More on Economics & Investing
Jan-Patrick Barnert
3 years ago
Wall Street's Bear Market May Stick Around
If history is any guide, this bear market might be long and severe.
This is the S&P 500 Index's fourth such incident in 20 years. The last bear market of 2020 was a "shock trade" caused by the Covid-19 pandemic, although earlier ones in 2000 and 2008 took longer to bottom out and recover.
Peter Garnry, head of equities strategy at Saxo Bank A/S, compares the current selloff to the dotcom bust of 2000 and the 1973-1974 bear market marked by soaring oil prices connected to an OPEC oil embargo. He blamed high tech valuations and the commodity crises.
"This drop might stretch over a year and reach 35%," Garnry wrote.
Here are six bear market charts.
Time/depth
The S&P 500 Index plummeted 51% between 2000 and 2002 and 58% during the global financial crisis; it took more than 1,000 trading days to recover. The former took 638 days to reach a bottom, while the latter took 352 days, suggesting the present selloff is young.
Valuations
Before the tech bubble burst in 2000, valuations were high. The S&P 500's forward P/E was 25 times then. Before the market fell this year, ahead values were near 24. Before the global financial crisis, stocks were relatively inexpensive, but valuations dropped more than 40%, compared to less than 30% now.
Earnings
Every stock crash, especially earlier bear markets, returned stocks to fundamentals. The S&P 500 decouples from earnings trends but eventually recouples.
Support
Central banks won't support equity investors just now. The end of massive monetary easing will terminate a two-year bull run that was among the strongest ever, and equities may struggle without cheap money. After years of "don't fight the Fed," investors must embrace a new strategy.
Bear Haunting Bear
If the past is any indication, rising government bond yields are bad news. After the financial crisis, skyrocketing rates and a falling euro pushed European stock markets back into bear territory in 2011.
Inflation/rates
The current monetary policy climate differs from past bear markets. This is the first time in a while that markets face significant inflation and rising rates.
This post is a summary. Read full article here
Ray Dalio
3 years ago
The latest “bubble indicator” readings.
As you know, I like to turn my intuition into decision rules (principles) that can be back-tested and automated to create a portfolio of alpha bets. I use one for bubbles. Having seen many bubbles in my 50+ years of investing, I described what makes a bubble and how to identify them in markets—not just stocks.
A bubble market has a high degree of the following:
- High prices compared to traditional values (e.g., by taking the present value of their cash flows for the duration of the asset and comparing it with their interest rates).
- Conditons incompatible with long-term growth (e.g., extrapolating past revenue and earnings growth rates late in the cycle).
- Many new and inexperienced buyers were drawn in by the perceived hot market.
- Broad bullish sentiment.
- Debt financing a large portion of purchases.
- Lots of forward and speculative purchases to profit from price rises (e.g., inventories that are more than needed, contracted forward purchases, etc.).
I use these criteria to assess all markets for bubbles. I have periodically shown you these for stocks and the stock market.
What Was Shown in January Versus Now
I will first describe the picture in words, then show it in charts, and compare it to the last update in January.
As of January, the bubble indicator showed that a) the US equity market was in a moderate bubble, but not an extreme one (ie., 70 percent of way toward the highest bubble, which occurred in the late 1990s and late 1920s), and b) the emerging tech companies (ie. As well, the unprecedented flood of liquidity post-COVID financed other bubbly behavior (e.g. SPACs, IPO boom, big pickup in options activity), making things bubbly. I showed which stocks were in bubbles and created an index of those stocks, which I call “bubble stocks.”
Those bubble stocks have popped. They fell by a third last year, while the S&P 500 remained flat. In light of these and other market developments, it is not necessarily true that now is a good time to buy emerging tech stocks.
The fact that they aren't at a bubble extreme doesn't mean they are safe or that it's a good time to get long. Our metrics still show that US stocks are overvalued. Once popped, bubbles tend to overcorrect to the downside rather than settle at “normal” prices.
The following charts paint the picture. The first shows the US equity market bubble gauge/indicator going back to 1900, currently at the 40% percentile. The charts also zoom in on the gauge in recent years, as well as the late 1920s and late 1990s bubbles (during both of these cases the gauge reached 100 percent ).
The chart below depicts the average bubble gauge for the most bubbly companies in 2020. Those readings are down significantly.
