How Payment for Order Flow (PFOF) Works
What is PFOF?
PFOF is a brokerage firm's compensation for directing orders to different parties for trade execution. The brokerage firm receives fractions of a penny per share for directing the order to a market maker.
Each optionable stock could have thousands of contracts, so market makers dominate options trades. Order flow payments average less than $0.50 per option contract.
Order Flow Payments (PFOF) Explained
The proliferation of exchanges and electronic communication networks has complicated equity and options trading (ECNs) Ironically, Bernard Madoff, the Ponzi schemer, pioneered pay-for-order-flow.
In a December 2000 study on PFOF, the SEC said, "Payment for order flow is a method of transferring trading profits from market making to brokers who route customer orders to specialists for execution."
Given the complexity of trading thousands of stocks on multiple exchanges, market making has grown. Market makers are large firms that specialize in a set of stocks and options, maintaining an inventory of shares and contracts for buyers and sellers. Market makers are paid the bid-ask spread. Spreads have narrowed since 2001, when exchanges switched to decimals. A market maker's ability to play both sides of trades is key to profitability.
Benefits, requirements
A broker receives fees from a third party for order flow, sometimes without a client's knowledge. This invites conflicts of interest and criticism. Regulation NMS from 2005 requires brokers to disclose their policies and financial relationships with market makers.
Your broker must tell you if it's paid to send your orders to specific parties. This must be done at account opening and annually. The firm must disclose whether it participates in payment-for-order-flow and, upon request, every paid order. Brokerage clients can request payment data on specific transactions, but the response takes weeks.
Order flow payments save money. Smaller brokerage firms can benefit from routing orders through market makers and getting paid. This allows brokerage firms to send their orders to another firm to be executed with other orders, reducing costs. The market maker or exchange benefits from additional share volume, so it pays brokerage firms to direct traffic.
Retail investors, who lack bargaining power, may benefit from order-filling competition. Arrangements to steer the business in one direction invite wrongdoing, which can erode investor confidence in financial markets and their players.
Pay-for-order-flow criticism
It has always been controversial. Several firms offering zero-commission trades in the late 1990s routed orders to untrustworthy market makers. During the end of fractional pricing, the smallest stock spread was $0.125. Options spreads widened. Traders found that some of their "free" trades cost them a lot because they weren't getting the best price.
The SEC then studied the issue, focusing on options trades, and nearly decided to ban PFOF. The proliferation of options exchanges narrowed spreads because there was more competition for executing orders. Options market makers said their services provided liquidity. In its conclusion, the report said, "While increased multiple-listing produced immediate economic benefits to investors in the form of narrower quotes and effective spreads, these improvements have been muted with the spread of payment for order flow and internalization."
The SEC allowed payment for order flow to continue to prevent exchanges from gaining monopoly power. What would happen to trades if the practice was outlawed was also unclear. SEC requires brokers to disclose financial arrangements with market makers. Since then, the SEC has watched closely.
2020 Order Flow Payment
Rule 605 and Rule 606 show execution quality and order flow payment statistics on a broker's website. Despite being required by the SEC, these reports can be hard to find. The SEC mandated these reports in 2005, but the format and reporting requirements have changed over the years, most recently in 2018.
Brokers and market makers formed a working group with the Financial Information Forum (FIF) to standardize order execution quality reporting. Only one retail brokerage (Fidelity) and one market maker remain (Two Sigma Securities). FIF notes that the 605/606 reports "do not provide the level of information that allows a retail investor to gauge how well a broker-dealer fills a retail order compared to the NBBO (national best bid or offer’) at the time the order was received by the executing broker-dealer."
In the first quarter of 2020, Rule 606 reporting changed to require brokers to report net payments from market makers for S&P 500 and non-S&P 500 equity trades and options trades. Brokers must disclose payment rates per 100 shares by order type (market orders, marketable limit orders, non-marketable limit orders, and other orders).
