Bernard Lawrence "Bernie" Madoff, the largest Ponzi scheme in history
Madoff who?
Bernie Madoff ran the largest Ponzi scheme in history, defrauding thousands of investors over at least 17 years, and possibly longer. He pioneered electronic trading and chaired Nasdaq in the 1990s. On April 14, 2021, he died while serving a 150-year sentence for money laundering, securities fraud, and other crimes.
Understanding Madoff
Madoff claimed to generate large, steady returns through a trading strategy called split-strike conversion, but he simply deposited client funds into a single bank account and paid out existing clients. He funded redemptions by attracting new investors and their capital, but the market crashed in late 2008. He confessed to his sons, who worked at his firm, on Dec. 10, 2008. Next day, they turned him in. The fund reported $64.8 billion in client assets.
Madoff pleaded guilty to 11 federal felony counts, including securities fraud, wire fraud, mail fraud, perjury, and money laundering. Ponzi scheme became a symbol of Wall Street's greed and dishonesty before the financial crisis. Madoff was sentenced to 150 years in prison and ordered to forfeit $170 billion, but no other Wall Street figures faced legal ramifications.
Bernie Madoff's Brief Biography
Bernie Madoff was born in Queens, New York, on April 29, 1938. He began dating Ruth (née Alpern) when they were teenagers. Madoff told a journalist by phone from prison that his father's sporting goods store went bankrupt during the Korean War: "You watch your father, who you idolize, build a big business and then lose everything." Madoff was determined to achieve "lasting success" like his father "whatever it took," but his career had ups and downs.
Early Madoff investments
At 22, he started Bernard L. Madoff Investment Securities LLC. First, he traded penny stocks with $5,000 he earned installing sprinklers and as a lifeguard. Family and friends soon invested with him. Madoff's bets soured after the "Kennedy Slide" in 1962, and his father-in-law had to bail him out.
Madoff felt he wasn't part of the Wall Street in-crowd. "We weren't NYSE members," he told Fishman. "It's obvious." According to Madoff, he was a scrappy market maker. "I was happy to take the crumbs," he told Fishman, citing a client who wanted to sell eight bonds; a bigger firm would turn it down.
Recognition
Success came when he and his brother Peter built electronic trading capabilities, or "artificial intelligence," that attracted massive order flow and provided market insights. "I had all these major banks coming down, entertaining me," Madoff told Fishman. "It was mind-bending."
By the late 1980s, he and four other Wall Street mainstays processed half of the NYSE's order flow. Controversially, he paid for much of it, and by the late 1980s, Madoff was making in the vicinity of $100 million a year. He was Nasdaq chairman from 1990 to 1993.
Madoff's Ponzi scheme
It is not certain exactly when Madoff's Ponzi scheme began. He testified in court that it began in 1991, but his account manager, Frank DiPascali, had been at the firm since 1975.
Why Madoff did the scheme is unclear. "I had enough money to support my family's lifestyle. "I don't know why," he told Fishman." Madoff could have won Wall Street's respect as a market maker and electronic trading pioneer.
Madoff told Fishman he wasn't solely responsible for the fraud. "I let myself be talked into something, and that's my fault," he said, without saying who convinced him. "I thought I could escape eventually. I thought it'd be quick, but I couldn't."
Carl Shapiro, Jeffry Picower, Stanley Chais, and Norm Levy have been linked to Bernard L. Madoff Investment Securities LLC for years. Madoff's scheme made these men hundreds of millions of dollars in the 1960s and 1970s.
Madoff told Fishman, "Everyone was greedy, everyone wanted to go on." He says the Big Four and others who pumped client funds to him, outsourcing their asset management, must have suspected his returns or should have. "How can you make 15%-18% when everyone else is making less?" said Madoff.
How Madoff Got Away with It for So Long
Madoff's high returns made clients look the other way. He deposited their money in a Chase Manhattan Bank account, which merged to become JPMorgan Chase & Co. in 2000. The bank may have made $483 million from those deposits, so it didn't investigate.
When clients redeemed their investments, Madoff funded the payouts with new capital he attracted by promising unbelievable returns and earning his victims' trust. Madoff created an image of exclusivity by turning away clients. This model let half of Madoff's investors profit. These investors must pay into a victims' fund for defrauded investors.
Madoff wooed investors with his philanthropy. He defrauded nonprofits, including the Elie Wiesel Foundation for Peace and Hadassah. He approached congregants through his friendship with J. Ezra Merkin, a synagogue officer. Madoff allegedly stole $1 billion to $2 billion from his investors.
Investors believed Madoff for several reasons:
- His public portfolio seemed to be blue-chip stocks.