The charts below compare the performance of a basket of emerging tech bubble stocks to the S&P 500. Prices have fallen noticeably, giving up most of their post-COVID gains.
The following charts show the price action of the bubble slice today and in the 1920s and 1990s. These charts show the same market dynamics and two key indicators. These are just two examples of how a lot of debt financing stock ownership coupled with a tightening typically leads to a bubble popping.
Everything driving the bubbles in this market segment is classic—the same drivers that drove the 1920s bubble and the 1990s bubble. For instance, in the last couple months, it was how tightening can act to prick the bubble. Review this case study of the 1920s stock bubble (starting on page 49) from my book Principles for Navigating Big Debt Crises to grasp these dynamics.
The following charts show the components of the US stock market bubble gauge. Since this is a proprietary indicator, I will only show you some of the sub-aggregate readings and some indicators.
Each of these six influences is measured using a number of stats. This is how I approach the stock market. These gauges are combined into aggregate indices by security and then for the market as a whole. The table below shows the current readings of these US equity market indicators. It compares current conditions for US equities to historical conditions. These readings suggest that we’re out of a bubble.
1. How High Are Prices Relatively?
This price gauge for US equities is currently around the 50th percentile.
2. Is price reduction unsustainable?
This measure calculates the earnings growth rate required to outperform bonds. This is calculated by adding up the readings of individual securities. This indicator is currently near the 60th percentile for the overall market, higher than some of our other readings. Profit growth discounted in stocks remains high.
Even more so in the US software sector. Analysts' earnings growth expectations for this sector have slowed, but remain high historically. P/Es have reversed COVID gains but remain high historical.
3. How many new buyers (i.e., non-existing buyers) entered the market?
Expansion of new entrants is often indicative of a bubble. According to historical accounts, this was true in the 1990s equity bubble and the 1929 bubble (though our data for this and other gauges doesn't go back that far). A flood of new retail investors into popular stocks, which by other measures appeared to be in a bubble, pushed this gauge above the 90% mark in 2020. The pace of retail activity in the markets has recently slowed to pre-COVID levels.
4. How Broadly Bullish Is Sentiment?
The more people who have invested, the less resources they have to keep investing, and the more likely they are to sell. Market sentiment is now significantly negative.
5. Are Purchases Being Financed by High Leverage?
Leveraged purchases weaken the buying foundation and expose it to forced selling in a downturn. The leverage gauge, which considers option positions as a form of leverage, is now around the 50% mark.
6. To What Extent Have Buyers Made Exceptionally Extended Forward Purchases?
Looking at future purchases can help assess whether expectations have become overly optimistic. This indicator is particularly useful in commodity and real estate markets, where forward purchases are most obvious. In the equity markets, I look at indicators like capital expenditure, or how much businesses (and governments) invest in infrastructure, factories, etc. It reflects whether businesses are projecting future demand growth. Like other gauges, this one is at the 40th percentile.
What one does with it is a tactical choice. While the reversal has been significant, future earnings discounting remains high historically. In either case, bubbles tend to overcorrect (sell off more than the fundamentals suggest) rather than simply deflate. But I wanted to share these updated readings with you in light of recent market activity.
Chritiaan Hetzner
3 years ago
Mystery of the $1 billion'meme stock' that went to $400 billion in days
Who is AMTD Digital?
An unknown Hong Kong corporation joined the global megacaps worth over $500 billion on Tuesday.
The American Depository Share (ADS) with the ticker code HKD gapped at the open, soaring 25% over the previous closing price as trading began, before hitting an intraday high of $2,555.
At its peak, its market cap was almost $450 billion, more than Facebook parent Meta or Alibaba.
Yahoo Finance reported a daily volume of 350,500 shares, the lowest since the ADS began trading and much below the average of 1.2 million.
Despite losing a fifth of its value on Wednesday, it's still worth more than Toyota, Nike, McDonald's, or Walt Disney.
The company sold 16 million shares at $7.80 each in mid-July, giving it a $1 billion market valuation.
Why the boom?
That market cap seems unjustified.
According to SEC reports, its income-generating assets barely topped $400 million in March. Fortune's emails and calls went unanswered.