Richard Repetto, Managing Director of New York-based Piper Sandler & Co., publishes a report on Rule 606 broker reports. Repetto focused on Charles Schwab, TD Ameritrade, E-TRADE, and Robinhood in Q2 2020. Repetto reported that payment for order flow was higher in the second quarter than the first due to increased trading activity, and that options paid more than equities.
Repetto says PFOF contributions rose overall. Schwab has the lowest options rates, while TD Ameritrade and Robinhood have the highest. Robinhood had the highest equity rating. Repetto assumes Robinhood's ability to charge higher PFOF reflects their order flow profitability and that they receive a fixed rate per spread (vs. a fixed rate per share by the other brokers).
Robinhood's PFOF in equities and options grew the most quarter-over-quarter of the four brokers Piper Sandler analyzed, as did their implied volumes. All four brokers saw higher PFOF rates.
TD Ameritrade took the biggest income hit when cutting trading commissions in fall 2019, and this report shows they're trying to make up the shortfall by routing orders for additional PFOF. Robinhood refuses to disclose trading statistics using the same metrics as the rest of the industry, offering only a vague explanation on their website.
Summary
Payment for order flow has become a major source of revenue as brokers offer no-commission equity (stock and ETF) orders. For retail investors, payment for order flow poses a problem because the brokerage may route orders to a market maker for its own benefit, not the investor's.
Infrequent or small-volume traders may not notice their broker's PFOF practices. Frequent traders and those who trade larger quantities should learn about their broker's order routing system to ensure they're not losing out on price improvement due to a broker prioritizing payment for order flow.
This post is a summary. Read full article here
More on Economics & Investing
Sam Hickmann
3 years ago
What is headline inflation?
Headline inflation is the raw Consumer price index (CPI) reported monthly by the Bureau of labour statistics (BLS). CPI measures inflation by calculating the cost of a fixed basket of goods. The CPI uses a base year to index the current year's prices.
Explaining Inflation
As it includes all aspects of an economy that experience inflation, headline inflation is not adjusted to remove volatile figures. Headline inflation is often linked to cost-of-living changes, which is useful for consumers.
The headline figure doesn't account for seasonality or volatile food and energy prices, which are removed from the core CPI. Headline inflation is usually annualized, so a monthly headline figure of 4% inflation would equal 4% inflation for the year if repeated for 12 months. Top-line inflation is compared year-over-year.
Inflation's downsides
Inflation erodes future dollar values, can stifle economic growth, and can raise interest rates. Core inflation is often considered a better metric than headline inflation. Investors and economists use headline and core results to set growth forecasts and monetary policy.
Core Inflation
Core inflation removes volatile CPI components that can distort the headline number. Food and energy costs are commonly removed. Environmental shifts that affect crop growth can affect food prices outside of the economy. Political dissent can affect energy costs, such as oil production.
From 1957 to 2018, the U.S. averaged 3.64 percent core inflation. In June 1980, the rate reached 13.60%. May 1957 had 0% inflation. The Fed's core inflation target for 2022 is 3%.
Central bank:
A central bank has privileged control over a nation's or group's money and credit. Modern central banks are responsible for monetary policy and bank regulation. Central banks are anti-competitive and non-market-based. Many central banks are not government agencies and are therefore considered politically independent. Even if a central bank isn't government-owned, its privileges are protected by law. A central bank's legal monopoly status gives it the right to issue banknotes and cash. Private commercial banks can only issue demand deposits.
What are living costs?
The cost of living is the amount needed to cover housing, food, taxes, and healthcare in a certain place and time. Cost of living is used to compare the cost of living between cities and is tied to wages. If expenses are higher in a city like New York, salaries must be higher so people can live there.
What's U.S. bureau of labor statistics?
BLS collects and distributes economic and labor market data about the U.S. Its reports include the CPI and PPI, both important inflation measures.
Trevor Stark
3 years ago
Economics is complete nonsense.
Mainstream economics haven't noticed.
What come to mind when I say the word "economics"?
Probably GDP, unemployment, and inflation.
If you've ever watched the news or listened to an economist, they'll use data like these to defend a political goal.
