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.

Ethereum's blockchain rules NFTs. Many consider it the one-stop shop for NFTs, and it's become the most talked-about and trafficked blockchain in existence.

Other blockchains are becoming popular in NFTs. Crypto-artists and NFT enthusiasts have sought new places to mint and trade NFTs due to Ethereum's high transaction costs and environmental impact.

When choosing a blockchain to mint on, there are several factors to consider. Size, creator costs, consumer spending habits, security, and community input are important. We've created a high-level summary of blockchains for NFTs to help clarify the fast-paced world of web3 tech.

Ethereum

Ethereum currently has the most NFTs. It's decentralized and provides financial and legal services without intermediaries. It houses popular NFT marketplaces (OpenSea), projects (CryptoPunks and the Bored Ape Yacht Club), and artists (Pak and Beeple).

It's also expensive and energy-intensive. This is because Ethereum works using a Proof-of-Work (PoW) mechanism. PoW requires computers to solve puzzles to add blocks and transactions to the blockchain. Solving these puzzles requires a lot of computer power, resulting in astronomical energy loss.

You should consider this blockchain first due to its popularity, security, decentralization, and ease of use.

Solana

Solana is a fast programmable blockchain. Its proof-of-history and proof-of-stake (PoS) consensus mechanisms eliminate complex puzzles. Reduced validation times and fees result.

PoS users stake their cryptocurrency to become a block validator. Validators get SOL. This encourages and rewards users to become stakers. PoH works with PoS to cryptographically verify time between events. Solana blockchain ensures transactions are in order and found by the correct leader (validator).

Solana's PoS and PoH mechanisms keep transaction fees and times low. Solana isn't as popular as Ethereum, so there are fewer NFT marketplaces and blockchain traders.

Tezos

Tezos is a greener blockchain. Tezos rose in 2021. Hic et Nunc was hailed as an economic alternative to Ethereum-centric marketplaces until Nov. 14, 2021.

Similar to Solana, Tezos uses a PoS consensus mechanism and only a PoS mechanism to reduce computational work. This blockchain uses two million times less energy than Ethereum. It's cheaper than Ethereum (but does cost more than Solana).

Tezos is a good place to start minting NFTs in bulk. Objkt is the largest Tezos marketplace.

Flow

Flow is a high-performance blockchain for NFTs, games, and decentralized apps (dApps). Flow is built with scalability in mind, so billions of people could interact with NFTs on the blockchain.

Flow became the NBA's blockchain partner in 2019. Flow, a product of Dapper labs (the team behind CryptoKitties), launched and hosts NBA Top Shot, making the blockchain integral to the popularity of non-fungible tokens.

Flow uses PoS to verify transactions, like Tezos. Developers are working on a model to handle 10,000 transactions per second on the blockchain. Low transaction fees.

Flow NFTs are tradeable on Blocktobay, OpenSea, Rarible, Foundation, and other platforms. NBA, NFL, UFC, and others have launched NFT marketplaces on Flow. Flow isn't as popular as Ethereum, resulting in fewer NFT marketplaces and blockchain traders.

Asset Exchange (WAX)

WAX is king of virtual collectibles. WAX is popular for digitalized versions of legacy collectibles like trading cards, figurines, memorabilia, etc.

Wax uses a PoS mechanism, but also creates carbon offset NFTs and partners with Climate Care. Like Flow, WAX transaction fees are low, and network fees are redistributed to the WAX community as an incentive to collectors.

WAX marketplaces host Topps, NASCAR, Hot Wheels, and cult classic film franchises like Godzilla, The Princess Bride, and Spiderman.

Binance Smart Chain

BSC is another good option for balancing fees and performance. High-speed transactions and low fees hurt decentralization. BSC is most centralized.

Binance Smart Chain uses Proof of Staked Authority (PoSA) to support a short block time and low fees. The 21 validators needed to run the exchange switch every 24 hours. 11 of the 21 validators are directly connected to the Binance Crypto Exchange, according to reports.

