanges, brokers, trading companies, and other sorts of network members, there is communication and the exchange of financial information.

Have you ever heard about ECN (electronic communication network)? If not, it's an automated system that automatically matches buy and sell orders. Yellow is a decentralized digital asset ECN.

Brokers can:

• Start trading right now without having to meet stringent requirements; all you need to do is integrate with Yellow Protocol and successfully complete some KYC verification.

• Access global aggregated crypto liquidity through a single point.

• B2B (Broker to Broker) liquidity channels that provide peer liquidity from other brokers. Orders from the other broker will appear in the order book of a broker who is peering with another broker on the market. It will enable a broker to broaden his offer and raise the total amount of liquidity that is available to his clients.

• Select a custodian or use non-custodial practices.

Comparing network crypto brokerage to other types:

• A licensed stand-alone brokerage business is much more difficult and time-consuming to launch than network brokerage, and

• Network brokerage, in contrast to crypto sub-brokerage, is scalable, independent, and offers limitless possibilities for revenue generation.

Yellow Network Whitepaper. has more details on how to start a brokerage business and what rewards you'll obtain.

Final thoughts

There are three ways to become a cryptocurrency broker, including the non-conventional liquidity network brokerage. The last option appears time/cost-effective.

Crypto brokerage isn't crowded yet. Act quickly to find your right place in this market.

Choose the way that works for you best and see you in crypto trading.

Discover Web3 & DeFi with Yellow Network!

Yellow, powered by Openware, is developing a cross-chain P2P liquidity aggregator to unite the crypto sector and provide global remittance services that aid people.

Join the Yellow Community and plunge into this decade's biggest product-oriented crypto project.

• Observe Yellow Twitter

• Enroll in Yellow Telegram

• Visit Yellow Discord.

• On Hacker Noon, look us up.

Yellow Network will expose development, technology, developer tools, crypto brokerage nodes software, and community liquidity mining.

I've been pondering product strategy and how to articulate it. Frameworks helped guide our thinking.

If your teams aren't working together or there's no clear path to victory, your product strategy may not be well-articulated or communicated (if you have one).

Before diving into a product strategy's details, it's important to understand its role in the bigger picture — the pieces that move your organization forward.

the overall picture

A product strategy is crucial, in my opinion. It's part of a successful product or business. It's the showpiece.

To simplify, we'll discuss four main components:

1. Vision

2. Product Management

3. Goals

4. Roadmap

Vision

Your company's mission? Your company/product in 35 years? Which headlines?

The vision defines everything your organization will do in the long term. It shows how your company impacted the world. It's your organization's rallying cry.

An ambitious but realistic vision is needed.

Without a clear vision, your product strategy may be inconsistent.

Product Management

Our main subject. Product strategy connects everything. It fulfills the vision.

In Part 2, we'll discuss product strategy.

Goals

This component can be goals, objectives, key results, targets, milestones, or whatever goal-tracking framework works best for your organization.

These product strategy metrics will help your team prioritize strategies and roadmaps.

Your company's goals should be unified. This fuels success.

Roadmap

The roadmap is your product strategy's timeline. It provides a prioritized view of your team's upcoming deliverables.

A roadmap is time-bound and includes measurable goals for your company. Your team's steps and capabilities for executing product strategy.

If your team has trouble prioritizing or defining a roadmap, your product strategy or vision is likely unclear.

Formulation of a Product Strategy

Now that we've discussed where your product strategy fits in the big picture, let's look at a framework.

A product strategy should include challenges, an approach, and actions.

Challenges

First, analyze the problems/situations you're solving. It can be customer- or company-focused.

The analysis should explain the problems and why they're important. Try to simplify the situation and identify critical aspects.

Some questions:

• What issues are we attempting to resolve?

• What obstacles—internal or otherwise—are we attempting to overcome?

• What is the opportunity, and why should we pursue it, in your opinion?

Decided Method

Second, describe your approach. This can be a set of company policies for handling the challenge. It's the overall approach to the first part's analysis.

The approach can be your company's bets, the solutions you've found, or how you'll solve the problems you've identified.

Again, these questions can help:

• What is the value that we hope to offer to our clients?

• Which market are we focusing on first?

• What makes us stand out? Our benefit over rivals?

Actions

Third, identify actions that result from your approach. Second-part actions should be these.

Coordinate these actions. You may need to add products or features to your roadmap, acquire new capabilities through partnerships, or launch new marketing campaigns. Whatever fits your challenges and strategy.

Final questions:

• What skills do we need to develop or obtain?

• What is the chosen remedy? What are the main outputs?

• What else ought to be added to our road map?

Put everything together

… and iterate!

Strategy isn't one-and-done. Changes occur. Economies change. Competitors emerge. Customer expectations change.

One unexpected event can make strategies obsolete quickly. Muscle it. Review, evaluate, and course-correct your strategies with your teams. Quarterly works. In a new or unstable industry, more often.

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.