The issue is that these statistics are total bunk.
I'm being provocative, but I mean it:
The economy is not measured by GDP.
How many people are unemployed is not counted in the unemployment rate.
Inflation is not measured by the CPI.
All orthodox economists' major economic statistics are either wrong or falsified.
Government institutions create all these stats. The administration wants to reassure citizens the economy is doing well.
GDP does not reflect economic expansion.
GDP measures a country's economic size and growth. It’s calculated by the BEA, a government agency.
The US has the world's largest (self-reported) GDP, growing 2-3% annually.
If GDP rises, the economy is healthy, say economists.
Why is the GDP flawed?
GDP measures a country's yearly spending.
The government may adjust this to make the economy look good.
GDP = C + G + I + NX
C = Consumer Spending
G = Government Spending
I = Investments (Equipment, inventories, housing, etc.)
NX = Exports minus Imports
GDP is a country's annual spending.
The government can print money to boost GDP. The government has a motive to increase and manage GDP.
Because government expenditure is part of GDP, printing money and spending it on anything will raise GDP.
They've done this. Since 1950, US government spending has grown 8% annually, faster than GDP.
In 2022, government spending accounted for 44% of GDP. It's the highest since WWII. In 1790-1910, it was 3% of GDP.
Who cares?
The economy isn't only spending. Focus on citizens' purchasing power or quality of life.
Since GDP just measures spending, the government can print money to boost GDP.
Even if Americans are poorer than last year, economists can say GDP is up and everything is fine.
How many people are unemployed is not counted in the unemployment rate.
The unemployment rate measures a country's labor market. If unemployment is high, people aren't doing well economically.
The BLS estimates the (self-reported) unemployment rate as 3-4%.
Why is the unemployment rate so high?
The US government surveys 100k persons to measure unemployment. They extrapolate this data for the country.
They come into 3 categories:
Employed
People with jobs are employed … duh.
Unemployed
People who are “jobless, looking for a job, and available for work” are unemployed
Not in the labor force
The “labor force” is the employed + the unemployed.
The unemployment rate is the percentage of unemployed workers.
Problem is unemployed definition. You must actively seek work to be considered unemployed.
You're no longer unemployed if you haven't interviewed in 4 weeks.
This shit makes no goddamn sense.
Why does this matter?
You can't interview if there are no positions available. You're no longer unemployed after 4 weeks.
In 1994, the BLS redefined "unemployed" to exclude discouraged workers.
If you haven't interviewed in 4 weeks, you're no longer counted in the unemployment rate.
If unemployment were measured by total unemployed, it would be 25%.
Because the government wants to keep the unemployment rate low, they modify the definition.
If every US resident was unemployed and had no job interviews, economists would declare 0% unemployment. Excellent!
Inflation is not measured by the CPI.
The BLS measures CPI. This month was the highest since 1981.
CPI measures the cost of a basket of products across time. Food, energy, shelter, and clothes are included.
A 9.1% CPI means the basket of items is 9.1% more expensive.
What is the CPI problem?
Here's a more detailed explanation of CPI's flaws.
In summary, CPI is manipulated to be understated.
Housing costs are understated to manipulate CPI. Housing accounts for 33% of the CPI because it's the biggest expense for most people.
This signifies it's the biggest CPI weight.
Rather than using actual house prices, the Bureau of Labor Statistics essentially makes shit up. You can read more about the process here.
Surprise! It’s bullshit
The BLS stated Shelter's price rose 5.5% this month.
House prices are up 11-21%. (Source 1, Source 2, Source 3)
Rents are up 14-26%. (Source 1, Source 2)
Why is this important?
If CPI included housing prices, it would be 12-15 percent this month, not 9.1 percent.
9% inflation is nuts. Your money's value halves every 7 years at 9% inflation.
Worse is 15% inflation. Your money halves every 4 years at 15% inflation.
If everyone realized they needed to double their wage every 4-5 years to stay wealthy, there would be riots.
Inflation drains our money's value so the government can keep printing it.