While many in the crypto and NFT ecosystems dislike centralization, the BSC NFT market picked up speed in 2021. OpenBiSea, AirNFTs, JuggerWorld, and others are gaining popularity despite not having as robust an ecosystem as Ethereum.

A fraud, free-market, antifragility tale

Crypto's only rival is public opinion.

In less than a week, mainstream media, bloggers, and TikTokers turned on FTX's founder.

While some were surprised, almost everyone with a keyboard and a Twitter account predicted the FTX collapse. These financial oracles should have warned the 1.2 million people Sam Bankman-Fried duped.

After happening, unexpected events seem obvious to our brains. It's a bug and a feature because it helps us cope with disasters and makes our reasoning suck.

Nobody predicted the FTX debacle. Bloomberg? Politicians. Non-famous. No cryptologists. Who?

When FTX imploded, taking billions of dollars with it, an outrage bomb went off, and the resulting shockwave threatens the crypto market's existence.

As someone who lost more than $78,000 in a crypto scam in 2020, I can only understand people’s reactions.  When the dust settles and rationality returns, we'll realize this is a natural occurrence in every free market.

What specifically occurred with FTX? (Skip if you are aware.)

FTX is a cryptocurrency exchange where customers can trade with cash. It reached #3 in less than two years as the fastest-growing platform of its kind.

FTX's performance helped make SBF the crypto poster boy. Other reasons include his altruistic public image, his support for the Democrats, and his company Alameda Research.

Alameda Research made a fortune arbitraging Bitcoin.

Arbitrage trading uses small price differences between two markets to make money. Bitcoin costs $20k in Japan and $21k in the US. Alameda Research did that for months, making $1 million per day.

Later, as its capital grew, Alameda expanded its trading activities and began investing in other companies.

Let's now discuss FTX.

SBF's diabolic master plan began when he used FTX-created FTT coins to inflate his trading company's balance sheets. He used inflated Alameda numbers to secure bank loans.

SBF used money he printed himself as collateral to borrow billions for capital. Coindesk exposed him in a report.

One of FTX's early investors tweeted that he planned to sell his FTT coins over the next few months. This would be a minor event if the investor wasn't Binance CEO Changpeng Zhao (CZ).

The crypto space saw a red WARNING sign when CZ cut ties with FTX. Everyone with an FTX account and a brain withdrew money. Two events followed. FTT fell from $20 to $4 in less than 72 hours, and FTX couldn't meet withdrawal requests, spreading panic.

SBF reassured FTX users on Twitter. Good assets.

He lied.

SBF falsely claimed FTX had a liquidity crunch. At the time of his initial claims, FTX owed about $8 billion to its customers. Liquidity shortages are usually minor. To get cash, sell assets. In the case of FTX, the main asset was printed FTT coins.

Sam wouldn't get out of trouble even if he slashed the discount (from $20 to $4) and sold every FTT. He'd flood the crypto market with his homemade coins, causing the price to crash.

SBF was trapped. He approached Binance about a buyout, which seemed good until Binance looked at FTX's books.

Binance's tweet ended SBF, and he had to apologize, resign as CEO, and file for bankruptcy.

Bloomberg estimated Sam's net worth to be zero by the end of that week. 0!

But that's not all. Twitter investigations exposed fraud at FTX and Alameda Research. SBF used customer funds to trade and invest in other companies.

Thanks to the Twitter indie reporters who made the mainstream press look amateurish. Some Twitter detectives didn't sleep for 30 hours to find answers. Others added to existing threads. Memes were hilarious.

One question kept repeating in my bald head as I watched the Blue Bird. Sam, WTF?

Then I understood.

SBF wanted that FTX becomes a bank.

Think about this. FTX seems healthy a few weeks ago. You buy 2 bitcoins using FTX. You'd expect the platform to take your dollars and debit your wallet, right?

No. They give I-Owe-Yous.

FTX records owing you 2 bitcoins in its internal ledger but doesn't credit your account. Given SBF's tricks, I'd bet on nothing.

