More on Web3 & Crypto
Vitalik
4 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
Nabil Alouani
3 years ago
Why Cryptocurrency Is Not Dead Despite the FTX Scam
A fraud, free-market, antifragility tale
Crypto's only rival is public opinion.
In less than a week, mainstream media, bloggers, and TikTokers turned on FTX's founder.
While some were surprised, almost everyone with a keyboard and a Twitter account predicted the FTX collapse. These financial oracles should have warned the 1.2 million people Sam Bankman-Fried duped.
After happening, unexpected events seem obvious to our brains. It's a bug and a feature because it helps us cope with disasters and makes our reasoning suck.
Nobody predicted the FTX debacle. Bloomberg? Politicians. Non-famous. No cryptologists. Who?
When FTX imploded, taking billions of dollars with it, an outrage bomb went off, and the resulting shockwave threatens the crypto market's existence.
As someone who lost more than $78,000 in a crypto scam in 2020, I can only understand people’s reactions. When the dust settles and rationality returns, we'll realize this is a natural occurrence in every free market.
What specifically occurred with FTX? (Skip if you are aware.)
FTX is a cryptocurrency exchange where customers can trade with cash. It reached #3 in less than two years as the fastest-growing platform of its kind.
FTX's performance helped make SBF the crypto poster boy. Other reasons include his altruistic public image, his support for the Democrats, and his company Alameda Research.
Alameda Research made a fortune arbitraging Bitcoin.
Arbitrage trading uses small price differences between two markets to make money. Bitcoin costs $20k in Japan and $21k in the US. Alameda Research did that for months, making $1 million per day.
Later, as its capital grew, Alameda expanded its trading activities and began investing in other companies.
Let's now discuss FTX.
SBF's diabolic master plan began when he used FTX-created FTT coins to inflate his trading company's balance sheets. He used inflated Alameda numbers to secure bank loans.
SBF used money he printed himself as collateral to borrow billions for capital. Coindesk exposed him in a report.
One of FTX's early investors tweeted that he planned to sell his FTT coins over the next few months. This would be a minor event if the investor wasn't Binance CEO Changpeng Zhao (CZ).
The crypto space saw a red WARNING sign when CZ cut ties with FTX. Everyone with an FTX account and a brain withdrew money. Two events followed. FTT fell from $20 to $4 in less than 72 hours, and FTX couldn't meet withdrawal requests, spreading panic.
SBF reassured FTX users on Twitter. Good assets.
He lied.
SBF falsely claimed FTX had a liquidity crunch. At the time of his initial claims, FTX owed about $8 billion to its customers. Liquidity shortages are usually minor. To get cash, sell assets. In the case of FTX, the main asset was printed FTT coins.
Sam wouldn't get out of trouble even if he slashed the discount (from $20 to $4) and sold every FTT. He'd flood the crypto market with his homemade coins, causing the price to crash.
SBF was trapped. He approached Binance about a buyout, which seemed good until Binance looked at FTX's books.
Binance's tweet ended SBF, and he had to apologize, resign as CEO, and file for bankruptcy.
Bloomberg estimated Sam's net worth to be zero by the end of that week. 0!
But that's not all. Twitter investigations exposed fraud at FTX and Alameda Research. SBF used customer funds to trade and invest in other companies.
Thanks to the Twitter indie reporters who made the mainstream press look amateurish. Some Twitter detectives didn't sleep for 30 hours to find answers. Others added to existing threads. Memes were hilarious.
One question kept repeating in my bald head as I watched the Blue Bird. Sam, WTF?
Then I understood.
SBF wanted that FTX becomes a bank.
Think about this. FTX seems healthy a few weeks ago. You buy 2 bitcoins using FTX. You'd expect the platform to take your dollars and debit your wallet, right?
No. They give I-Owe-Yous.
FTX records owing you 2 bitcoins in its internal ledger but doesn't credit your account. Given SBF's tricks, I'd bet on nothing.
What happens if they don't credit my account with 2 bitcoins? Your money goes into FTX's capital, where SBF and his friends invest in marketing, political endorsements, and buying other companies.
Over its two-year existence, FTX invested in 130 companies. Once they make a profit on their purchases, they'll pay you and keep the rest.
One detail makes their strategy dumb. If all FTX customers withdraw at once, everything collapses.
Financially savvy people think FTX's collapse resembles a bank run, and they're right. SBF designed FTX to operate like a bank.
You expect your bank to open a drawer with your name and put $1,000 in it when you deposit $1,000. They deposit $100 in your drawer and create an I-Owe-You for $900. What happens to $900?
Let's sum it up: It's boring and headache-inducing.
When you deposit money in a bank, they can keep 10% and lend the rest. Fractional Reserve Banking is a popular method. Fractional reserves operate within and across banks.
Fractional reserve banking generates $10,000 for every $1,000 deposited. People will pay off their debt plus interest.
