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

Elnaz Sarraf
3 years ago
Why Bitcoin's Crash Could Be Good for Investors

The crypto market crashed in June 2022. Bitcoin and other cryptocurrencies hit their lowest prices in over a year, causing market panic. Some believe this crash will benefit future investors.
Before I discuss how this crash might help investors, let's examine why it happened. Inflation in the U.S. reached a 30-year high in 2022 after Russia invaded Ukraine. In response, the U.S. Federal Reserve raised interest rates by 0.5%, the most in almost 20 years. This hurts cryptocurrencies like Bitcoin. Higher interest rates make people less likely to invest in volatile assets like crypto, so many investors sold quickly.

The crypto market collapsed. Bitcoin, Ethereum, and Binance dropped 40%. Other cryptos crashed so hard they were delisted from almost every exchange. Bitcoin peaked in April 2022 at $41,000, but after the May interest rate hike, it crashed to $28,000. Bitcoin investors were worried. Even in bad times, this crash is unprecedented.
Bitcoin wasn't "doomed." Before the crash, LUNA was one of the top 5 cryptos by market cap. LUNA was trading around $80 at the start of May 2022, but after the rate hike?
Less than 1 cent. LUNA lost 99.99% of its value in days and was removed from every crypto exchange. Bitcoin's "crash" isn't as devastating when compared to LUNA.
Many people said Bitcoin is "due" for a LUNA-like crash and that the only reason it hasn't crashed is because it's bigger. Still false. If so, Bitcoin should be worth zero by now. We didn't. Instead, Bitcoin reached 28,000, then 29k, 30k, and 31k before falling to 18k. That's not the world's greatest recovery, but it shows Bitcoin's safety.
Bitcoin isn't falling constantly. It fell because of the initial shock of interest rates, but not further. Now, Bitcoin's value is more likely to rise than fall. Bitcoin's low price also attracts investors. They know what prices Bitcoin can reach with enough hype, and they want to capitalize on low prices before it's too late.

Bitcoin's crash was bad, but in a way it wasn't. To understand, consider 2021. In March 2021, Bitcoin surpassed $60k for the first time. Elon Musk's announcement in May that he would no longer support Bitcoin caused a massive crash in the crypto market. In May 2017, Bitcoin's price hit $29,000. Elon Musk's statement isn't worth more than the Fed raising rates. Many expected this big announcement to kill Bitcoin.

Not so. Bitcoin crashed from $58k to $31k in 2021. Bitcoin fell from $41k to $28k in 2022. This crash is smaller. Bitcoin's price held up despite tensions and stress, proving investors still believe in it. What happened after the initial crash in the past?
Bitcoin fell until mid-July. This is also something we’re not seeing today. After a week, Bitcoin began to improve daily. Bitcoin's price rose after mid-July. Bitcoin's price fluctuated throughout the rest of 2021, but it topped $67k in November. Despite no major changes, the peak occurred after the crash. Elon Musk seemed uninterested in crypto and wasn't likely to change his mind soon. What triggered this peak? Nothing, really. What really happened is that people got over the initial statement. They forgot.
Internet users have goldfish-like attention spans. People quickly forgot the crash's cause and were back investing in crypto months later. Despite the market's setbacks, more crypto investors emerged by the end of 2017. Who gained from these peaks? Bitcoin investors who bought low. Bitcoin not only recovered but also doubled its ROI. It was like a movie, and it shows us what to expect from Bitcoin in the coming months.
The current Bitcoin crash isn't as bad as the last one. LUNA is causing market panic. LUNA and Bitcoin are different cryptocurrencies. LUNA crashed because Terra wasn’t able to keep its peg with the USD. Bitcoin is unanchored. It's one of the most decentralized investments available. LUNA's distrust affected crypto prices, including Bitcoin, but it won't last forever.
This is why Bitcoin will likely rebound in the coming months. In 2022, people will get over the rise in interest rates and the crash of LUNA, just as they did with Elon Musk's crypto stance in 2021. When the world moves on to the next big controversy, Bitcoin's price will soar.
Bitcoin may recover for another reason. Like controversy, interest rates fluctuate. The Russian invasion caused this inflation. World markets will stabilize, prices will fall, and interest rates will drop.
Next, lower interest rates could boost Bitcoin's price. Eventually, it will happen. The U.S. economy can't sustain such high interest rates. Investors will put every last dollar into Bitcoin if interest rates fall again.
Bitcoin has proven to be a stable investment. This boosts its investment reputation. Even if Ethereum dethrones Bitcoin as crypto king one day (or any other crypto, for that matter). Bitcoin may stay on top of the crypto ladder for a while. We'll have to wait a few months to see if any of this is true.
This post is a summary. Read the full article here.