Website discloses little about company model. Its one-minute business presentation film uses a Star Wars–like design to sell the company as a "one-stop digital solutions platform in Asia"
The SEC prospectus explains.
AMTD Digital sells a "SpiderNet Ecosystems Solutions" kind of club membership that connects enterprises. This is the bulk of its $25 million annual revenue in April 2021.
Pretax profits have been higher than top line over the past three years due to fair value accounting gains on Appier, DayDayCook, WeDoctor, and five Asian fintechs.
AMTD Group, the company's parent, specializes in investment banking, hotel services, luxury education, and media and entertainment. AMTD IDEA, a $14 billion subsidiary, is also traded on the NYSE.
“Significant volatility”
Why AMTD Digital listed in the U.S. is unknown, as it informed investors in its share offering prospectus that could delist under SEC guidelines.
Beijing's red tape prevents the Sarbanes-Oxley Board from inspecting its Chinese auditor.
This frustrates Chinese stock investors. If the U.S. and China can't achieve a deal, 261 Chinese companies worth $1.3 trillion might be delisted.
Calvin Choi left UBS to become AMTD Group's CEO.
His capitalist background and status as a Young Global Leader with the World Economic Forum don't stop him from praising China's Communist party or celebrating the "glory and dream of the Great Rejuvenation of the Chinese nation" a century after its creation.
Despite having an executive vice chairman with a record of battling corruption and ties to Carrie Lam, Beijing's previous proconsul in Hong Kong, Choi is apparently being targeted for a two-year industry ban by the city's securities regulator after an investor accused Choi of malfeasance.
Some CMIG-funded initiatives produced money, but he didn't give us the proceeds, a corporate official told China's Caixin in October 2020. We don't know if he misappropriated or lost some money.
A seismic anomaly
In fundamental analysis, where companies are valued based on future cash flows, AMTD Digital's mind-boggling market cap is a statistical aberration that should occur once every hundred years.
AMTD Digital doesn't know why it's so valuable. In a thank-you letter to new shareholders, it said it was confused by the stock's performance.
Since its IPO, the company has seen significant ADS price volatility and active trading volume, it said Tuesday. "To our knowledge, there have been no important circumstances, events, or other matters since the IPO date."
Permabears awoke after the jump. Jim Chanos asked if "we're all going to ignore the $400 billion meme stock in the room," while Nate Anderson called AMTD Group "sketchy."
It happened the same day SEC Chair Gary Gensler praised the 20th anniversary of the Sarbanes-Oxley Act, aimed to restore trust in America's financial markets after the Enron and WorldCom accounting fraud scandals.
The run-up revived unpleasant memories of Robinhood's decision to limit retail investors' ability to buy GameStop, regarded as a measure to protect hedge funds invested in the meme company.
Why wasn't HKD's buy button removed? Because retail wasn't behind it?" tweeted Gensler on Tuesday. "Real stock fraud. "You're worthless."
You might also like
Caspar Mahoney
2 years ago
Changing Your Mindset From a Project to a Product
Product game mindsets? How do these vary from Project mindset?
1950s spawned the Iron Triangle. Project people everywhere know and live by it. In stakeholder meetings, it is used to stretch the timeframe, request additional money, or reduce scope.
Quality was added to this triangle as things matured.
Quality was intended to be transformative, but none of these principles addressed why we conduct projects.
Value and benefits are key.
Product value is quantified by ROI, revenue, profit, savings, or other metrics. For me, every project or product delivery is about value.
Most project managers, especially those schooled 5-10 years or more ago (thousands working in huge corporations worldwide), understand the world in terms of the iron triangle. What does that imply? They worry about:
a) enough time to get the thing done.
b) have enough resources (budget) to get the thing done.
c) have enough scope to fit within (a) and (b) >> note, they never have too little scope, not that I have ever seen! although, theoretically, this could happen.
Boom—iron triangle.
To make the triangle function, project managers will utilize formal governance (Steering) to move those things. Increase money, scope, or both if time is short. Lacking funds? Increase time, scope, or both.
In current product development, shifting each item considerably may not yield value/benefit.
Even terrible. This approach will fail because it deprioritizes Value/Benefit by focusing the major stakeholders (Steering participants) and delivery team(s) on Time, Scope, and Budget restrictions.
Pre-agile, this problem was terrible. IT projects failed wildly. History is here.