As long as banks work together and the economy grows, their model works well.
SBF tried to replicate the system but forgot two details. First, traditional banks need verifiable collateral like real estate, jewelry, art, stocks, and bonds, not digital coupons. Traditional banks developed a liquidity buffer. The Federal Reserve (or Central Bank) injects massive cash into troubled banks.
Massive cash injections come from taxpayers. You and I pay for bankers' mistakes and annual bonuses. Yes, you may think banking is rigged. It's rigged, but it's the best financial game in 150 years. We accept its flaws, including bailouts for too-big-to-fail companies.
Anyway.
SBF wanted Binance's bailout. Binance said no, which was good for the crypto market.
Free markets are resilient.
Nassim Nicholas Taleb coined the term antifragility.
“Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile. Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.”
The easiest way to understand how antifragile systems behave is to compare them with other types of systems.
Glass is like a fragile system. It snaps when shocked.
Similar to rubber, a resilient system. After a stressful episode, it bounces back.
A system that is antifragile is similar to a muscle. As it is torn in the gym, it gets stronger.
Time-changed things are antifragile. Culture, tech innovation, restaurants, revolutions, book sales, cuisine, economic success, and even muscle shape. These systems benefit from shocks and randomness in different ways, but they all pay a price for antifragility.
Same goes for the free market and financial institutions. Taleb's book uses restaurants as an example and ends with a reference to the 2008 crash.
“Restaurants are fragile. They compete with each other. But the collective of local restaurants is antifragile for that very reason. Had restaurants been individually robust, hence immortal, the overall business would be either stagnant or weak and would deliver nothing better than cafeteria food — and I mean Soviet-style cafeteria food. Further, it [the overall business] would be marred with systemic shortages, with once in a while a complete crisis and government bailout.”
Imagine the same thing with banks.
Independent banks would compete to offer the best services. If one of these banks fails, it will disappear. Customers and investors will suffer, but the market will recover from the dead banks' mistakes.
This idea underpins a free market. Bitcoin and other cryptocurrencies say this when criticizing traditional banking.
The traditional banking system's components never die. When a bank fails, the Federal Reserve steps in with a big taxpayer-funded check. This hinders bank evolution. If you don't let banking cells die and be replaced, your financial system won't be antifragile.
The interdependence of banks (centralization) means that one bank's mistake can sink the entire fleet, which brings us to SBF's ultimate travesty with FTX.
FTX has left the cryptocurrency gene pool.
FTX should be decentralized and independent. The super-star scammer invested in more than 130 crypto companies and linked them, creating a fragile banking-like structure. FTX seemed to say, "We exist because centralized banks are bad." But we'll be good, unlike the centralized banking system.
FTX saved several companies, including BlockFi and Voyager Digital.
FTX wanted to be a crypto bank conglomerate and Federal Reserve. SBF wanted to monopolize crypto markets. FTX wanted to be in bed with as many powerful people as possible, so SBF seduced politicians and celebrities.
Worst? People who saw SBF's plan flaws praised him. Experts, newspapers, and crypto fans praised FTX. When billions pour in, it's hard to realize FTX was acting against its nature.
Then, they act shocked when they realize FTX's fall triggered a domino effect. Some say the damage could wipe out the crypto market, but that's wrong.
Cell death is different from body death.
FTX is out of the game despite its size. Unfit, it fell victim to market natural selection.
Next?
The challengers keep coming. The crypto economy will improve with each failure.
Free markets are antifragile because their fragile parts compete, fostering evolution. With constructive feedback, evolution benefits customers and investors.
FTX shows that customers don't like being scammed, so the crypto market's health depends on them. Charlatans and con artists are eliminated quickly or slowly.
Crypto isn't immune to collapse. Cryptocurrencies can go extinct like biological species. Antifragility isn't immortality. A few more decades of evolution may be enough for humans to figure out how to best handle money, whether it's bitcoin, traditional banking, gold, or something else.
Keep your BS detector on. Start by being skeptical of this article's finance-related claims. Even if you think you understand finance, join the conversation.
We build a better future through dialogue. So listen, ask, and share. When you think you can't find common ground with the opposing view, remember:
Sam Bankman-Fried lied.
Jayden Levitt
3 years ago
The country of El Salvador's Bitcoin-obsessed president lost $61.6 million.
It’s only a loss if you sell, right?
Nayib Bukele proclaimed himself “the world’s coolest dictator”.
His jokes aren't clear.
El Salvador's 43rd president self-proclaimed “CEO of El Salvador” couldn't be less presidential.
His thin jeans, aviator sunglasses, and baseball caps like a cartel lord.
He's popular, though.
Bukele won 53% of the vote by fighting violent crime and opposition party corruption.
El Salvador's 6.4 million inhabitants are riding the cryptocurrency volatility wave.