The Solution
Most individuals know the existing system doesn't work, but can't explain why.
People work hard yet lag behind. The government lies about the economy's data.
In reality:
GDP has been down since 2008
25% of Americans are unemployed
Inflation is actually 15%
People might join together to vote out kleptocratic politicians if they knew the reality.
Having reliable economic data is the first step.
People can't understand the situation without sufficient information. Instead of immigrants or billionaires, people would blame liar politicians.
Here’s the vision:
A decentralized, transparent, and global dashboard that tracks economic data like GDP, unemployment, and inflation for every country on Earth.
Government incentives influence economic statistics.
ShadowStats has already started this effort, but the calculations must be transparent, decentralized, and global to be effective.
If interested, email me at trevorstark02@gmail.com.
Here are some links to further your research:
Tanya Aggarwal
3 years ago
What I learned from my experience as a recent graduate working in venture capital
Every week I meet many people interested in VC. Many of them ask me what it's like to be a junior analyst in VC or what I've learned so far.
Looking back, I've learned many things as a junior VC, having gone through an almost-euphoric peak bull market, failed tech IPOs of 2019 including WeWorks' catastrophic fall, and the beginnings of a bearish market.
1. Network, network, network!
VCs spend 80% of their time networking. Junior VCs source deals or manage portfolios. You spend your time bringing startups to your fund or helping existing portfolio companies grow. Knowing stakeholders (corporations, star talent, investors) in your particular areas of investment helps you develop your portfolio.
Networking was one of my strengths. When I first started in the industry, I'd go to startup events and meet 50 people a month. Over time, I realized these relationships were shallow and I was only getting business cards. So I stopped seeing networking as a transaction. VC is a long-term game, so you should work with people you like. Now I know who I click with and can build deeper relationships with them. My network is smaller but more valuable than before.
2. The Most Important Metric Is Founder
People often ask how we pick investments. Why some companies can raise money and others can't is a mystery. The founder is the most important metric for VCs. When a company is young, the product, environment, and team all change, but the founder remains constant. VCs bet on the founder, not the company.
How do we decide which founders are best after 2-3 calls? When looking at a founder's profile, ask why this person can solve this problem. The founders' track record will tell. If the founder is a serial entrepreneur, you know he/she possesses the entrepreneur DNA and will likely succeed again. If it's his/her first startup, focus on industry knowledge to deliver the best solution.
3. A company's fate can be determined by macrotrends.
Macro trends are crucial. A company can have the perfect product, founder, and team, but if it's solving the wrong problem, it won't succeed. I've also seen average companies ride the wave to success. When you're on the right side of a trend, there's so much demand that more companies can get a piece of the pie.
In COVID-19, macro trends made or broke a company. Ed-tech and health-tech companies gained unicorn status and raised funding at inflated valuations due to sudden demand. With the easing of pandemic restrictions and the start of a bear market, many of these companies' valuations are in question.
4. Look for methods to ACTUALLY add value.
You only need to go on VC twitter (read: @vcstartterkit and @vcbrags) for 5 minutes or look at fin-meme accounts on Instagram to see how much VCs claim to add value but how little they actually do. VC is a long-term game, though. Long-term, founders won't work with you if you don't add value.
How can we add value when we're young and have no network? Leaning on my strengths helped me. Instead of viewing my age and limited experience as a disadvantage, I realized that I brought a unique perspective to the table.
As a VC, you invest in companies that will be big in 5-7 years, and millennials and Gen Z will have the most purchasing power. Because you can relate to that market, you can offer insights that most Partners at 40 can't. I added value by helping with hiring because I had direct access to university talent pools and by finding university students for product beta testing.
5. Develop your personal brand.
Generalists or specialists run most funds. This means that funds either invest across industries or have a specific mandate. Most funds are becoming specialists, I've noticed. Top-tier founders don't lack capital, so funds must find other ways to attract them. Why would a founder work with a generalist fund when a specialist can offer better industry connections and partnership opportunities?
