An approximate introduction to how zk-SNARKs are possible (part 1)
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has two very powerful applications:
- Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
- Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.
But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.
Why ZK-SNARKs "should" be hard
Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.
A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.
One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?
Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.
But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.
It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.
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? There is a clever solution.
see part 2
(Edited)
More on Web3 & Crypto

Sam Bourgi
3 years ago
NFT was used to serve a restraining order on an anonymous hacker.
The international law firm Holland & Knight used an NFT built and airdropped by its asset recovery team to serve a defendant in a hacking case.
The law firms Holland & Knight and Bluestone used a nonfungible token to serve a defendant in a hacking case with a temporary restraining order, marking the first documented legal process assisted by an NFT.
The so-called "service token" or "service NFT" was served to an unknown defendant in a hacking case involving LCX, a cryptocurrency exchange based in Liechtenstein that was hacked for over $8 million in January. The attack compromised the platform's hot wallets, resulting in the loss of Ether (ETH), USD Coin (USDC), and other cryptocurrencies, according to Cointelegraph at the time.
On June 7, LCX claimed that around 60% of the stolen cash had been frozen, with investigations ongoing in Liechtenstein, Ireland, Spain, and the United States. Based on a court judgment from the New York Supreme Court, Centre Consortium, a company created by USDC issuer Circle and crypto exchange Coinbase, has frozen around $1.3 million in USDC.
The monies were laundered through Tornado Cash, according to LCX, but were later tracked using "algorithmic forensic analysis." The organization was also able to identify wallets linked to the hacker as a result of the investigation.
In light of these findings, the law firms representing LCX, Holland & Knight and Bluestone, served the unnamed defendant with a temporary restraining order issued on-chain using an NFT. According to LCX, this system "was allowed by the New York Supreme Court and is an example of how innovation can bring legitimacy and transparency to a market that some say is ungovernable."

rekt
3 years ago
LCX is the latest CEX to have suffered a private key exploit.
The attack began around 10:30 PM +UTC on January 8th.
Peckshield spotted it first, then an official announcement came shortly after.
We’ve said it before; if established companies holding millions of dollars of users’ funds can’t manage their own hot wallet security, what purpose do they serve?
The Unique Selling Proposition (USP) of centralised finance grows smaller by the day.
The official incident report states that 7.94M USD were stolen in total, and that deposits and withdrawals to the platform have been paused.
LCX hot wallet: 0x4631018f63d5e31680fb53c11c9e1b11f1503e6f
Hacker’s wallet: 0x165402279f2c081c54b00f0e08812f3fd4560a05
Stolen funds:
- 162.68 ETH (502,671 USD)
- 3,437,783.23 USDC (3,437,783 USD)
- 761,236.94 EURe (864,840 USD)
- 101,249.71 SAND Token (485,995 USD)
- 1,847.65 LINK (48,557 USD)
- 17,251,192.30 LCX Token (2,466,558 USD)
- 669.00 QNT (115,609 USD)
- 4,819.74 ENJ (10,890 USD)
- 4.76 MKR (9,885 USD)
**~$1M worth of $LCX remains in the address, along with 611k EURe which has been frozen by Monerium.
The rest, a total of 1891 ETH (~$6M) was sent to Tornado Cash.**
Why can’t they keep private keys private?
Is it really that difficult for a traditional corporate structure to maintain good practice?
CeFi hacks leave us with little to say - we can only go on what the team chooses to tell us.
Next time, they can write this article themselves.
See below for a template.

Percy Bolmér
3 years ago
Ethereum No Longer Consumes A Medium-Sized Country's Electricity To Run
The Merge cut Ethereum's energy use by 99.5%.
The Crypto community celebrated on September 15, 2022. This day, Ethereum Merged. The entire blockchain successfully merged with the Beacon chain, and it was so smooth you barely noticed.
Many have waited, dreaded, and longed for this day.
Some investors feared the network would break down, while others envisioned a seamless merging.
Speculators predict a successful Merge will lead investors to Ethereum. This could boost Ethereum's popularity.
What Has Changed Since The Merge
The merging transitions Ethereum mainnet from PoW to PoS.
PoW sends a mathematical riddle to computers worldwide (miners). First miner to solve puzzle updates blockchain and is rewarded.
The puzzles sent are power-intensive to solve, so mining requires a lot of electricity. It's sent to every miner competing to solve it, requiring duplicate computation.
PoS allows investors to stake their coins to validate a new transaction. Instead of validating a whole block, you validate a transaction and get the fees.
You can validate instead of mine. A validator stakes 32 Ethereum. After staking, the validator can validate future blocks.