Value, or benefit, is central to the product method. Product managers spend most of their time planning value-delivery paths.
Product people consider risk, schedules, scope, and budget, but value comes first. Let me illustrate.
Imagine managing internal products in an enterprise. Your core customer team needs a rapid text record of a chat to fix a problem. The consumer wants a feature/features added to a product you're producing because they think it's the greatest spot.
Project-minded, I may say;
Ok, I have budget as this is an existing project, due to run for a year. This is a new requirement to add to the features we’re already building. I think I can keep the deadline, and include this scope, as it sounds related to the feature set we’re building to give the desired result”.
This attitude repeats Scope, Time, and Budget.
Since it meets those standards, a project manager will likely approve it. If they have a backlog, they may add it and start specking it out assuming it will be built.
Instead, think like a product;
What problem does this feature idea solve? Is that problem relevant to the product I am building? Can that problem be solved quicker/better via another route ? Is it the most valuable problem to solve now? Is the problem space aligned to our current or future strategy? or do I need to alter/update the strategy?
A product mindset allows you to focus on timing, resource/cost, feasibility, feature detail, and so on after answering the aforementioned questions.
The above oversimplifies because
Leadership in discovery
Project managers are facilitators of ideas. This is as far as they normally go in the ‘idea’ space.
Business Requirements collection in classic project delivery requires extensive upfront documentation.
Agile project delivery analyzes requirements iteratively.
However, the project manager is a facilitator/planner first and foremost, therefore topic knowledge is not expected.
I mean business domain, not technical domain (to confuse matters, it is true that in some instances, it can be both technical and business domains that are important for a single individual to master).
Product managers are domain experts. They will become one if they are training/new.
They lead discovery.
Product Manager-led discovery is much more than requirements gathering.
Requirements gathering involves a Business Analyst interviewing people and documenting their requests.
The project manager calculates what fits and what doesn't using their Iron Triangle (presumably in their head) and reports back to Steering.
If this requirements-gathering exercise failed to identify requirements, what would a project manager do? or bewildered by project requirements and scope?
They would tell Steering they need a Business SME or Business Lead assigning or more of their time.
Product discovery requires the Product Manager's subject knowledge and a new mindset.
How should a Product Manager handle confusing requirements?
Product Managers handle these challenges with their talents and tools. They use their own knowledge to fill in ambiguity, but they have the discipline to validate those assumptions.
To define the problem, they may perform qualitative or quantitative primary research.
They might discuss with UX and Engineering on a whiteboard and test assumptions or hypotheses.
Do Product Managers escalate confusing requirements to Steering/Senior leaders? They would fix that themselves.
Product managers raise unclear strategy and outcomes to senior stakeholders. Open talks, soft skills, and data help them do this. They rarely raise requirements since they have their own means of handling them without top stakeholder participation.
Discovery is greenfield, exploratory, research-based, and needs higher-order stakeholder management, user research, and UX expertise.
Product Managers also aid discovery. They lead discovery. They will not leave customer/user engagement to a Business Analyst. Administratively, a business analyst could aid. In fact, many product organizations discourage business analysts (rely on PM, UX, and engineer involvement with end-users instead).
The Product Manager must drive user interaction, research, ideation, and problem analysis, therefore a Product professional must be skilled and confident.
Creating vs. receiving and having an entrepreneurial attitude
Product novices and project managers focus on details rather than the big picture. Project managers prefer spreadsheets to strategy whiteboards and vision statements.
These folks ask their manager or senior stakeholders, "What should we do?"
They then elaborate (in Jira, in XLS, in Confluence or whatever).
They want that plan populated fast because it reduces uncertainty about what's going on and who's supposed to do what.
Skilled Product Managers don't only ask folks Should we?
They're suggesting this, or worse, Senior stakeholders, here are some options. After asking and researching, they determine what value this product adds, what problems it solves, and what behavior it changes.
Therefore, to move into Product, you need to broaden your view and have courage in your ability to discover ideas, find insightful pieces of information, and collate them to form a valuable plan of action. You are constantly defining RoI and building Business Cases, so much so that you no longer create documents called Business Cases, it is simply ingrained in your work through metrics, intelligence, and insights.
Product Management is not a free lunch.
Plateless.
