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.

Corn Kid got viral on TikTok after being interviewed by Recess Therapy. Tariq, called the Corn Kid, ate a buttery ear of corn in the video. He's corn crazy. He thinks everyone just has to try it. It turns out, whether we know it or not, we already have.

Corn is a fruit, veggie, and grain. It's the second-most-grown crop. Corn makes up 36% of U.S. exports. In the U.S., it's easy to grow and provides high yields, as proven by the vast corn belt spanning the Midwest, Great Plains, and Texas panhandle. Since 1950, the corn crop has doubled to 10 billion bushels.

You say, "Fine." We shouldn't just grow because we can. Why so much corn? What's this corn for?

Why is practical and political. Michael Pollan's The Omnivore's Dilemma has the full narrative. Early 1970s food costs increased. Nixon subsidized maize to feed the public. Monsanto genetically engineered corn seeds to make them hardier, and soon there was plenty of corn. Everyone ate. Woot! Too much corn followed. The powers-that-be had to decide what to do with leftover corn-on-the-cob.

They are fortunate that corn has a wide range of uses.

First, the edible variants. I divide corn into obvious and stealth.

Obvious corn includes popcorn, canned corn, and corn on the cob. This form isn't always digested and often comes out as entire, polka-dotting poop. Cornmeal can be ground to make cornbread, polenta, and corn tortillas. Corn provides antioxidants, minerals, and vitamins in moderation. Most synthetic Vitamin C comes from GMO maize.

Corn oil, corn starch, dextrose (a sugar), and high-fructose corn syrup are often overlooked. They're stealth corn because they sneak into practically everything. Corn oil is used for frying, baking, and in potato chips, mayonnaise, margarine, and salad dressing. Baby food, bread, cakes, antibiotics, canned vegetables, beverages, and even dairy and animal products include corn starch. Dextrose appears in almost all prepared foods, excluding those with high-fructose corn syrup. HFCS isn't as easily digested as sucrose (from cane sugar). It can also cause other ailments, which we'll discuss later.

Most foods contain corn. It's fed to almost all food animals. 96% of U.S. animal feed is corn. 39% of U.S. corn is fed to livestock. But animals prefer other foods. Omnivore chickens prefer insects, worms, grains, and grasses. Captive cows are fed a total mixed ration, which contains corn. These animals' products, like eggs and milk, are also corn-fed.

There are numerous non-edible by-products of corn that are employed in the production of items like:

1. fuel-grade ethanol

2. plastics

3. batteries

4. cosmetics

5. meds/vitamins binder

6. carpets, fabrics

7. glutathione

8. crayons

9. Paint/glue

How does corn influence you? Consider quick food for dinner. You order a cheeseburger, fries, and big Coke at the counter (or drive-through in the suburbs). You tell yourself, "No corn." All that contains corn. Deconstruct:

Cows fed corn produce meat and cheese. Meat and cheese were bonded with corn syrup and starch (same). The bun (corn flour and dextrose) and fries were fried in maize oil. High fructose corn syrup sweetens the drink and helps make the cup and straw.

Just about everything contains corn. Then what? A cornspiracy, perhaps? Is eating too much maize an issue, or should we strive to stay away from it whenever possible?

As I've said, eating some maize can be healthy. 92% of U.S. corn is genetically modified, according to the Center for Food Safety. The adjustments are expected to boost corn yields. Some sweet corn is genetically modified to produce its own insecticide, a protein deadly to insects made by Bacillus thuringiensis. It's safe to eat in sweet corn. Concerns exist about feeding agricultural animals so much maize, modified or not.

High fructose corn syrup should be consumed in moderation. Fructose, a sugar, isn't easily metabolized. Fructose causes diabetes, fatty liver, obesity, and heart disease. It causes inflammation, which might aggravate gout. Candy, packaged sweets, soda, fast food, juice drinks, ice cream, ice cream topping syrups, sauces & condiments, jams, bread, crackers, and pancake syrup contain the most high fructose corn syrup. Everyday foods with little nutrients. Check labels and choose cane sugar or sucrose-sweetened goods. Or, eat corn like the Corn Kid.