- His returns were high (10-20%) but consistent and not outlandish. In a 1992 interview with Madoff, the Wall Street Journal reported: "[Madoff] insists the returns were nothing special, given that the S&P 500-stock index returned 16.3% annually from 1982 to 1992. 'I'd be surprised if anyone thought matching the S&P over 10 years was remarkable,' he says.
- "He said he was using a split-strike collar strategy. A collar protects underlying shares by purchasing an out-of-the-money put option.
SEC inquiry
The Securities and Exchange Commission had been investigating Madoff and his securities firm since 1999, which frustrated many after he was prosecuted because they felt the biggest damage could have been prevented if the initial investigations had been rigorous enough.
Harry Markopolos was a whistleblower. In 1999, he figured Madoff must be lying in an afternoon. The SEC ignored his first Madoff complaint in 2000.
Markopolos wrote to the SEC in 2005: "The largest Ponzi scheme is Madoff Securities. This case has no SEC reward, so I'm turning it in because it's the right thing to do."
Many believed the SEC's initial investigations could have prevented Madoff's worst damage.
Markopolos found irregularities using a "Mosaic Method." Madoff's firm claimed to be profitable even when the S&P fell, which made no mathematical sense given what he was investing in. Markopolos said Madoff Securities' "undisclosed commissions" were the biggest red flag (1 percent of the total plus 20 percent of the profits).
Markopolos concluded that "investors don't know Bernie Madoff manages their money." Markopolos learned Madoff was applying for large loans from European banks (seemingly unnecessary if Madoff's returns were high).
The regulator asked Madoff for trading account documentation in 2005, after he nearly went bankrupt due to redemptions. The SEC drafted letters to two of the firms on his six-page list but didn't send them. Diana Henriques, author of "The Wizard of Lies: Bernie Madoff and the Death of Trust," documents the episode.
In 2008, the SEC was criticized for its slow response to Madoff's fraud.
Confession, sentencing of Bernie Madoff
Bernard L. Madoff Investment Securities LLC reported 5.6% year-to-date returns in November 2008; the S&P 500 fell 39%. As the selling continued, Madoff couldn't keep up with redemption requests, and on Dec. 10, he confessed to his sons Mark and Andy, who worked at his firm. "After I told them, they left, went to a lawyer, who told them to turn in their father, and I never saw them again. 2008-12-11: Bernie Madoff arrested.
Madoff insists he acted alone, but several of his colleagues were jailed. Mark Madoff died two years after his father's fraud was exposed. Madoff's investors committed suicide. Andy Madoff died of cancer in 2014.
2009 saw Madoff's 150-year prison sentence and $170 billion forfeiture. Marshals sold his three homes and yacht. Prisoner 61727-054 at Butner Federal Correctional Institution in North Carolina.
Madoff's lawyers requested early release on February 5, 2020, claiming he has a terminal kidney disease that may kill him in 18 months. Ten years have passed since Madoff's sentencing.
Bernie Madoff's Ponzi scheme aftermath
The paper trail of victims' claims shows Madoff's complexity and size. Documents show Madoff's scam began in the 1960s. His final account statements show $47 billion in "profit" from fake trades and shady accounting.
Thousands of investors lost their life savings, and multiple stories detail their harrowing loss.
Irving Picard, a New York lawyer overseeing Madoff's bankruptcy, has helped investors. By December 2018, Picard had recovered $13.3 billion from Ponzi scheme profiteers.
A Madoff Victim Fund (MVF) was created in 2013 to help compensate Madoff's victims, but the DOJ didn't start paying out the $4 billion until late 2017. Richard Breeden, a former SEC chair who oversees the fund, said thousands of claims were from "indirect investors"
Breeden and his team had to reject many claims because they weren't direct victims. Breeden said he based most of his decisions on one simple rule: Did the person invest more than they withdrew? Breeden estimated 11,000 "feeder" investors.
Breeden wrote in a November 2018 update for the Madoff Victim Fund, "We've paid over 27,300 victims 56.65% of their losses, with thousands more to come." In December 2018, 37,011 Madoff victims in the U.S. and around the world received over $2.7 billion. Breeden said the fund expected to make "at least one more significant distribution in 2019"
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More on Economics & Investing

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.

Ben Carlson
3 years ago
Bear market duration and how to invest during one
Bear markets don't last forever, but that's hard to remember. Jamie Cullen's illustration
A bear market is a 20% decline from peak to trough in stock prices.
The S&P 500 was down 24% from its January highs at its low point this year. Bear market.
The U.S. stock market has had 13 bear markets since WWII (including the current one). Previous 12 bear markets averaged –32.7% losses. From peak to trough, the stock market averaged 12 months. The average time from bottom to peak was 21 months.