Plates and food must be prepared.
In conclusion, Product Managers must make at least three mentality shifts:
You put value first in all things. Time, money, and scope are not as important as knowing what is valuable.
You have faith in the field and have the ability to direct the search. YYou facilitate, but you don’t just facilitate. You wouldn't want to limit your domain expertise in that manner.
You develop concepts, strategies, and vision. You are not a waiter or an inbox where other people can post suggestions; you don't merely ask folks for opinion and record it. However, you excel at giving things that aren't clearly spoken or written down physical form.
Hudson Rennie
3 years ago
Meet the $5 million monthly controversy-selling King of Toxic Masculinity.
Trigger warning — Andrew Tate is running a genius marketing campaign
Andrew Tate is a 2022 internet celebrity.
Kickboxing world champion became rich playboy with controversial views on gender roles.
Andrew's get-rich-quick scheme isn't new. His social media popularity is impressive.
He’s currently running one of the most genius marketing campaigns in history.
He pulls society's pendulum away from diversity and inclusion and toward diversion and exclusion. He's unstoppable.
Here’s everything you need to know about Andrew Tate. And how he’s playing chess while the world plays checkers.
Cobra Tate is the name he goes by.
American-born, English-raised entrepreneur Andrew Tate lives in Romania.
Romania? Says Andrew,
“I prefer a country in which corruption is available to everyone.”
Andrew was a professional kickboxer with the ring moniker Cobra before starting Hustlers University.
Before that, he liked chess and worshipped his father.
Emory Andrew Tate III is named after his grandmaster chess player father.
Emory was the first black-American chess champion. He was military, martial arts-trained, and multilingual. A superhuman.
He lived in his car to make ends meet.
Andrew and Tristan relocated to England with their mother when their parents split.
It was there that Andrew began his climb toward becoming one of the internet’s greatest villains.
Andrew fell in love with kickboxing.
Andrew spent his 20s as a professional kickboxer and reality TV star, featuring on Big Brother UK and The Ultimate Traveller.
These 3 incidents, along with a chip on his shoulder, foreshadowed Andrews' social media breakthrough.
Chess
Combat sports
Reality television
A dangerous trio.
Andrew started making money online after quitting kickboxing in 2017 due to an eye issue.
Andrew didn't suddenly become popular.
Andrew's web work started going viral in 2022.
Due to his contentious views on patriarchy and gender norms, he's labeled the King of Toxic Masculinity. His most contentious views (trigger warning):
“Women are intrinsically lazy.”
“Female promiscuity is disgusting.”
“Women shouldn’t drive cars or fly planes.”
“A lot of the world’s problems would be solved if women had their body count tattooed on their foreheads.”
Andrew's two main beliefs are:
“These are my personal opinions based on my experiences.”
2. “I believe men are better at some things and women are better at some things. We are not equal.”
Andrew intentionally offends.
Andrew's thoughts began circulating online in 2022.
In July 2022, he was one of the most Googled humans, surpassing:
Joe Biden
Donald Trump
Kim Kardashian
Andrews' rise is a mystery since no one can censure or suppress him. This is largely because Andrew nor his team post his clips.
But more on that later.
Andrew's path to wealth.
Andrew Tate is a self-made millionaire. His morality is uncertain.
Andrew and Tristan needed money soon after retiring from kickboxing.
“I owed some money to some dangerous people. I had $70K and needed $100K to stay alive.”
Andrews lost $20K on roulette at a local casino.
Andrew had one week to make $50,000, so he started planning. Andrew locked himself in a chamber like Thomas Edison to solve an energy dilemma.
He listed his assets.
Physical strength (but couldn’t fight)
a BMW (worth around $20K)
Intelligence (but no outlet)
A lightbulb.
He had an epiphany after viewing a webcam ad. He sought aid from women, ironically. His 5 international girlfriends are assets.
Then, a lightbulb.
Andrew and Tristan messaged and flew 7 women to a posh restaurant. Selling desperation masked as opportunity, Andrew pitched his master plan:
A webcam business — with a 50/50 revenue split.
5 women left.
2 stayed.
Andrew Tate, a broke kickboxer, became Top G, Cobra Tate.
The business model was simple — yet sad.
Andrew's girlfriends moved in with him and spoke online for 15+ hours a day. Andrew handled ads and equipment as the women posed.