America should avoid BRICS

Vladimir Putin has watched videos of Muammar Gaddafi's CIA-backed demise.

Gaddafi...

Thief.

Did you know Gaddafi wanted a gold-backed dinar for Africa? Because he considered our global financial system was a Ponzi scheme, he wanted to discontinue trading oil in US dollars.

Or, Gaddafi's Libya enjoyed Africa's highest quality of living before becoming freed. Pictured:

Vladimir Putin is a nasty guy, but he had his reasons for not mentioning NATO assisting Ukraine in resisting US imperialism. Nobody tells you. Sure.

The US dollar's corruption post-2008, debasement by quantitative easing, and lack of value are key factors. BRICS will replace the dollar.

BRICS aren't bricks.

Economy-related.

Brazil, Russia, India, China, and South Africa have cooperated for 14 years to fight U.S. hegemony with a new international currency: BRICS.

BRICS is mostly comical. Now. Saudi Arabia, the second-largest oil hegemon, wants to join.

So what?

The New World Currency is BRICS

Russia was kicked out of G8 for its aggressiveness in Crimea in 2014.

It's now G7.

No biggie, said Putin, he said, and I quote, “Bon appetite.”

He was prepared. China, India, and Brazil lead the New World Order.

Together, they constitute 40% of the world's population and, according to the IMF, 50% of the world's GDP by 2030.

Here’s what the BRICS president Marcos Prado Troyjo had to say earlier this year about no longer needing the US dollar: “We have implemented the mechanism of mutual settlements in rubles and rupees, and there is no need for our countries to use the dollar in mutual settlements. And today a similar mechanism of mutual settlements in rubles and yuan is being developed by China.”

Ick. That's D.C. and NYC warmongers licking their chops for WW3 nasty.

Here's a lovely picture of BRICS to relax you:

If Saudi Arabia joins BRICS, as President Mohammed Bin Salman has expressed interest, a majority of the Middle East will have joined forces to construct a new world order not based on the US currency.

I'm not sure of the new acronym.

SBRICSS? CIRBSS? CRIBSS?

The Reason America Is Harvesting What It Sowed

BRICS began 14 years ago.

14 years ago, what occurred? Concentrate. It involved CDOs, bad subprime mortgages, and Wall Street quants crunching numbers.

2008 recession

When two nations trade, they do so in US dollars, not Euros or gold.

What happened when 2008, an avoidable crisis caused by US banks' cupidity and ignorance, what happened?

Everyone WORLDWIDE felt the pain.

Mostly due to corporate America's avarice.

This should have been a warning that China and Russia had enough of our bs. Like when France sent a battleship to America after Nixon scrapped the gold standard. The US was warned to shape up or be dethroned (or at least try).

Nixon improved in 1971. Kinda. Invented PetroDollar.

Another BS system that unfairly favors America and possibly pushed Russia, China, and Saudi Arabia into BRICS.

The PetroDollar forces oil-exporting nations to trade in US dollars and invest in US Treasury bonds. Brilliant. Genius evil.

Our misdeeds are:

• In conflicts that are not its concern, the USA uses the global reserve currency as a weapon.

• Targeted nations abandon the dollar, and rightfully so, as do nations that depend on them for trade in vital resources.

• The dollar's position as the world's reserve currency is in jeopardy, which could have disastrous economic effects.

• Although we have actually sown our own doom, we appear astonished. According to the Bible, whomever sows to appease his sinful nature will reap destruction from that nature whereas whoever sows to appease the Spirit will reap eternal life from the Spirit.

Americans, even our leaders, lack caution and delayed pleasure. When our unsustainable systems fail, we double down. Bailouts of the banks in 2008 were myopic, puerile, and another nail in America's hegemony.