What happens if they don't credit my account with 2 bitcoins? Your money goes into FTX's capital, where SBF and his friends invest in marketing, political endorsements, and buying other companies.

Over its two-year existence, FTX invested in 130 companies. Once they make a profit on their purchases, they'll pay you and keep the rest.

One detail makes their strategy dumb. If all FTX customers withdraw at once, everything collapses.

Financially savvy people think FTX's collapse resembles a bank run, and they're right. SBF designed FTX to operate like a bank.

You expect your bank to open a drawer with your name and put $1,000 in it when you deposit $1,000. They deposit $100 in your drawer and create an I-Owe-You for $900. What happens to $900?

Let's sum it up: It's boring and headache-inducing.

When you deposit money in a bank, they can keep 10% and lend the rest. Fractional Reserve Banking is a popular method. Fractional reserves operate within and across banks.

Fractional reserve banking generates $10,000 for every $1,000 deposited. People will pay off their debt plus interest.

As long as banks work together and the economy grows, their model works well.

SBF tried to replicate the system but forgot two details. First, traditional banks need verifiable collateral like real estate, jewelry, art, stocks, and bonds, not digital coupons. Traditional banks developed a liquidity buffer. The Federal Reserve (or Central Bank) injects massive cash into troubled banks.

Massive cash injections come from taxpayers. You and I pay for bankers' mistakes and annual bonuses. Yes, you may think banking is rigged. It's rigged, but it's the best financial game in 150 years. We accept its flaws, including bailouts for too-big-to-fail companies.

Anyway.

SBF wanted Binance's bailout. Binance said no, which was good for the crypto market.

Free markets are resilient.

Nassim Nicholas Taleb coined the term antifragility.

“Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile. Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.”

The easiest way to understand how antifragile systems behave is to compare them with other types of systems.

• Glass is like a fragile system. It snaps when shocked.

• Similar to rubber, a resilient system. After a stressful episode, it bounces back.

• A system that is antifragile is similar to a muscle. As it is torn in the gym, it gets stronger.

Time-changed things are antifragile. Culture, tech innovation, restaurants, revolutions, book sales, cuisine, economic success, and even muscle shape. These systems benefit from shocks and randomness in different ways, but they all pay a price for antifragility.

Same goes for the free market and financial institutions. Taleb's book uses restaurants as an example and ends with a reference to the 2008 crash.

“Restaurants are fragile. They compete with each other. But the collective of local restaurants is antifragile for that very reason. Had restaurants been individually robust, hence immortal, the overall business would be either stagnant or weak and would deliver nothing better than cafeteria food — and I mean Soviet-style cafeteria food. Further, it [the overall business] would be marred with systemic shortages, with once in a while a complete crisis and government bailout.”

Imagine the same thing with banks.

Independent banks would compete to offer the best services. If one of these banks fails, it will disappear. Customers and investors will suffer, but the market will recover from the dead banks' mistakes.

This idea underpins a free market. Bitcoin and other cryptocurrencies say this when criticizing traditional banking.

The traditional banking system's components never die. When a bank fails, the Federal Reserve steps in with a big taxpayer-funded check. This hinders bank evolution. If you don't let banking cells die and be replaced, your financial system won't be antifragile.

The interdependence of banks (centralization) means that one bank's mistake can sink the entire fleet, which brings us to SBF's ultimate travesty with FTX.

FTX has left the cryptocurrency gene pool.

FTX should be decentralized and independent. The super-star scammer invested in more than 130 crypto companies and linked them, creating a fragile banking-like structure. FTX seemed to say, "We exist because centralized banks are bad." But we'll be good, unlike the centralized banking system.

FTX saved several companies, including BlockFi and Voyager Digital.

FTX wanted to be a crypto bank conglomerate and Federal Reserve. SBF wanted to monopolize crypto markets. FTX wanted to be in bed with as many powerful people as possible, so SBF seduced politicians and celebrities.

