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.

Decentralized perpetual may be the next crypto market boom; with tons of perpetual popping up, let's look at two protocols that offer organic, non-inflationary yields.

Decentralized derivatives exchanges' market share has increased tenfold in a year, but it's still 2% of CEXs'. DEXs have a long way to go before they can compete with centralized exchanges in speed, liquidity, user experience, and composability.

I'll cover gains.trade and GMX protocol in Polygon, Avalanche, and Arbitrum. Both protocols support leveraged perpetual crypto, stock, and Forex trading.

Why these protocols?

Decentralized GMX Gains protocol

Organic yield: path to sustainability

I've never trusted Defi's non-organic yields. Example: XYZ protocol. 20–75% of tokens may be set aside as farming rewards to provide liquidity, according to tokenomics.

Say you provide ETH-USDC liquidity. They advertise a 50% APR reward for this pair, 10% from trading fees and 40% from farming rewards. Only 10% is real, the rest is "Ponzi." The "real" reward is in protocol tokens.

Why keep this token? Governance voting or staking rewards are promoted services.

Most liquidity providers expect compensation for unused tokens. Basic psychological principles then? — Profit.

Nobody wants governance tokens. How many out of 100 care about the protocol's direction and will vote?

Staking increases your token's value. Currently, they're mostly non-liquid. If the protocol is compromised, you can't withdraw funds. Most people are sceptical of staking because of this.

"Free tokens," lack of use cases, and skepticism lead to tokens moving south. No farming reward protocols have lasted.

It may have shown strength in a bull market, but what about a bear market?

What is decentralized perpetual?

A perpetual contract is a type of futures contract that doesn't expire. So one can hold a position forever.

You can buy/sell any leveraged instruments (Long-Short) without expiration.

In centralized exchanges like Binance and coinbase, fees and revenue (liquidation) go to the exchanges, not users.

Users can provide liquidity that traders can use to leverage trade, and the revenue goes to liquidity providers.

Gains.trade and GMX protocol are perpetual trading platforms with a non-inflationary organic yield for liquidity providers.

GMX protocol

GMX is an Arbitrum and Avax protocol that rewards in ETH and Avax. GLP uses a fast oracle to borrow the "true price" from other trading venues, unlike a traditional AMM.

GLP and GMX are protocol tokens. GLP is used for leveraged trading, swapping, etc.

GLP is a basket of tokens, including ETH, BTC, AVAX, stablecoins, and UNI, LINK, and Stablecoins.

GLP composition on arbitrum

GLP composition on Avalanche

GLP token rebalances based on usage, providing liquidity without loss.

Protocol "runs" on Staking GLP. Depending on their chain, the protocol will reward users with ETH or AVAX. Current rewards are 22 percent (15.71 percent in ETH and the rest in escrowed GMX) and 21 percent (15.72 percent in AVAX and the rest in escrowed GMX). escGMX and ETH/AVAX percentages fluctuate.

Where is the yield coming from?

Swap fees, perpetual interest, and liquidations generate yield. 70% of fees go to GLP stakers, 30% to GMX. Organic yields aren't paid in inflationary farm tokens.

Escrowed GMX is vested GMX that unlocks in 365 days. To fully unlock GMX, you must farm the Escrowed GMX token for 365 days. That means less selling pressure for the GMX token.

GMX's status

These are the fees in Arbitrum in the past 11 months by GMX.

GMX works like a casino, which increases fees. Most fees come from Margin trading, which means most traders lose money; this money goes to the casino, or GLP stakers.

Strategies

My personal strategy is to DCA into GLP when markets hit bottom and stake it; GLP will be less volatile with extra staking rewards.

GLP YoY return vs. naked buying

Let's say I invested $10,000 in BTC, AVAX, and ETH in January.

• BTC price: 47665$

• ETH price: 3760$

• AVAX price: $145

Current prices

• BTC $21,000 (Down 56 percent )

• ETH $1233 (Down 67.2 percent )

• AVAX $20.36 (Down 85.95 percent )

Your $10,000 investment is now worth around $3,000.

How about GLP? My initial investment is 50% stables and 50% other assets ( Assuming the coverage ratio for stables is 50 percent at that time)

Without GLP staking yield, your value is $6500.

Let's assume the average APR for GLP staking is 23%, or $1500. So 8000$ total. It's 50% safer than holding naked assets in a bear market.