America has screwed everyone.

We're unpopular.

The BRICS's future

It's happened before.

Saddam Hussein sold oil in Euros in 2000, and the US invaded Iraq a month later. The media has devalued the word conspiracy. The Iraq conspiracy.

There were no WMDs, but NYT journalists like Judy Miller drove Americans into a warmongering frenzy because Saddam would ruin the PetroDollar. Does anyone recall that this war spawned ISIS?

I think America has done good for the world. You can make a convincing case that we're many people's villain.

Learn more in Confessions of an Economic Hitman, The Devil's Chessboard, or Tyranny of the Federal Reserve. Or ignore it. That's easier.

We, America, should extend an olive branch, ask for forgiveness, and learn from our faults, as the Tao Te Ching advises. Unlikely. Our population is apathetic and stupid, and our government is corrupt.

Argentina, Iran, Egypt, and Turkey have also indicated interest in joining BRICS. They're also considering making it gold-backed, making it a new world reserve currency.

You should pay attention.

Thanks for reading!

ZERO GRACE/ZERO MALICE

Amazon's purchase of One Medical could speed up American healthcare

The U.S. healthcare industry is a 7-ton seal bleeding at sea. Predators are circling. Unearned margin: price increases relative to inflation without quality improvements. Amazon is the 11-foot megalodon with 7-inch teeth. Amazon is no longer circling... but attacking.

In 2020 dollars, per capita U.S. healthcare spending increased from $2,968 in 1980 to $12,531. The result is a massive industry with 13% of the nation's workers and a fifth of GDP.

Doctor No

In 40 years, healthcare has made progress. From 73.7 in 1980 to 78.8 in 2019, life expectancy rose (before Covid knocked it back down a bit). Pharmacological therapies have revolutionized, and genetic research is paying off. The financial return, improvement split by cost increases, is terrible. No country has expense rises like the U.S., and no one spends as much per capita as we do. Developed countries have longer life expectancies, healthier populations, and less economic hardship.

Two-thirds of U.S. personal bankruptcies are due to medical expenses and/or missed work. Mom or Dad getting cancer could bankrupt many middle-class American families. 40% of American adults delayed or skipped needed care due to cost. Every healthcare improvement seems to have a downside. Same pharmacological revolution that helped millions caused opioid epidemic. Our results are poor in many areas: The U.S. has a high infant mortality rate.

Healthcare is the second-worst retail industry in the country. Gas stations are #1. Imagine walking into a Best Buy to buy a TV and a Blue Shirt associate requests you fill out the same 14 pages of paperwork you filled out yesterday. Then you wait in a crowded room until they call you, 20 minutes after the scheduled appointment you were asked to arrive early for, to see the one person in the store who can talk to you about TVs, who has 10 minutes for you. The average emergency room wait time in New York is 6 hours and 10 minutes.

If it's bad for the customer, it's worse for the business. Physicians spend 27% of their time helping patients; 49% on EHRs. Documentation, order entry, billing, and inbox management. Spend a decade getting an M.D., then become a bureaucrat.

No industry better illustrates scale diseconomies. If we got the same return on healthcare spending as other countries, we'd all live to 100. We could spend less, live longer and healthier, and pay off the national debt in 15 years. U.S. healthcare is the worst ever.

What now? Competition is at the heart of capitalism, the worst system of its kind.

Priority Time

Amazon is buying One Medical for $3.9 billion. I think this deal will liberate society. Two years in, I think One Medical is great. When I got Covid, I pressed the One Medical symbol on my phone; a nurse practitioner prescribed Paxlovid and told me which pharmacies had it in stock.