In the past seven decades, a bear market roundtrip to breakeven has averaged less than three years.
Long-term averages can vary widely, as with all historical market data. Investors can learn from past market crashes.
Historical bear markets offer lessons.
Bear market duration
A bear market can cost investors money and time. Most of the pain comes from stock market declines, but bear markets can be long.
Here are the longest U.S. stock bear markets since World war 2:
Stock market crashes can make it difficult to break even. After the 2008 financial crisis, the stock market took 4.5 years to recover. After the dotcom bubble burst, it took seven years to break even.
The longer you're underwater in the market, the more suffering you'll experience, according to research. Suffering can lead to selling at the wrong time.
Bear markets require patience because stocks can take a long time to recover.
Stock crash recovery
Bear markets can end quickly. The Corona Crash in early 2020 is an example.
The S&P 500 fell 34% in 23 trading sessions, the fastest bear market from a high in 90 years. The entire crash lasted one month. Stocks broke even six months after bottoming. Stocks rose 100% from those lows in 15 months.
Seven bear markets have lasted two years or less since 1945.
The 2020 recovery was an outlier, but four other bear markets have made investors whole within 18 months.
During a bear market, you don't know if it will end quickly or feel like death by a thousand cuts.
Recessions vs. bear markets
Many people believe the U.S. economy is in or heading for a recession.
I agree. Four-decade high inflation. Since 1945, inflation has exceeded 5% nine times. Each inflationary spike caused a recession. Only slowing economic demand seems to stop price spikes.
This could happen again. Stocks seem to be pricing in a recession.
Recessions almost always cause a bear market, but a bear market doesn't always equal a recession. In 1946, the stock market fell 27% without a recession in sight. Without an economic slowdown, the stock market fell 22% in 1966. Black Monday in 1987 was the most famous stock market crash without a recession. Stocks fell 30% in less than a week. Many believed the stock market signaled a depression. The crash caused no slowdown.
Economic cycles are hard to predict. Even Wall Street makes mistakes.
Bears vs. bulls
Bear markets for U.S. stocks always end. Every stock market crash in U.S. history has been followed by new all-time highs.
How should investors view the recession? Investing risk is subjective.
You don't have as long to wait out a bear market if you're retired or nearing retirement. Diversification and liquidity help investors with limited time or income. Cash and short-term bonds drag down long-term returns but can ensure short-term spending.
Young people with years or decades ahead of them should view this bear market as an opportunity. Stock market crashes are good for net savers in the future. They let you buy cheap stocks with high dividend yields.
You need discipline, patience, and planning to buy stocks when it doesn't feel right.
Bear markets aren't fun because no one likes seeing their portfolio fall. But stock market downturns are a feature, not a bug. If stocks never crashed, they wouldn't offer such great long-term returns.

Cody Collins
2 years ago
The direction of the economy is as follows.
What quarterly bank earnings reveal
Big banks know the economy best. Unless we’re talking about a housing crisis in 2007…
Banks are crucial to the U.S. economy. The Fed, communities, and investments exchange money.
An economy depends on money flow. Banks' views on the economy can affect their decision-making.
Most large banks released quarterly earnings and forward guidance last week. Others were pessimistic about the future.
What Makes Banks Confident
Bank of America's profit decreased 30% year-over-year, but they're optimistic about the economy. Comparatively, they're bullish.
Who banks serve affects what they see. Bank of America supports customers.
They think consumers' future is bright. They believe this for many reasons.
The average customer has decent credit, unless the system is flawed. Bank of America's new credit card and mortgage borrowers averaged 771. New-car loan and home equity borrower averages were 791 and 797.
2008's housing crisis affected people with scores below 620.
Bank of America and the economy benefit from a robust consumer. Major problems can be avoided if individuals maintain spending.
Reasons Other Banks Are Less Confident
Spending requires income. Many companies, mostly in the computer industry, have announced they will slow or freeze hiring. Layoffs are frequently an indication of poor times ahead.
BOA is positive, but investment banks are bearish.
Jamie Dimon, CEO of JPMorgan, outlined various difficulties our economy could confront.
But geopolitical tension, high inflation, waning consumer confidence, the uncertainty about how high rates have to go and the never-before-seen quantitative tightening and their effects on global liquidity, combined with the war in Ukraine and its harmful effect on global energy and food prices are very likely to have negative consequences on the global economy sometime down the road.
That's more headwinds than tailwinds.
JPMorgan, which helps with mergers and IPOs, is less enthusiastic due to these concerns. Incoming headwinds signal drying liquidity, they say. Less business will be done.
Final Reflections
I don't think we're done. Yes, stocks are up 10% from a month ago. It's a long way from old highs.