Same for fund members. Founders want quality investors. Become a thought leader in your industry to meet founders. Create content and share your thoughts on industry-related social media. When I first started building my brand, I found it helpful to interview industry veterans to create better content than I could on my own. Over time, my content attracted quality founders so I didn't have to look for them.
These are my biggest VC lessons. This list isn't exhaustive, but it's my industry survival guide.
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Isaiah McCall
3 years ago
Is TikTok slowly destroying a new generation?
It's kids' digital crack
TikTok is a destructive social media platform.
The interface shortens attention spans and dopamine receptors.
TikTok shares more data than other apps.
Seeing an endless stream of dancing teens on my glowing box makes me feel like a Blade Runner extra.
TikTok did in one year what MTV, Hollywood, and Warner Music tried to do in 20 years. TikTok has psychotized the two-thirds of society Aldous Huxley said were hypnotizable.
Millions of people, mostly kids, are addicted to learning a new dance, lip-sync, or prank, and those who best dramatize this collective improvisation get likes, comments, and shares.
TikTok is a great app. So what?
The Commercial Magnifying Glass TikTok made me realize my generation's time was up and the teenage Zoomers were the target.
I told my 14-year-old sister, "Enjoy your time under the commercial magnifying glass."
TikTok sells your every move, gesture, and thought. Data is the new oil. If you tell someone, they'll say, "Yeah, they collect data, but who cares? I have nothing to hide."
It's a George Orwell novel's beginning. Look up Big Brother Award winners to see if TikTok won.
TikTok shares your data more than any other social media app, and where it goes is unclear. TikTok uses third-party trackers to monitor your activity after you leave the app.
Consumers can't see what data is shared or how it will be used. — Genius URL
32.5 percent of Tiktok's users are 10 to 19 and 29.5% are 20 to 29.
TikTok is the greatest digital marketing opportunity in history, and they'll use it to sell you things, track you, and control your thoughts. Any of its users will tell you, "I don't care, I just want to be famous."
TikTok manufactures mental illness
TikTok's effect on dopamine and the brain is absurd. Dopamine controls the brain's pleasure and reward centers. It's like a switch that tells your brain "this feels good, repeat."
Dr. Julie Albright, a digital culture and communication sociologist, said TikTok users are "carried away by dopamine." It's hypnotic, you'll keep watching."
TikTok constantly releases dopamine. A guy on TikTok recently said he didn't like books because they were slow and boring.
The US didn't ban Tiktok.
Biden and Trump agree on bad things. Both agree that TikTok threatens national security and children's mental health.
The Chinese Communist Party owns and operates TikTok, but that's not its only problem.
There’s borderline child porn on TikTok
It's unsafe for children and violated COPPA.
It's also Chinese spyware. I'm not a Trump supporter, but I was glad he wanted TikTok regulated and disappointed when he failed.
Full-on internet censorship is rare outside of China, so banning it may be excessive. US should regulate TikTok more.
We must reject a low-quality present for a high-quality future.
TikTok vs YouTube
People got mad when I wrote about YouTube's death.
They didn't like when I said TikTok was YouTube's first real challenger.
Indeed. TikTok is the fastest-growing social network. In three years, the Chinese social media app TikTok has gained over 1 billion active users. In the first quarter of 2020, it had the most downloads of any app in a single quarter.
TikTok is the perfect social media app in many ways. It's brief and direct.
Can you believe they had a YouTube vs TikTok boxing match? We are doomed as a species.
YouTube hosts my favorite videos. That’s why I use it. That’s why you use it. New users expect more. They want something quicker, more addictive.
TikTok's impact on other social media platforms frustrates me. YouTube copied TikTok to compete.
It's all about short, addictive content.
I'll admit I'm probably wrong about TikTok. My friend says his feed is full of videos about food, cute animals, book recommendations, and hot lesbians.
Whatever.
TikTok makes us bad
TikTok is the opposite of what the Ancient Greeks believed about wisdom.
It encourages people to be fake. It's like a never-ending costume party where everyone competes.