Miguel Saldana
3 years ago
Crypto Inheritance's Catch-22
Security, privacy, and a strategy!
How to manage digital assets in worst-case scenarios is a perennial crypto concern. Since blockchain and bitcoin technology is very new, this hasn't been a major issue. Many early developers are still around, and many groups created around this technology are young and feel they have a lot of life remaining. This is why inheritance and estate planning in crypto should be handled promptly. As cryptocurrency's intrinsic worth rises, many people in the ecosystem are holding on to assets that might represent generational riches. With that much value, it's crucial to have a plan. Creating a solid plan entails several challenges.
the initial hesitation in coming up with a plan
The technical obstacles to ensuring the assets' security and privacy
the passing of assets from a deceased or incompetent person
Legal experts' lack of comprehension and/or understanding of how to handle and treat cryptocurrency.
This article highlights several challenges, a possible web3-native solution, and how to learn more.
The Challenge of Inheritance:
One of the biggest hurdles to inheritance planning is starting the conversation. As humans, we don't like to think about dying. Early adopters will experience crazy gains as cryptocurrencies become more popular. Creating a plan is crucial if you wish to pass on your riches to loved ones. Without a plan, the technical and legal issues I barely mentioned above would erode value by requiring costly legal fees and/or taxes, and you could lose everything if wallets and assets are not distributed appropriately (associated with the private keys). Raising awareness of the consequences of not having a plan should motivate people to make one.
Controlling Change:
Having an inheritance plan for your digital assets is crucial, but managing the guts and bolts poses a new set of difficulties. Privacy and security provided by maintaining your own wallet provide different issues than traditional finances and assets. Traditional finance is centralized (say a stock brokerage firm). You can assign another person to handle the transfer of your assets. In crypto, asset transfer is reimagined. One may suppose future transaction management is doable, but the user must consent, creating an impossible loop.
I passed away and must send a transaction to the person I intended to deliver it to.
I have to confirm or authorize the transaction, but I'm dead.
In crypto, scheduling a future transaction wouldn't function. To transfer the wallet and its contents, we'd need the private keys and/or seed phrase. Minimizing private key exposure is crucial to protecting your crypto from hackers, social engineering, and phishing. People have lost private keys after utilizing Life Hack-type tactics to secure them. People that break and hide their keys, lose them, or make them unreadable won't help with managing and/or transferring. This will require a derived solution.
Legal Challenges and Implications
Unlike routine cryptocurrency transfers and transactions, local laws may require special considerations. Even in the traditional world, estate/inheritance taxes, how assets will be split, and who executes the will must be considered. Many lawyers aren't crypto-savvy, which complicates the matter. There will be many hoops to jump through to safeguard your crypto and traditional assets and give them to loved ones.
Knowing RUFADAA/UFADAA, depending on your state, is vital for Americans. UFADAA offers executors and trustees access to online accounts (which crypto wallets would fall into). RUFADAA was changed to limit access to the executor to protect assets. RUFADAA outlines how digital assets are administered following death and incapacity in the US.
A Succession Solution
Having a will and talking about who would get what is the first step to having a solution, but using a Dad Mans Switch is a perfect tool for such unforeseen circumstances. As long as the switch's controller has control, nothing happens. Losing control of the switch initiates a state transition.
Subway or railway operations are examples. Modern control systems need the conductor to hold a switch to keep the train going. If they can't, the train stops.
Enter Sarcophagus
Sarcophagus is a decentralized dead man's switch built on Ethereum and Arweave. Sarcophagus allows actors to maintain control of their possessions even while physically unable to do so. Using a programmable dead man's switch and dual encryption, anything can be kept and passed on. This covers assets, secrets, seed phrases, and other use cases to provide authority and control back to the user and release trustworthy services from this work. Sarcophagus is built on a decentralized, transparent open source codebase. Sarcophagus is there if you're unprepared.