In a bull market, naked assets are preferable to GLP.

Short farming using GLP

Simple GLP short farming.

You use a stable asset as collateral to borrow AVAX. Sell it and buy GLP. Even if GLP rises, it won't rise as fast as AVAX, so we can get yields.

Let's do the maths

You deposit $10,000 USDT in Aave and borrow Avax. Say you borrow $8,000; you sell it, buy GLP, and risk 20%.

After a year, ETH, AVAX, and BTC rise 20%. GLP is $8800. $800 vanishes. 20% yields $1600. You're profitable. Shorting Avax costs $1600. (Assumptions-ETH, AVAX, BTC move the same, GLP yield is 20%. GLP has a 50:50 stablecoin/others ratio. Aave won't liquidate

In naked Avax shorting, Avax falls 20% in a year. You'll make $1600. If you buy GLP and stake it using the sold Avax and BTC, ETH and Avax go down by 20% - your profit is 20%, but with the yield, your total gain is $2400.

Issues with GMX

GMX's historical funding rates are always net positive, so long always pays short. This makes long-term shorts less appealing.

Oracle price discovery isn't enough. This limitation doesn't affect Bitcoin and ETH, but it affects less liquid assets. Traders can buy and sell less liquid assets at a lower price than their actual cost as long as GMX exists.

As users must provide GLP liquidity, adding more assets to GMX will be difficult. Next iteration will have synthetic assets.

Gains Protocol

Best leveraged trading platform. Smart contract-based decentralized protocol. 46 crypto pairs can be leveraged 5–150x and 10 Forex pairs 5–1000x. $10 DAI @ 150x (min collateral x leverage pos size is $1500 DAI). No funding fees, no KYC, trade DAI from your wallet, keep funds.

DAI single-sided staking and the GNS-DAI pool are important parts of Gains trading. GNS-DAI stakers get 90% of trading fees and 100% swap fees. 10 percent of trading fees go to DAI stakers, which is currently 14 percent!

Trade volume

When a trader opens a trade, the leverage and profit are pulled from the DAI pool. If he loses, the protocol yield goes to the stakers.

If the trader's win rate is high and the DAI pool slowly depletes, the GNS token is minted and sold to refill DAI. Trader losses are used to burn GNS tokens. 25%+ of GNS is burned, making it deflationary.

Due to high leverage and volatility of crypto assets, most traders lose money and the protocol always wins, keeping GNS deflationary.

Gains uses a unique decentralized oracle for price feeds, which is better for leverage trading platforms. Let me explain.

Gains uses chainlink price oracles, not its own price feeds. Chainlink oracles only query centralized exchanges for price feeds every minute, which is unsuitable for high-precision trading.

Gains created a custom oracle that queries the eight chainlink nodes for the current price and, on average, for trade confirmation. This model eliminates every-second inquiries, which waste gas but are more efficient than chainlink's per-minute price.

This price oracle helps Gains open and close trades instantly, eliminate scam wicks, etc.

Other benefits include:

• Stop-loss guarantee (open positions updated)

• No scam wicks

• Spot-pricing

• Highest possible leverage

• Fixed-spreads. During high volatility, a broker can increase the spread, which can hit your stop loss without the price moving.

• Trade directly from your wallet and keep your funds.

• >90% loss before liquidation (Some platforms liquidate as little as -50 percent)

• KYC-free

• Directly trade from wallet; keep funds safe

Further improvements

GNS-DAI liquidity providers fear the impermanent loss, so the protocol is migrating to its own liquidity and single staking GNS vaults. This allows users to stake GNS without permanent loss and obtain 90% DAI trading fees by staking. This starts in August.

Their upcoming improvements can be found here.

Gains constantly add new features and change pairs. It's an interesting protocol.

Conclusion

Next bull run, watch decentralized perpetual protocols. Effective tokenomics and non-inflationary yields may attract traders and liquidity providers. But still, there is a long way for them to develop, and I don't see them tackling the centralized exchanges any time soon until they fix their inherent problems and improve fast enough.

Read the full post here.

I've summarized each.

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Let's get started!

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Finding online classes is much easier. Class Central has classes from Harvard, Stanford, Coursera, Udemy, and Google, Amazon, etc. in one spot.

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Do you know any free, useful websites?