It does not mean that Gen Z is doomed.
They could be the saviors of the world for all I know.
TikTok feels like a step towards Mike Judge's "Idiocracy," where the average person is a pleasure-seeking moron.
Tim Denning
3 years ago
Elon Musk’s Rich Life Is a Nightmare
I'm sure you haven't read about Elon's other side.
Elon divorced badly.
Nobody's surprised.
Imagine you're a parent. Someone isn't home year-round. What's next?
That’s what happened to YOLO Elon.
He can do anything. He can intervene in wars, shoot his mouth off, bang anyone he wants, avoid tax, make cool tech, buy anything his ego desires, and live anywhere exotic.
Few know his billionaire backstory. I'll tell you so you don't worship his lifestyle. It’s a cult.
Only his career succeeds. His life is a nightmare otherwise.
Psychopaths' schedule
Elon has said he works 120-hour weeks.
As he told the reporter about his job, he choked up, which was unusual for him.
His crazy workload and lack of sleep forced him to scold innocent Wall Street analysts. Later, he apologized.
In the same interview, he admits he hadn't taken more than a week off since 2001, when he was bedridden with malaria. Elon stays home after a near-death experience.
He's rarely outside.
Elon says he sometimes works 3 or 4 days straight.
He admits his crazy work schedule has cost him time with his kids and friends.
Elon's a slave
Elon's birthday description made him emotional.
Elon worked his entire birthday.
"No friends, nothing," he said, stuttering.
His brother's wedding in Catalonia was 48 hours after his birthday. That meant flying there from Tesla's factory prison.
He arrived two hours before the big moment, barely enough time to eat and change, let alone see his brother.
Elon had to leave after the bouquet was tossed to a crowd of billionaire lovers. He missed his brother's first dance with his wife.
Shocking.
He went straight to Tesla's prison.
The looming health crisis
Elon was asked if overworking affected his health.
Not great. Friends are worried.
Now you know why Elon tweets dumb things. Working so hard has probably caused him mental health issues.
Mental illness removed my reality filter. You do stupid things because you're tired.
Astronauts pelted Elon
Elon's overwork isn't the first time his life has made him emotional.
When asked about Neil Armstrong and Gene Cernan criticizing his SpaceX missions, he got emotional. Elon's heroes.
They're why he started the company, and they mocked his work. In another interview, we see how Elon’s business obsession has knifed him in the heart.
Once you have a company, you must feed, nurse, and care for it, even if it destroys you.
"Yep," Elon says, tearing up.
In the same interview, he's asked how Tesla survived the 2008 recession. Elon stopped the interview because he was crying. When Tesla and SpaceX filed for bankruptcy in 2008, he nearly had a nervous breakdown. He called them his "children."
All the time, he's risking everything.
Jack Raines explains best:
Too much money makes you a slave to your net worth.
Elon's emotions are admirable. It's one of the few times he seems human, not like an alien Cyborg.
Stop idealizing Elon's lifestyle
Building a side business that becomes a billion-dollar unicorn startup is a nightmare.
"Billionaire" means financially wealthy but otherwise broke. A rich life includes more than business and money.
This post is a summary. Read full article here
Farhan Ali Khan
2 years ago
Introduction to Zero-Knowledge Proofs: The Art of Proving Without Revealing
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).
In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.
As Alex made his decision, Jack entered the cave and asked him to exit from the B path.
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:
Alex walks into the cave.
Alex follows a random route.
Jack walks into the cave.
Alex is asked to follow a random route by Jack.
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
Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.
Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.
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:
You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.
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.
You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.
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:
Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.
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.
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:
One of the two coins is chosen at random, and you secretly flip it more than once.
You show your pal the following series of coin flips without revealing which coin you actually flipped.
Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.
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.
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:
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.
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.
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:
You determine a new number s = r2 mod n by computing a random number r.
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.
A random number (either 0 or 1) is selected by your friend and sent to you.
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.
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:
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.
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.
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:
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.
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:
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.
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.
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.
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.
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.