Onchain Wizard
3 years ago
Three Arrows Capital & Celsius Updates
I read 1k+ page 3AC liquidation documentation so you don't have to. Also sharing revised Celsius recovery plans.
3AC's liquidation documents:
Someone disclosed 3AC liquidation records in the BVI courts recently. I'll discuss the leak's timeline and other highlights.
Three Arrows Capital began trading traditional currencies in emerging markets in 2012. They switched to equities and crypto, then purely crypto in 2018.
By 2020, the firm had $703mm in net assets and $1.8bn in loans (these guys really like debt).
The firm's net assets under control reached $3bn in April 2022, according to the filings. 3AC had $600mm of LUNA/UST exposure before May 9th 2022, which put them over.
LUNA and UST go to zero quickly (I wrote about the mechanics of the blowup here). Kyle Davies, 3AC co-founder, told Blockchain.com on May 13 that they have $2.4bn in assets and $2.3bn NAV vs. $2bn in borrowings. As BTC and ETH plunged 33% and 50%, the company became insolvent by mid-2022.
3AC sent $32mm to Tai Ping Shen, a Cayman Islands business owned by Su Zhu and Davies' partner, Kelly Kaili Chen (who knows what is going on here).
3AC had borrowed over $3.5bn in notional principle, with Genesis ($2.4bn) and Voyager ($650mm) having the most exposure.
Genesis demanded $355mm in further collateral in June.
Deribit (another 3AC investment) called for $80 million in mid-June.
Even in mid-June, the corporation was trying to borrow more money to stay afloat. They approached Genesis for another $125mm loan (to pay another lender) and HODLnauts for BTC & ETH loans.
Pretty crazy. 3AC founders used borrowed money to buy a $50 million boat, according to the leak.
Su requesting for $5m + Chen Kaili Kelly asserting they loaned $65m unsecured to 3AC are identified as creditors.
Celsius:
This bankruptcy presentation shows the Celsius breakdown from March to July 14, 2022. From $22bn to $4bn, crypto assets plummeted from $14.6bn to $1.8bn (ouch). $16.5bn in user liabilities dropped to $4.72bn.
In my recent post, I examined if "forced selling" is over, with Celsius' crypto assets being a major overhang. In this presentation, it looks that Chapter 11 will provide clients the opportunity to accept cash at a discount or remain long crypto. Provided that a fresh source of money is unlikely to enter the Celsius situation, cash at a discount or crypto given to customers will likely remain a near-term market risk - cash at a discount will likely come from selling crypto assets, while customers who receive crypto could sell at any time. I'll share any Celsius updates I find.
Conclusion
Only Celsius and the Mt Gox BTC unlock remain as forced selling catalysts. While everything went through a "relief" pump, with ETH up 75% from the bottom and numerous alts multiples higher, there are still macro dangers to equities + risk assets. There's a lot of wealth waiting to be deployed in crypto ($153bn in stables), but fund managers are risk apprehensive (lower than 2008 levels).
We're hopefully over crypto's "bottom," with peak anxiety and forced selling behind us, but we may chop around.
To see the full article, click here.
You might also like