Andrew eventually took over their keyboards, believing he knew what men wanted more than women.
Andrew detailed on the Full Send Podcast how he emotionally manipulated men for millions. They sold houses, automobiles, and life savings to fuel their companionship addiction.
When asked if he felt bad, Andrew said,
“F*ck no.“
Andrew and Tristan wiped off debts, hired workers, and diversified.
Tristan supervised OnlyFans models.
Andrew bought Romanian casinos and MMA league RXF (Real Xtreme Fighting).
Pandemic struck suddenly.
Andrew couldn't run his 2 businesses without a plan. Another easy moneymaker.
He banked on Hustlers University.
The actual cause of Andrew's ubiquity.
On a Your Mom’s House episode Andrew's 4 main revenue sources:
Hustler’s University
2. Owning casinos in Romania
3. Owning 10% of the Romanian MMA league “RXF”
4. “The War Room” — a society of rich and powerful men
When the pandemic hit, 3/4 became inoperable.
So he expanded Hustlers University.
But what is Hustler’s University?
Andrew says Hustlers University teaches 18 wealth-building tactics online. Examples:
Real estate
Copywriting
Amazon FBA
Dropshipping
Flipping Cryptos
How to swiftly become wealthy.
Lessons are imprecise, rudimentary, and macro-focused, say reviews. Invest wisely, etc. Everything is free online.
You pay for community. One unique income stream.
The only money-making mechanism that keeps the course from being a scam.
The truth is, many of Andrew’s students are actually making money. Maybe not from the free YouTube knowledge Andrew and his professors teach in the course, but through Hustler’s University’s affiliate program.
Affiliates earn 10% commission for each new student = $5.
Students can earn $10 for each new referral in the first two months.
Andrew earns $50 per membership per month.
This affiliate program isn’t anything special — in fact, it’s on the lower end of affiliate payouts. Normally, it wouldn’t be very lucrative.
But it has one secret weapon— Andrew and his viral opinions.
Andrew is viral. Andrew went on a media tour in January 2022 after appearing on Your Mom's House.
And many, many more…
He chatted with Twitch streamers. Hustlers University wanted more controversy (and clips).
Here’s the strategy behind Hustler’s University that has (allegedly) earned students upwards of $10K per month:
Make a social media profile with Andrew Tates' name and photo.
Post any of the online videos of Andrews that have gone viral.
Include a referral link in your bio.
Effectively simple.
Andrew's controversy attracts additional students. More student clips circulate as more join. Andrew's students earn more and promote the product as he goes viral.
A brilliant plan that's functioning.
At the beginning of his media tour, Hustler’s University had 5,000 students. 6 months in, and he now has over 100,000.
One income stream generates $5 million every month.
Andrew's approach is not new.
But it is different.
In the early 2010s, Tai Lopez dominated the internet.
His viral video showed his house.
“Here in my garage. Just bought this new Lamborghini.”
Tais' marketing focused on intellect, not strength, power, and wealth to attract women.
How reading quicker leads to financial freedom in 67 steps.
Years later, it was revealed that Tai Lopez rented the mansion and Lamborghini as a marketing ploy to build social proof. Meanwhile, he was living in his friend’s trailer.
Faked success is an old tactic.
Andrew is doing something similar. But with one major distinction.
Andrew outsources his virality — making him nearly impossible to cancel.
In 2022, authorities searched Andrews' estate over human trafficking suspicions. Investigation continues despite withdrawn charges.
Andrew's divisive nature would normally get him fired. Andrew's enterprises and celebrity don't rely on social media.
He doesn't promote or pay for ads. Instead, he encourages his students and anyone wishing to get rich quick to advertise his work.
Because everything goes through his affiliate program. Old saying:
“All publicity is good publicity.”
Final thoughts: it’s ok to feel triggered.
Tate is divisive.
His emotionally charged words are human nature. Andrews created the controversy.
It's non-personal.
His opinions are those of one person. Not world nor generational opinion.
Briefly:
It's easy to understand why Andrews' face is ubiquitous. Money.
The world wide web is a chessboard. Misdirection is part of it.
It’s not personal, it’s business.
Controversy sells
Sometimes understanding the ‘why’, can help you deal with the ‘what.’
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.