Once a validator validates a block, it's sent to a randomly selected group of other validators. This group verifies that a validator is not malicious and doesn't validate fake blocks.
This way, only one computer needs to solve or validate the transaction, instead of all miners. The validated block must be approved by a small group of validators, causing duplicate computation.
PoS is more secure because validating fake blocks results in slashing. You lose your bet tokens. If a validator signs a bad block or double-signs conflicting blocks, their ETH is burned.
Theoretically, Ethereum has one block every 12 seconds, so a validator forging a block risks burning 1 Ethereum for 12 seconds of transactions. This makes mistakes expensive and risky.
What Impact Does This Have On Energy Use?
Cryptocurrency is a natural calamity, sucking electricity and eating away at the earth one transaction at a time.
Many don't know the environmental impact of cryptocurrencies, yet it's tremendous.
A single Ethereum transaction used to use 200 kWh and leave a large carbon imprint. This update reduces global energy use by 0.2%.
Ethereum will submit a challenge to one validator, and that validator will forward it to randomly selected other validators who accept it.
This reduces the needed computing power.
They expect a 99.5% reduction, therefore a single transaction should cost 1 kWh.
Carbon footprint is 0.58 kgCO2, or 1,235 VISA transactions.
This is a big Ethereum blockchain update.
I love cryptocurrency and Mother Earth.
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Suzie Glassman
3 years ago
How I Stay Fit Despite Eating Fast Food and Drinking Alcohol
Here's me. Perfectionism is unnecessary.
This post isn't for people who gag at the prospect of eating french fries. I've been ridiculed for stating you can lose weight eating carbs and six-pack abs aren't good.
My family eats frozen processed meals and quick food most weeks (sometimes more). Clean eaters may think I'm unqualified to give fitness advice. I get it.
Hear me out, though. I’m a 44-year-old raising two busy kids with a weekly-traveling husband. Tutoring, dance, and guitar classes fill weeknights. I'm also juggling my job and freelancing.
I'm as worried and tired as my clients. I wish I ate only kale smoothies and salads. I can’t. Despite my mistakes, I'm fit. I won't promise you something just because it worked for me. But here’s a look at how I manage.
What I largely get right about eating
I have a flexible diet and track my daily intake. I count protein, fat, and carbs. Only on vacation or exceptional occasions do I not track.
My protein goal is 1 g per lb. I consume a lot of chicken breasts, eggs, turkey, and lean ground beef. I also occasionally drink protein shakes.
I eat 220–240 grams of carbs daily. My carb count depends on training volume and goals. I'm trying to lose weight slowly. If I want to lose weight faster, I cut carbs to 150-180.
My carbs include white rice, Daves Killer Bread, fruit, pasta, and veggies. I don't eat enough vegetables, so I take Athletic Greens. Also, V8.
Fat grams over 50 help me control my hormones. Recently, I've reached 70-80 grams. Cooking with olive oil. I eat daily dark chocolate. Eggs, butter, milk, and cheese contribute to the rest.
Those frozen meals? What can I say? Stouffer’s lasagna is sometimes needed. I order the healthiest fast food I can find (although I can never bring myself to order the salad). That's a chicken sandwich or a kid's hamburger. I rarely order fries. I eat slowly and savor each bite to feel full.
Potato chips and sugary cereals are in the pantry, but I'm not tempted. My kids eat them because I'd rather teach them moderation than total avoidance. If I eat them, I only eat one portion.
If you're not hungry and eating enough protein and fat, you won't want to eat everything in sight.
I drink once or twice a week. As a result, I rarely overdo it.
Food tracking is tedious and frustrating for many. Taking breaks and using estimates when eating out help. Not perfect, but realistic.
I practice a prolonged fast to enhance metabolic adaptability
Metabolic flexibility is the ability to switch between fuel sources (fat and carbs) based on activity intensity and time since eating. At rest or during low to moderate exertion, your body burns fat. Your body burns carbs after eating and during intense exercise.
Our metabolic flexibility can be hampered by lack of exercise, overeating, and stress. Our bodies become lousy fat burners, making weight loss difficult.
Once a week, I skip dinner (usually around 24 hours). Long-term fasting teaches my body to burn fat. It provides me one low-calorie day a week (I break the fast with a normal-sized dinner).
Fasting day helps me maintain my weight on weekends, when I typically overeat and drink.
Try an extended fast slowly. Delay breakfast by two hours. Next week, add two hours, etc. It takes practice to go that long without biting off your arm. I also suggest consulting your doctor.
I stay active.
I've always been active. As a child, I danced many nights a week, was on the high school dance team, and ran marathons in my 20s.
Often, I feel driven by an internal engine. Working from home makes it easy to exercise. If that’s not you, I get it. Everyone can benefit from raising their baseline.