I don't think the stock market is a strong economic indicator.
Many executives foresee a 2023 recession. According to the traditional definition, we may be in a recession when Q2 GDP statistics are released next week.
Regardless of criteria, I predict the economy will have a terrible year.
Weekly layoffs are announced. Inflation persists. Will prices return to 2020 levels if inflation cools? Perhaps. Still expensive energy. Ukraine's war has global repercussions.
I predict BOA's next quarter earnings won't be as bullish about the consumer's strength.
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Katherine Kornei
3 years ago
The InSight lander from NASA has recorded the greatest tremor ever felt on Mars.
The magnitude 5 earthquake was responsible for the discharge of energy that was 10 times greater than the previous record holder.
Any Martians who happen to be reading this should quickly learn how to duck and cover.
NASA's Jet Propulsion Laboratory in Pasadena, California, reported that on May 4, the planet Mars was shaken by an earthquake of around magnitude 5, making it the greatest Marsquake ever detected to this point. The shaking persisted for more than six hours and unleashed more than ten times as much energy as the earthquake that had previously held the record for strongest.
The event was captured on record by the InSight lander, which is operated by the United States Space Agency and has been researching the innards of Mars ever since it touched down on the planet in 2018 (SN: 11/26/18). The epicenter of the earthquake was probably located in the vicinity of Cerberus Fossae, which is located more than 1,000 kilometers away from the lander.
The surface of Cerberus Fossae is notorious for being broken up and experiencing periodic rockfalls. According to geophysicist Philippe Lognonné, who is the lead investigator of the Seismic Experiment for Interior Structure, the seismometer that is onboard the InSight lander, it is reasonable to assume that the ground is moving in that area. "This is an old crater from a volcanic eruption."
Marsquakes, which are similar to earthquakes in that they give information about the interior structure of our planet, can be utilized to investigate what lies beneath the surface of Mars (SN: 7/22/21). And according to Lognonné, who works at the Institut de Physique du Globe in Paris, there is a great deal that can be gleaned from analyzing this massive earthquake. Because the quality of the signal is so high, we will be able to focus on the specifics.

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.

The woman
3 years ago
Because he worked on his side projects during working hours, my junior was fired and sued.
Many developers do it, but I don't approve.
Aren't many programmers part-time? Many work full-time but also freelance. If the job agreement allows it, I see no problem.
Tech businesses' policies vary. I have a friend in Google, Germany. According to his contract, he couldn't do an outside job. Google owns any code he writes while employed.
I was shocked. Later, I found that different Google regions have different policies.
A corporation can normally establish any agreement before hiring you. They're negotiable. When there's no agreement, state law may apply. In court, law isn't so simple.
I won't delve into legal details. Instead, let’s talk about the incident.
How he was discovered
In one month, he missed two deadlines. His boss was frustrated because the assignment wasn't difficult to miss twice. When a team can't finish work on time, they all earn bad grades.
He annoyed the whole team. One team member (anonymous) told the project manager he worked on side projects during office hours. He may have missed deadlines because of this.
The project manager was furious. He needed evidence. The manager caught him within a week. The manager told higher-ups immediately.
The company wanted to set an example
Management could terminate him and settle the problem. But the company wanted to set an example for those developers who breached the regulation.
Because dismissal isn't enough. Every organization invests heavily in developer hiring. If developers depart or are fired after a few months, the company suffers.
The developer spent 10 months there. The employer sacked him and demanded ten months' pay. Or they'd sue him.
It was illegal and unethical. The youngster paid the fine and left the company quietly to protect his career.
Right or wrong?
Is the developer's behavior acceptable? Let's discuss developer malpractice.
During office hours, may developers work on other projects? If they're bored during office hours, they might not. Check the employment contract or state law.
If there's no employment clause, check country/state law. Because you can't justify breaking the law. Always. Most employers own their employees' work hours unless it's a contractual position.
If the company agrees, it's fine.
I also oppose companies that force developers to work overtime without pay.
Most states and countries have laws that help companies and workers. Law supports employers in this case. If any of the following are true, the company/employer owns the IP under California law.
using the business's resources
any equipment, including a laptop used for business.
company's mobile device.
offices of the company.
business time as well. This is crucial. Because this occurred in the instance of my junior.
Company resources are dangerous. Because your company may own the product's IP. If you have seen the TV show Silicon Valley, you have seen a similar situation there, right?
Conclusion
Simple rule. I avoid big side projects. I work on my laptop on weekends for side projects. I'm safe. But I also know that my company might not be happy with that.
As an employee, I suppose I can. I can make side money. I won't promote it, but I'll respect their time, resources, and task. I also sometimes work extra time to finish my company’s deadlines.
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