Worst? People who saw SBF's plan flaws praised him. Experts, newspapers, and crypto fans praised FTX. When billions pour in, it's hard to realize FTX was acting against its nature.

Then, they act shocked when they realize FTX's fall triggered a domino effect. Some say the damage could wipe out the crypto market, but that's wrong.

Cell death is different from body death.

FTX is out of the game despite its size. Unfit, it fell victim to market natural selection.

Next?

The challengers keep coming. The crypto economy will improve with each failure.

Free markets are antifragile because their fragile parts compete, fostering evolution. With constructive feedback, evolution benefits customers and investors.

FTX shows that customers don't like being scammed, so the crypto market's health depends on them. Charlatans and con artists are eliminated quickly or slowly.

Crypto isn't immune to collapse. Cryptocurrencies can go extinct like biological species. Antifragility isn't immortality. A few more decades of evolution may be enough for humans to figure out how to best handle money, whether it's bitcoin, traditional banking, gold, or something else.

Keep your BS detector on. Start by being skeptical of this article's finance-related claims. Even if you think you understand finance, join the conversation.

We build a better future through dialogue. So listen, ask, and share. When you think you can't find common ground with the opposing view, remember:

Sam Bankman-Fried lied.

Learn or earn

In 2020, I started software engineering. My base wage has progressed as follows:

Amazon (2020): $112,000

Microsoft (2021): $123,000

Google (2022): $169,000

I didn't major in math, but those jumps appear more than a 7% wage increase. Here's a deeper look at the three.

The Three Categories of Compensation

Most software engineering compensation packages at IT organizations follow this format.

Minimum Salary

Base salary is pre-tax income. Most organizations give a base pay. This is paid biweekly, twice monthly, or monthly.

Recruiting Bonus

Sign-On incentives are one-time rewards to new hires. Companies need an incentive to switch. If you leave early, you must pay back the whole cost or a pro-rated amount.

Equity

Equity is complex and requires its own post. A company will promise to give you a certain amount of company stock but when you get it depends on your offer. 25% per year for 4 years, then it's gone.

If a company gives you $100,000 and distributes 25% every year for 4 years, expect $25,000 worth of company stock in your stock brokerage on your 1 year work anniversary.

Performance Bonus

Tech offers may include yearly performance bonuses. Depends on performance and funding. I've only seen 0-20%.

Engineers' overall compensation usually includes:

Base Salary + Sign-On + (Total Equity)/4 + Average Performance Bonus

Amazon: (TC: 150k)

Base Pay System

Amazon pays Seattle employees monthly on the first work day. I'd rather have my money sooner than later, even if it saves processing and pay statements.

The company upped its base pay cap from $160,000 to $350,000 to compete with other tech companies.

Performance Bonus

Amazon has no performance bonus, so you can work as little or as much as you like and get paid the same. Amazon is savvy to avoid promising benefits it can't deliver.

Sign-On Bonus

Amazon gives two two-year sign-up bonuses. First-year workers could receive $20,000 and second-year workers $15,000. It's probably to make up for the company's strange equity structure.

If you leave during the first year, you'll owe the entire money and a prorated amount for the second year bonus.

Equity

Most organizations prefer a 25%, 25%, 25%, 25% equity structure. Amazon takes a different approach with end-heavy equity:

• the first year, 5%

• 15% after one year.

• 20% then every six months

We thought it was constructed this way to keep staff longer.

Microsoft (TC: 185k)

Base Pay System

Microsoft paid biweekly.

Gainful Performance

My offer letter suggested a 0%-20% performance bonus. Everyone will be satisfied with a 10% raise at year's end.

But misleading press where the budget for the bonus is doubled can upset some employees because they won't earn double their expected bonus. Still barely 10% for 2022 average.

Sign-On Bonus

Microsoft's sign-on bonus is a one-time payout. The contract can require 2-year employment. You must negotiate 1 year. It's pro-rated, so that's fair.

Equity

Microsoft is one of those companies that has standard 25% equity structure. Except if you’re a new graduate.