They were powerless.
Their autocratic leader, a former Yamaha Motors salesperson and Bitcoin believer, wants to help 70% unbanked locals.
He intended to give the citizens a way to save money and cut the country's $200 million remittance cost.
Transfer and deposit costs.
This makes logical sense when the president’s theatrics don’t blind you.
El Salvador's Bukele revealed plans to make bitcoin legal tender.
Remittances total $5.9 billion (23%) of the country's expenses.
Anything that reduces costs could boost the economy.
The country’s unbanked population is staggering. Here’s the data by % of people who either have a bank account (Blue) or a mobile money account (Black).
According to Bukele, 46% of the population has downloaded the Chivo Bitcoin Wallet.
In 2021, 36% of El Salvadorans had bank accounts.
Large rural countries like Kenya seem to have resolved their unbanked dilemma.
An economy surfaced where village locals would sell, trade and store network minutes and data as a store of value.
Kenyan phone networks realized unbanked people needed a safe way to accumulate wealth and have an emergency fund.
96% of Kenyans utilize M-PESA, which doesn't require a bank account.
The software involves human agents who hang out with cash and a phone.
These people are like ATMs.
You offer them cash to deposit money in your mobile money account or withdraw cash.
In a country with a faulty banking system, cash availability and a safe place to deposit it are important.
William Jack and Tavneet Suri found that M-PESA brought 194,000 Kenyan households out of poverty by making transactions cheaper and creating a safe store of value.
Mobile money, a service that allows monetary value to be stored on a mobile phone and sent to other users via text messages, has been adopted by most Kenyan households. We estimate that access to the Kenyan mobile money system M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty.
The impacts, which are more pronounced for female-headed households, appear to be driven by changes in financial behaviour — in particular, increased financial resilience and saving. Mobile money has therefore increased the efficiency of the allocation of consumption over time while allowing a more efficient allocation of labour, resulting in a meaningful reduction of poverty in Kenya.
Currently, El Salvador has 2,301 Bitcoin.
At publication, it's worth $44 million. That remains 41% of Bukele's original $105.6 million.
Unknown if the country has sold Bitcoin, but Bukeles keeps purchasing the dip.
It's still falling.
This might be a fantastic move for the impoverished country over the next five years, if they can live economically till Bitcoin's price recovers.
The evidence demonstrates that a store of value pulls individuals out of poverty, but others say Bitcoin is premature.
You may regard it as an aggressive endeavor to front run the next wave of adoption, offering El Salvador a financial upside.
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Rajesh Gupta
3 years ago
Why Is It So Difficult to Give Up Smoking?
I started smoking in 2002 at IIT BHU. Most of us thought it was enjoyable at first. I didn't realize the cost later.
In 2005, during my final semester, I lost my father. Suddenly, I felt more accountable for my mother and myself.
I quit before starting my first job in Bangalore. I didn't see any smoking friends in my hometown for 2 months before moving to Bangalore.
For the next 5-6 years, I had no regimen and smoked only when drinking.
Due to personal concerns, I started smoking again after my 2011 marriage. Now smoking was a constant guilty pleasure.
I smoked 3-4 cigarettes a day, but never in front of my family or on weekends. I used to excuse this with pride! First office ritual: smoking. Even with guilt, I couldn't stop this time because of personal concerns.
After 8-9 years, in mid 2019, a personal development program solved all my problems. I felt complete in myself. After this, I just needed one cigarette each day.
The hardest thing was leaving this final cigarette behind, even though I didn't want it.
James Clear's Atomic Habits was published last year. I'd only read 2-3 non-tech books before reading this one in August 2021. I knew everything but couldn't use it.
In April 2022, I realized the compounding effect of a bad habit thanks to my subconscious mind. 1 cigarette per day (excluding weekends) equals 240 = 24 packs per year, which is a lot. No matter how much I did, it felt negative.
Then I applied the 2nd principle of this book, identifying the trigger. I tried to identify all the major triggers of smoking. I found social drinking is one of them & If I am able to control it during that time, I can easily control it in other situations as well. Going further whenever I drank, I was pre-determined to ignore the craving at any cost. Believe me, it was very hard initially but gradually this craving started fading away even with drinks.
I've been smoke-free for 3 months. Now I know a bad habit's effects. After realizing the power of habits, I'm developing other good habits which I ignored all my life.
Will Lockett
3 years ago
Tesla recently disclosed its greatest secret.
The VP has revealed a secret that should frighten the rest of the EV world.
Tesla led the EV revolution. Elon Musk's invention offers a viable alternative to gas-guzzlers. Tesla has lost ground in recent years. VW, BMW, Mercedes, and Ford offer EVs with similar ranges, charging speeds, performance, and cost. Tesla's next-generation 4680 battery pack, Roadster, Cybertruck, and Semi were all delayed. CATL offers superior batteries than the 4680. Martin Viecha, Tesla's Vice President, recently told Business Insider something that startled the EV world and will establish Tesla as the EV king.