After taking the kids to school, I walk two miles around the neighborhood. When I need to think, I switch off podcasts. First thing in the morning, I go for a walk.
I lift weights Monday, Wednesday, and Friday. 45 minutes is typical. I run 45-90 minutes on Tuesday and Thursday. I'm slow but reliable. On Saturdays and Sundays, I walk and add a short spin class if I'm not too tired.
I almost never forgo sleep.
I rarely stay up past 10 p.m., much to my night-owl husband's dismay. My 7-8-hour nights help me recover from workouts and handle stress. Without it, I'm grumpy.
I suppose sleep duration matters more than bedtime. Some people just can't fall asleep early. Internal clock and genetics determine sleep and wake hours.
Prioritize sleep.
Last thoughts
Fitness and diet advice is often useless. Some of the advice is inaccurate, dangerous, or difficult to follow if you have a life. I want to throw a shoe at my screen when I see headlines promising to speed up my metabolism or help me lose fat.
I studied exercise physiology for years. No shortcuts exist. No medications or cleanses reset metabolism. I play the hand I'm dealt. I realize that just because something works for me, it won't for you.
If I wanted 15% body fat and ripped abs, I'd have to be stricter. I occasionally think I’d like to get there. But then I remember I’m happy with my life. I like fast food and beer. Pizza and margaritas are favorites (not every day).
You can get it mostly right and live a healthy life.

Sylvain Saurel
3 years ago
A student trader from the United States made $110 million in one month and rose to prominence on Wall Street.
Genius or lucky?
From the title, you might think I'm selling advertising for a financial influencer, a dubious trading site, or a training organization to attract clients. I'm suspicious. Better safe than sorry.
But not here.
Jake Freeman, 20, made $110 million in a month, according to the Financial Times. At 18, he ran for president. He made his name in markets, not politics. Two years later, he's Wall Street's prince. Interview requests flood the prodigy.
Jake Freeman bought 5 million Bed Bath & Beyond Group shares for $5.5 in July 2022 and sold them for $27 a month later. He thought the stock might double. Since speculation died down, he sold well. The stock fell 40.5% to 11 dollars on Friday, 19 August 2022. On August 22, 2022, it fell 16% to $9.
Smallholders have been buying the stock for weeks and will lose heavily if it falls further. Bed Bath & Beyond is the second most popular stock after Foot Locker, ahead of GameStop and Apple.
Jake Freeman earned $110 million thanks to a significant stock market flurry.
Online broker customers aren't the only ones with jitters. By June 2022, Ken Griffin's Citadel and Stephen Mandel's Lone Pine Capital held nearly a third of the company's capital. Did big managers sell before the stock plummeted?
Recent stock movements (derivatives) and rumors could prompt a SEC investigation.
Jake Freeman wrote to the board of directors after his investment to call for a turnaround, given the company's persistent problems and short sellers. The bathroom and kitchen products distribution group's stock soared in July 2022 due to renewed buying by private speculators, who made it one of their meme stocks with AMC and GameStop.
Second-quarter 2022 results and financial health worsened. He didn't celebrate his miraculous operation in a nightclub. He told a British newspaper, "I'm shocked." His parents dined in New York. He returned to Los Angeles to study math and economics.
Jake Freeman founded Freeman Capital Management with his savings and $25 million from family, friends, and acquaintances. They are the ones who are entitled to the $110 million he raised in one month. Will his investors pocket and withdraw all or part of their profits or will they trust the young prodigy for new stunts on Wall Street?
His operation should attract new clients. Well-known hedge funds may hire him.
Jake Freeman didn't listen to gurus or former traders. At 17, he interned at a quantitative finance and derivatives hedge fund, Volaris. At 13, he began investing with his pharmaceutical executive uncle. All countries have increased their Google searches for the young trader in the last week.
Naturally, his success has inspired resentment.
His success stirs jealousy, and he's attacked on social media. On Reddit, people who lost money on Bed Bath & Beyond, Jake Freeman's fortune, are mourning.
Several conspiracy theories circulate about him, including that he doesn't exist or is working for a Taiwanese amusement park.
If all 20 million American students had the same trading skills, they would have generated $1.46 trillion. Jake Freeman is unique. Apprentice traders' careers are often short, disillusioning, and tragic.
Two years ago, 20-year-old Robinhood client Alexander Kearns committed suicide after losing $750,000 trading options. Great traders start young. Michael Platt of BlueCrest invested in British stocks at age 12 under his grandmother's supervision and made a £30,000 fortune. Paul Tudor Jones started trading before he turned 18 with his uncle. Warren Buffett, at age 10, was discussing investments with Goldman Sachs' head. Oracle of Omaha tells all.