In that case it’ll be

• 25% six months later

• 25% each year following that

New grads will acquire equity in 3.5 years, not 4. I'm guessing it's to keep new grads around longer.

Google (TC: 300k)

Base Pay Structure

Google pays biweekly.

Performance Bonus

Google's offer letter specifies a 15% bonus. It's wonderful there's no cap, but I might still get 0%. A little more than Microsoft’s 10% and a lot more than Amazon’s 0%.

Sign-On Bonus

Google gave a 1-year sign-up incentive. If the contract is only 1 year, I can move without any extra obligations.

Not as fantastic as Amazon's sign-up bonuses, but the remainder of the package might compensate.

Equity

We covered Amazon's tail-heavy compensation structure, so Google's front-heavy equity structure may surprise you.

Annual structure breakdown

• 33% Year 1

• 33% Year 2

• 22% Year 3

• 12% Year 4

The goal is to get them to Google and keep them there.

Final Thoughts

This post hopefully helped you understand the 3 firms' compensation arrangements.

There's always more to discuss, such as refreshers, 401k benefits, and business discounts, but I hope this shows a distinction between these 3 firms.

Skip this if you don't want to discover why your lively, no-brainer pitch isn't making $10k a month.

You don't want to be repulsive as an entrepreneur or anyone else. Making friends, influencing people, and converting strangers into customers will be difficult if your words evoke disgust, distrust, or disrespect. You may be one of many entrepreneurs who do this obliviously and involuntarily.

I've had to master selling my skills to recruiters (to land 6-figure jobs on Wall Street), selling companies to buyers in M&A transactions, and selling my own companies' products to strangers-turned-customers. I probably committed every cardinal sin of sales repulsion before realizing it was me or my poor salesmanship strategy.

If you're launching a new business, frustrated by low conversion rates, or just curious if you're repelling customers, read on to identify (and avoid) the 6 fatal errors that can kill any sales pitch.

1. The first indication

So many people fumble before they even speak because they assume their role is to convince the buyer. In other words, they expect to pressure, arm-twist, and combat objections until they convert the buyer. Actuality, the approach stinks of disgust, and emotionally-aware buyers would feel "gross" immediately.

Instead of trying to persuade a customer to buy, ask questions that will lead them to do so on their own. When a customer discovers your product or service on their own, they need less outside persuasion. Why not position your offer in a way that leads customers to sell themselves on it?

2. A flawless performance

Are you memorizing a sales script, tweaking video testimonials, and expunging historical blemishes before hitting "publish" on your new campaign? If so, you may be hurting your conversion rate.

Perfection may be a step too far and cause prospects to mistrust your sincerity. Become a great conversationalist to boost your sales. Seriously. Being charismatic is hard without being genuine and showing a little vulnerability.

People like vulnerability, even if it dents your perfect facade. Show the customer's stuttering testimonial. Open up about your or your company's past mistakes (and how you've since improved). Make your sales pitch a two-way conversation. Let the customer talk about themselves to build rapport. Real people sell, not canned scripts and movie-trailer testimonials.

If marketing or sales calls feel like a performance, you may be doing something wrong or leaving money on the table.

3. Your greatest phobia

Three minutes into prospect talks, I'd start sweating. I was talking 100 miles per hour, covering as many bases as possible to avoid the ones I feared. I knew my then-offering was inadequate and my firm had fears I hadn't addressed. So I word-vomited facts, features, and everything else to avoid the customer's concerns.

Do my prospects know I'm insecure? Maybe not, but it added an unnecessary and unhelpful layer of paranoia that kept me stressed, rushed, and on edge instead of connecting with the prospect. Skirting around a company, product, or service's flaws or objections is a poor, temporary, lazy (and cowardly) decision.

How can you project confidence and trust if you're afraid? Before you make another sales call, face your shortcomings, weak points, and objections. Your company won't be everyone's cup of tea, but you should have answers to every question or objection. You should be your business's top spokesperson and defender.