Alex Mathers
3 years ago
8 guidelines to help you achieve your objectives 5x fast
If you waste time every day, even though you're ambitious, you're not alone.
Many of us could use some new time-management strategies, like these:
Focus on the following three.
You're thinking about everything at once.
You're overpowered.
It's mental. We just have what's in front of us. So savor the moment's beauty.
Prioritize 1-3 things.
To be one of the most productive people you and I know, follow these steps.
Get along with boredom.
Many of us grow bored, sweat, and turn on Netflix.
We shout, "I'm rarely bored!" Look at me! I'm happy.
Shut it, Sally.
You're not making wonderful things for the world. Boredom matters.
If you can sit with it for a second, you'll get insight. Boredom? Breathe.
Go blank.
Then watch your creativity grow.
Check your MacroVision once more.
We don't know what to do with our time, which contributes to time-wasting.
Nobody does, either. Jeff Bezos won't hand-deliver that crap to you.
Daily vision checks are required.
Also:
What are 5 things you'd love to create in the next 5 years?
You're soul-searching. It's food.
Return here regularly, and you'll adore the high you get from doing valuable work.
Improve your thinking.
What's Alex's latest nonsense?
I'm talking about overcoming our own thoughts. Worrying wastes so much time.
Too many of us are assaulted by lies, myths, and insecurity.
Stop letting your worries massage you into a worried coma like a Thai woman.
Optimizing your thoughts requires accepting what you can't control.
It means letting go of unhelpful thoughts and returning to the moment.
Keep your blood sugar level.
I gave up gluten, donuts, and sweets.
This has really boosted my energy.
Blood-sugar-spiking carbs make us irritable and tired.
These day-to-day ups and downs aren't productive. It's crucial.
Know how your diet affects insulin levels. Now I have more energy and can do more without clenching my teeth.
Reduce harmful carbs to boost energy.
Create a focused setting for yourself.
When we optimize the mind, we have more energy and use our time better because we're not tense.
Changing our environment can also help us focus. Disabling alerts is one example.
Too hot makes me procrastinate and irritable.
List five items that hinder your productivity.
You may be amazed at how much you may improve by removing distractions.
Be responsible.
Accountability is a time-saver.
Creating an emotional pull to finish things.
Writing down our goals makes us accountable.
We can engage a coach or work with an accountability partner to feel horrible if we don't show up and finish on time.
‘Hey Jake, I’m going to write 1000 words every day for 30 days — you need to make sure I do.’ ‘Sure thing, Nathan, I’ll be making sure you check in daily with me.’
Tick.
You might also blog about your ambitions to show your dedication.
Now you can't hide when you promised to appear.
Acquire a liking for bravery.
Boldness changes everything.
I sometimes feel lazy and wonder why. If my food and sleep are in order, I should assess my footing.
Most of us live backward. Doubtful. Uncertain. Feelings govern us.
Backfooting isn't living. It's lame, and you'll soon melt. Live boldly now.
Be assertive.
Get disgustingly into everything. Expand.
Even if it's hard, stop being a b*tch.
Those that make Mr. Bold Bear their spirit animal benefit. Save time to maximize your effect.
Chritiaan Hetzner
3 years ago
Mystery of the $1 billion'meme stock' that went to $400 billion in days
Who is AMTD Digital?
An unknown Hong Kong corporation joined the global megacaps worth over $500 billion on Tuesday.
The American Depository Share (ADS) with the ticker code HKD gapped at the open, soaring 25% over the previous closing price as trading began, before hitting an intraday high of $2,555.
At its peak, its market cap was almost $450 billion, more than Facebook parent Meta or Alibaba.
Yahoo Finance reported a daily volume of 350,500 shares, the lowest since the ADS began trading and much below the average of 1.2 million.
Despite losing a fifth of its value on Wednesday, it's still worth more than Toyota, Nike, McDonald's, or Walt Disney.
The company sold 16 million shares at $7.80 each in mid-July, giving it a $1 billion market valuation.
Why the boom?
That market cap seems unjustified.
According to SEC reports, its income-generating assets barely topped $400 million in March. Fortune's emails and calls went unanswered.
Website discloses little about company model. Its one-minute business presentation film uses a Star Wars–like design to sell the company as a "one-stop digital solutions platform in Asia"
The SEC prospectus explains.
AMTD Digital sells a "SpiderNet Ecosystems Solutions" kind of club membership that connects enterprises. This is the bulk of its $25 million annual revenue in April 2021.
Pretax profits have been higher than top line over the past three years due to fair value accounting gains on Appier, DayDayCook, WeDoctor, and five Asian fintechs.
AMTD Group, the company's parent, specializes in investment banking, hotel services, luxury education, and media and entertainment. AMTD IDEA, a $14 billion subsidiary, is also traded on the NYSE.
“Significant volatility”
Why AMTD Digital listed in the U.S. is unknown, as it informed investors in its share offering prospectus that could delist under SEC guidelines.
Beijing's red tape prevents the Sarbanes-Oxley Board from inspecting its Chinese auditor.
This frustrates Chinese stock investors. If the U.S. and China can't achieve a deal, 261 Chinese companies worth $1.3 trillion might be delisted.
Calvin Choi left UBS to become AMTD Group's CEO.
His capitalist background and status as a Young Global Leader with the World Economic Forum don't stop him from praising China's Communist party or celebrating the "glory and dream of the Great Rejuvenation of the Chinese nation" a century after its creation.
Despite having an executive vice chairman with a record of battling corruption and ties to Carrie Lam, Beijing's previous proconsul in Hong Kong, Choi is apparently being targeted for a two-year industry ban by the city's securities regulator after an investor accused Choi of malfeasance.
Some CMIG-funded initiatives produced money, but he didn't give us the proceeds, a corporate official told China's Caixin in October 2020. We don't know if he misappropriated or lost some money.
A seismic anomaly
In fundamental analysis, where companies are valued based on future cash flows, AMTD Digital's mind-boggling market cap is a statistical aberration that should occur once every hundred years.
AMTD Digital doesn't know why it's so valuable. In a thank-you letter to new shareholders, it said it was confused by the stock's performance.
Since its IPO, the company has seen significant ADS price volatility and active trading volume, it said Tuesday. "To our knowledge, there have been no important circumstances, events, or other matters since the IPO date."
Permabears awoke after the jump. Jim Chanos asked if "we're all going to ignore the $400 billion meme stock in the room," while Nate Anderson called AMTD Group "sketchy."
It happened the same day SEC Chair Gary Gensler praised the 20th anniversary of the Sarbanes-Oxley Act, aimed to restore trust in America's financial markets after the Enron and WorldCom accounting fraud scandals.
The run-up revived unpleasant memories of Robinhood's decision to limit retail investors' ability to buy GameStop, regarded as a measure to protect hedge funds invested in the meme company.
Why wasn't HKD's buy button removed? Because retail wasn't behind it?" tweeted Gensler on Tuesday. "Real stock fraud. "You're worthless."