Clive Thompson
2 years ago
Small Pieces of Code That Revolutionized the World
Few sentences can have global significance.
Ethan Zuckerman invented the pop-up commercial in 1997.
He was working for Tripod.com, an online service that let people make little web pages for free. Tripod offered advertising to make money. Advertisers didn't enjoy seeing their advertising next to filthy content, like a user's anal sex website.
Zuckerman's boss wanted a solution. Wasn't there a way to move the ads away from user-generated content?
When you visited a Tripod page, a pop-up ad page appeared. So, the ad isn't officially tied to any user page. It'd float onscreen.
Here’s the thing, though: Zuckerman’s bit of Javascript, that created the popup ad? It was incredibly short — a single line of code:
window.open('http://tripod.com/navbar.html'
"width=200, height=400, toolbar=no, scrollbars=no, resizable=no, target=_top");Javascript tells the browser to open a 200-by-400-pixel window on top of any other open web pages, without a scrollbar or toolbar.
Simple yet harmful! Soon, commercial websites mimicked Zuckerman's concept, infesting the Internet with pop-up advertising. In the early 2000s, a coder for a download site told me that most of their revenue came from porn pop-up ads.
Pop-up advertising are everywhere. You despise them. Hopefully, your browser blocks them.
Zuckerman wrote a single line of code that made the world worse.
I read Zuckerman's story in How 26 Lines of Code Changed the World. Torie Bosch compiled a humorous anthology of short writings about code that tipped the world.
Most of these samples are quite short. Pop-cultural preconceptions about coding say that important code is vast and expansive. Hollywood depicts programmers as blurs spouting out Niagaras of code. Google's success was formerly attributed to its 2 billion lines of code.
It's usually not true. Google's original breakthrough, the piece of code that propelled Google above its search-engine counterparts, was its PageRank algorithm, which determined a web page's value based on how many other pages connected to it and the quality of those connecting pages. People have written their own Python versions; it's only a few dozen lines.
Google's operations, like any large tech company's, comprise thousands of procedures. So their code base grows. The most impactful code can be brief.
The examples are fascinating and wide-ranging, so read the whole book (or give it to nerds as a present). Charlton McIlwain wrote a chapter on the police beat algorithm developed in the late 1960s to anticipate crime hotspots so law enforcement could dispatch more officers there. It created a racial feedback loop. Since poor Black neighborhoods were already overpoliced compared to white ones, the algorithm directed more policing there, resulting in more arrests, which convinced it to send more police; rinse and repeat.
Kelly Chudler's You Are Not Expected To Understand This depicts the police-beat algorithm.
Even shorter code changed the world: the tracking pixel.
Lily Hay Newman's chapter on monitoring pixels says you probably interact with this code every day. It's a snippet of HTML that embeds a single tiny pixel in an email. Getting an email with a tracking code spies on me. As follows: My browser requests the single-pixel image as soon as I open the mail. My email sender checks to see if Clives browser has requested that pixel. My email sender can tell when I open it.
Adding a tracking pixel to an email is easy:
<img src="URL LINKING TO THE PIXEL ONLINE" width="0" height="0">An older example: Ellen R. Stofan and Nick Partridge wrote a chapter on Apollo 11's lunar module bailout code. This bailout code operated on the lunar module's tiny on-board computer and was designed to prioritize: If the computer grew overloaded, it would discard all but the most vital work.
When the lunar module approached the moon, the computer became overloaded. The bailout code shut down anything non-essential to landing the module. It shut down certain lunar module display systems, scaring the astronauts. Module landed safely.
22-line code
POODOO INHINT
CA Q
TS ALMCADR
TC BANKCALL
CADR VAC5STOR # STORE ERASABLES FOR DEBUGGING PURPOSES.
INDEX ALMCADR
CAF 0
ABORT2 TC BORTENT
OCT77770 OCT 77770 # DONT MOVE
CA V37FLBIT # IS AVERAGE G ON
MASK FLAGWRD7
CCS A
TC WHIMPER -1 # YES. DONT DO POODOO. DO BAILOUT.
TC DOWNFLAG
ADRES STATEFLG
TC DOWNFLAG
ADRES REINTFLG
TC DOWNFLAG
ADRES NODOFLAG
TC BANKCALL
CADR MR.KLEAN
TC WHIMPERThis fun book is worth reading.
I'm a contributor to the New York Times Magazine, Wired, and Mother Jones. I've also written Coders: The Making of a New Tribe and the Remaking of the World and Smarter Than You Think: How Technology is Changing Our Minds. Twitter and Instagram: @pomeranian99; Mastodon: @clive@saturation.social.