Amazon enables the company's vision. One Medical's stock is down to $10 from $40 at the start of 2021. Last year, it lost $250 million and needs cash (Amazon has $60 billion). ONEM must grow. The service has 736,000 members. Half of U.S. households have Amazon Prime. Finally, delivery. One Medical is a digital health/physical office hybrid, but you must pick up medication at the pharmacy. Upgrade your Paxlovid delivery time after a remote consultation. Amazon's core competency means it'll happen. Healthcare speed and convenience will feel alien.

It's been a long, winding road to disruption. Amazon, JPMorgan, and Berkshire Hathaway formed Haven four years ago to provide better healthcare for their 1.5 million employees. It rocked healthcare stocks the morning of the press release, but folded in 2021.

Amazon Care is an employee-focused service. Home-delivered virtual health services and nurses. It's doing well, expanding nationwide, and providing healthcare for other companies. Hilton is Amazon Care's biggest customer. The acquisition of One Medical will bring 66 million Prime households capital, domain expertise, and billing infrastructure. Imagine:

"Alexa, I'm hot and my back hurts."

"Connecting you to a Prime doctor now."

Want to vs. Have to

I predicted Amazon entering healthcare years ago. Why? For the same reason Apple is getting into auto. Amazon's P/E is 56, double Walmart's. The corporation must add $250 billion in revenue over the next five years to retain its share price. White-label clothes or smart home products won't generate as much revenue. It must enter a huge market without scale, operational competence, and data skills.

Current Situation

Healthcare reform benefits both consumers and investors. In 2015, healthcare services had S&P 500-average multiples. The market is losing faith in public healthcare businesses' growth. Healthcare services have lower EV/EBITDA multiples than the S&P 500.

Amazon isn't the only prey-hunter. Walmart and Alibaba are starting pharmacies. Uber is developing medical transportation. Private markets invested $29 billion in telehealth last year, up 95% from 2020.

The pandemic accelerated telehealth, the immediate unlock. After the first positive Covid case in the U.S., services that had to be delivered in person shifted to Zoom... We lived. We grew. Video house calls continued after in-person visits were allowed. McKinsey estimates telehealth visits are 38 times pre-pandemic levels. Doctors adopted the technology, regulators loosened restrictions, and patients saved time. We're far from remote surgery, but many patient visits are unnecessary. A study of 40 million patients during lockdown found that for chronic disease patients, online visits didn't affect outcomes. This method of care will only improve.

Amazon's disruption will be significant and will inspire a flood of capital, startups, and consumer brands. Mark Cuban launched a pharmacy that eliminates middlemen in January. Outcome? A 90-day supply of acid-reflux medication costs $17. Medicare could have saved $3.6 billion by buying generic drugs from Cuban's pharmacy. Other apex predators will look at different limbs of the carcass for food. Nike could enter healthcare via orthopedics, acupuncture, and chiropractic. LVMH, L'Oréal, and Estée Lauder may launch global plastic surgery brands. Hilton and Four Seasons may open hospitals. Lennar and Pulte could build "Active Living" communities that Nana would leave feet first, avoiding the expense and tragedy of dying among strangers.

Risks

Privacy matters: HIV status is different from credit card and billing address. Most customers (60%) feel fine sharing personal health data via virtual technologies, though. Unavoidable. 85% of doctors believe data-sharing and interoperability will become the norm. Amazon is the most trusted tech company for handling personal data. Not Meta: Amazon.

What about antitrust, then?

Amazon should be required to spin off AWS and/or Amazon Fulfillment and banned from promoting its own products. It should be allowed to acquire hospitals. One Medical's $3.9 billion acquisition is a drop in the bucket compared to UnitedHealth's $498 billion market valuation.

Antitrust enforcement shouldn't assume some people/firms are good/bad. It should recognize that competition is good and focus on making markets more competitive in each deal. The FTC should force asset divestitures in e-commerce, digital marketing, and social media. These companies can also promote competition in a social ill.

U.S. healthcare makes us fat, depressed, and broke. Competition has produced massive value and prosperity across most of our economy.

Dear Amazon … bring it.