Eitan Levy
3 years ago
The Top 8 Growth Hacking Techniques for Startups
The Top 8 Growth Hacking Techniques for Startups

These startups, and how they used growth-hack marketing to flourish, are some of the more ethical ones, while others are less so.
Before the 1970 World Cup began, Puma paid footballer Pele $120,000 to tie his shoes. The cameras naturally focused on Pele and his Pumas, causing people to realize that Puma was the top football brand in the world.
Early workers of Uber canceled over 5,000 taxi orders made on competing applications in an effort to financially hurt any of their rivals.
PayPal developed a bot that advertised cheap goods on eBay, purchased them, and paid for them with PayPal, fooling eBay into believing that customers preferred this payment option. Naturally, Paypal became eBay's primary method of payment.
Anyone renting a space on Craigslist had their emails collected by AirBnB, who then urged them to use their service instead. A one-click interface was also created to list immediately on AirBnB from Craigslist.
To entice potential single people looking for love, Tinder developed hundreds of bogus accounts of attractive people. Additionally, for at least a year, users were "accidentally" linked.
Reddit initially created a huge number of phony accounts and forced them all to communicate with one another. It eventually attracted actual users—the real meaning of "fake it 'til you make it"! Additionally, this gave Reddit control over the tone of voice they wanted for their site, which is still present today.
To disrupt the conferences of their main rival, Salesforce recruited fictitious protestors. The founder then took over all of the event's taxis and gave a 45-minute pitch for his startup. No place to hide!
When a wholesaler required a minimum purchase of 10, Amazon CEO Jeff Bezos wanted a way to purchase only one book from them. A wholesaler would deliver the one book he ordered along with an apology for the other eight books after he discovered a loophole and bought the one book before ordering nine books about lichens. On Amazon, he increased this across all of the users.
Original post available here