4. The unintentional apologies

Have you ever begged for a sale? I'm going to say no, however you may be unknowingly emitting sorry, inferior, insecure energy.

Young founders, first-time entrepreneurs, and those with severe imposter syndrome may elevate their target customer. This is common when trying to get first customers for obvious reasons.

• Since you're truly new at this, you naturally lack experience.

• You don't have the self-confidence boost of thousands or hundreds of closed deals or satisfied client results to remind you that your good or service is worthwhile.

• Getting those initial few clients seems like the most difficult task, as if doing so will decide the fate of your company as a whole (it probably won't, and you shouldn't actually place that much emphasis on any one transaction).

Customers can smell fear, insecurity, and anxiety just like they can smell B.S. If you believe your product or service improves clients' lives, selling it should feel like a benevolent act of service, not a sleazy money-grab. If you're a sincere entrepreneur, prospects will believe your proposition; if you're apprehensive, they'll notice.

Approach every sale as if you're fine with or without it. This has improved my salesmanship, marketing skills, and mental health. When you put pressure on yourself to close a sale or convince a difficult prospect "or else" (your company will fail, your rent will be late, your electricity will be cut), you emit desperation and lower the quality of your pitch. There's no point.

5. The endless promises

We've all read a million times how to answer or disprove prospects' arguments and add extra incentives to speed or secure the close. Some objections shouldn't be refuted. What if I told you not to offer certain incentives, bonuses, and promises? What if I told you to walk away from some prospects, even if it means losing your sales goal?

If you market to enough people, make enough sales calls, or grow enough companies, you'll encounter prospects who can't be satisfied. These prospects have endless questions, concerns, and requests for more, more, more that you'll never satisfy. These people are a distraction, a resource drain, and a test of your ability to cut losses before they erode your sanity and profit margin.

To appease or convert these insatiably needy, greedy Nellies into customers, you may agree with or acquiesce to every request and demand — even if you can't follow through. Once you overpromise and answer every hole they poke, their trust in you may wane quickly.

Telling a prospect what you can't do takes courage and integrity. If you're honest, upfront, and willing to admit when a product or service isn't right for the customer, you'll gain respect and positive customer experiences. Sometimes honesty is the most refreshing pitch and the deal-closer.

6. No matter what

Have you ever said, "I'll do anything to close this sale"? If so, you've probably already been disqualified. If a prospective customer haggles over a price, requests a discount, or continues to wear you down after you've made three concessions too many, you have a metal hook in your mouth, not them, and it may not end well. Why?

If you're so willing to cut a deal that you cut prices, comp services, extend payment plans, waive fees, etc., you betray your own confidence that your product or service was worth the stated price. They wonder if anyone is paying those prices, if you've ever had a customer (who wasn't a blood relative), and if you're legitimate or worth your rates.

Once a prospect senses that you'll do whatever it takes to get them to buy, their suspicions rise and they wonder why.

• Why are you cutting pricing if something is wrong with you or your service?

• Why are you so desperate for their sale?

• Why aren't more customers waiting in line to pay your pricing, and if they aren't, what on earth are they doing there?

That's what a prospect thinks when you reveal your lack of conviction, desperation, and willingness to give up control. Some prospects will exploit it to drain you dry, while others will be too frightened to buy from you even if you paid them.

Walking down a two-way street. Be casual.

If we track each act of repulsion to an uneasiness, fear, misperception, or impulse, it's evident that these sales and marketing disasters were forced communications. Stiff, imbalanced, divisive, combative, bravado-filled, and desperate. They were unnatural and accepted a power struggle between two sparring, suspicious, unequal warriors, rather than a harmonious oneness of two natural, but opposite parties shaking hands.

Sales should be natural, harmonious. Sales should feel good for both parties, not like one party is having their arm twisted.

You may be doing sales wrong if it feels repulsive, icky, or degrading. If you're thinking cringe-worthy thoughts about yourself, your product, service, or sales pitch, imagine what you're projecting to prospects. Don't make it unpleasant, repulsive, or cringeworthy.

For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.