Viecha mentioned that Tesla's production costs have dropped 57% since 2017. This isn't due to cheaper batteries or devices like Model 3. No, this is due to amazing factory efficiency gains.
Musk wasn't crazy to want a nearly 100% automated production line, and Tesla's strategy of sticking with one model and improving it has paid off. Others change models every several years. This implies they must spend on new R&D, set up factories, and modernize service and parts systems. All of this costs a ton of money and prevents them from refining production to cut expenses.
Meanwhile, Tesla updates its vehicles progressively. Everything from the backseats to the screen has been enhanced in a 2022 Model 3. Tesla can refine, standardize, and cheaply produce every part without changing the production line.
In 2017, Tesla's automobile production averaged $84,000. In 2022, it'll be $36,000.
Mr. Viecha also claimed that new factories in Shanghai and Berlin will be significantly cheaper to operate once fully operating.
Tesla's hand is visible. Tesla selling $36,000 cars for $60,000 This barely beats the competition. Model Y long-range costs just over $60,000. Tesla makes $24,000+ every sale, giving it a 40% profit margin, one of the best in the auto business.
VW I.D4 costs about the same but makes no profit. Tesla's rivals face similar challenges. Their EVs make little or no profit.
Tesla costs the same as other EVs, but they're in a different league.
But don't forget that the battery pack accounts for 40% of an EV's cost. Tesla may soon fully utilize its 4680 battery pack.
The 4680 battery pack has larger cells and a unique internal design. This means fewer cells are needed for a car, making it cheaper to assemble and produce (per kWh). Energy density and charge speeds increase slightly.
Tesla underestimated the difficulty of making this revolutionary new cell. Each time they try to scale up production, quality drops and rejected cells rise.
Tesla recently installed this battery pack in Model Ys and is scaling production. If they succeed, Tesla battery prices will plummet.
Tesla's Model Ys 2170 battery costs $11,000. The same size pack with 4680 cells costs $3,400 less. Once scaled, it could be $5,500 (50%) less. The 4680 battery pack could reduce Tesla production costs by 20%.
With these cost savings, Tesla could sell Model Ys for $40,000 while still making a profit. They could offer a $25,000 car.
Even with new battery technology, it seems like other manufacturers will struggle to make EVs profitable.
Teslas cost about the same as competitors, so don't be fooled. Behind the scenes, they're still years ahead, and the 4680 battery pack and new factories will only increase that lead. Musk faces a first. He could sell Teslas at current prices and make billions while other manufacturers struggle. Or, he could massively undercut everyone and crush the competition once and for all. Tesla and Elon win.
The Velocipede
2 years ago
Stolen wallet
How a misplaced item may change your outlook
Losing your wallet means life stops. Money vanishes. No credit. Your identity is unverifiable. As you check your pockets for the missing object, you can't drive. You can't borrow a library book.
Last seen? intuitively. Every kid asks this, including yours. However, you know where you lost it: On the Providence River cycling trail. While pedaling vigorously, the wallet dropped out of your back pocket and onto the pavement.
A woman you know—your son's art teacher—says it will be returned. Faith.
You want that faith. Losing a wallet is all-consuming. You must presume it has been stolen and is being used to buy every diamond and non-fungible token on the market. Your identity may have been used to open bank accounts and fake passports. Because he used your license address, a ski mask-wearing man may be driving slowly past your house.
As you delete yourself by canceling cards, these images run through your head. You wait in limbo for replacements. Digital text on the DMV website promises your new license will come within 60 days and be approved by local and state law enforcement. In the following two months, your only defense is a screenshot.
Your wallet was ordinary. A worn, overstuffed leather rectangle. You understand how tenuous your existence has always been since you've never lost a wallet. You barely breathe without your documents.
Ironically, you wore a wallet-belt chain. You adored being a 1993 slacker for 15 years. Your wife just convinced you last year that your office job wasn't professional. You nodded and hid the chain.
Never lost your wallet. Until now.
Angry. Feeling stupid. How could you drop something vital? Why? Is the world cruel? No more dumb luck. You're always one pedal-stroke from death.
Then you get a call: We have your wallet.
Local post office, not cops.
The clerk said someone returned it. Due to trying to identify you, it's a chaos. It has your cards but no cash.
Your automobile screeches down the highway. You yell at the windshield, amazed. Submitted. Art teacher was right. Have some trust.
You thank the postmaster. You ramble through the story. The clerk doesn't know the customer, simply a neighborhood Good Samaritan. You wish you could thank that person for lifting your spirits.
You get home, beaming with gratitude. You thumb through your wallet, amazed that it’s all intact. Then you dig out your chain and reattach it.
Because even faith could use a little help.