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

Chris
2 years ago
What the World's Most Intelligent Investor Recently Said About Crypto
Cryptoshit. This thing is crazy to buy.
Charlie Munger is revered and powerful in finance.
Munger, vice chairman of Berkshire Hathaway, is noted for his wit, no-nonsense attitude to investment, and ability to spot promising firms and markets.
Munger's crypto views have upset some despite his reputation as a straight shooter.
“There’s only one correct answer for intelligent people, just totally avoid all the people that are promoting it.” — Charlie Munger
The Munger Interview on CNBC (4:48 secs)
This Monday, CNBC co-anchor Rebecca Quick interviewed Munger and brought up his 2007 statement, "I'm not allowed to have an opinion on this subject until I can present the arguments against my viewpoint better than the folks who are supporting it."
Great investing and life advice!
If you can't explain the opposing reasons, you're not informed enough to have an opinion.
In today's world, it's important to grasp both sides of a debate before supporting one.
Rebecca inquired:
Does your Wall Street Journal article on banning cryptocurrency apply? If so, would you like to present the counterarguments?
Mungers reply:
I don't see any viable counterarguments. I think my opponents are idiots, hence there is no sensible argument against my position.
Consider his words.
Do you believe Munger has studied both sides?
He said, "I assume my opponents are idiots, thus there is no sensible argument against my position."
This is worrisome, especially from a guy who once encouraged studying both sides before forming an opinion.
Munger said:
National currencies have benefitted humanity more than almost anything else.
Hang on, I think we located the perpetrator.
Munger thinks crypto will replace currencies.
False.
I doubt he studied cryptocurrencies because the name is deceptive.
He misread a headline as a Dollar destroyer.
Cryptocurrencies are speculations.
Like Tesla, Amazon, Apple, Google, Microsoft, etc.
Crypto won't replace dollars.
In the interview with CNBC, Munger continued:
“I’m not proud of my country for allowing this crap, what I call the cryptoshit. It’s worthless, it’s no good, it’s crazy, it’ll do nothing but harm, it’s anti-social to allow it.” — Charlie Munger
Not entirely inaccurate.
Daily cryptos are established solely to pump and dump regular investors.
Let's get into Munger's crypto aversion.
Rat poison is bitcoin.
Munger famously dubbed Bitcoin rat poison and a speculative bubble that would implode.
Partially.
But the bubble broke. Since 2021, the market has fallen.
Scam currencies and NFTs are being eliminated, which I like.
Whoa.
Why does Munger doubt crypto?
Mungers thinks cryptocurrencies has no intrinsic value.
He worries about crypto fraud and money laundering.
Both are valid issues.
Yet grouping crypto is intellectually dishonest.
Ethereum, Bitcoin, Solana, Chainlink, Flow, and Dogecoin have different purposes and values (not saying they’re all good investments).
Fraudsters who hurt innocents will be punished.
Therefore, complaining is useless.
Why not stop it? Repair rather than complain.
Regrettably, individuals today don't offer solutions.
Blind Areas for Mungers
As with everyone, Mungers' bitcoin views may be impacted by his biases and experiences.
OK.
But Munger has always advocated classic value investing and may be wary of investing in an asset outside his expertise.
Mungers' banking and insurance investments may influence his bitcoin views.
Could a coworker or acquaintance have told him crypto is bad and goes against traditional finance?
Right?
Takeaways
Do you respect Charlie Mungers?
Yes and no, like any investor or individual.
To understand Mungers' bitcoin beliefs, you must be critical.
Mungers is a successful investor, but his views about bitcoin should be considered alongside other viewpoints.
Munger’s success as an investor has made him an influencer in the space.
Influence gives power.
He controls people's thoughts.
Munger's ok. He will always be heard.
I'll do so cautiously.

Protos
3 years ago
StableGains lost $42M in Anchor Protocol.
StableGains lost millions of dollars in customer funds in Anchor Protocol without telling its users. The Anchor Protocol offered depositors 19-20% APY before its parent ecosystem, Terra LUNA, lost tens of billions of dollars in market capitalization as LUNA fell below $0.01 and its stablecoin (UST) collapsed.
A Terra Research Forum member raised the alarm. StableGains changed its homepage and Terms and Conditions to reflect how it mitigates risk, a tacit admission that it should have done so from the start.
StableGains raised $600,000 in YCombinator's W22 batch. Moonfire, Broom Ventures, and Goodwater Capital invested $3 million more.
StableGains' 15% yield product attracted $42 million in deposits. StableGains kept most of its deposits in Anchor's UST pool earning 19-20% APY, kept one-quarter of the interest as a management fee, and then gave customers their promised 15% APY. It lost almost all customer funds when UST melted down. It changed withdrawal times, hurting customers.
- StableGains said de-pegging was unlikely. According to its website, 1 UST can be bought and sold for $1 of LUNA. LUNA became worthless, and Terra shut down its blockchain.
- It promised to diversify assets across several stablecoins to reduce the risk of one losing its $1 peg, but instead kept almost all of them in one basket.
- StableGains promised withdrawals in three business days, even if a stablecoin needed time to regain its peg. StableGains uses Coinbase for deposits and withdrawals, and customers receive the exact amount of USDC requested.
StableGains scrubs its website squeaky clean
StableGains later edited its website to say it only uses the "most trusted and tested stablecoins" and extended withdrawal times from three days to indefinite time "in extreme cases."
Previously, USDC, TerraUST (UST), and Dai were used (DAI). StableGains changed UST-related website content after the meltdown. It also removed most references to DAI.
Customers noticed a new clause in the Terms and Conditions denying StableGains liability for withdrawal losses. This new clause would have required customers to agree not to sue before withdrawing funds, avoiding a class-action lawsuit.
Customers must sign a waiver to receive a refund.
Erickson Kramer & Osborne law firm has asked StableGains to preserve all internal documents on customer accounts, marketing, and TerraUSD communications. The firm has not yet filed a lawsuit.
Thousands of StableGains customers lost an estimated $42 million.
Celsius Network customers also affected
CEL used Terra LUNA's Anchor Protocol. Celsius users lost money in the crypto market crash and UST meltdown. Many held CEL and LUNA as yielding deposits.
CEO Alex Mashinsky accused "unknown malefactors" of targeting Celsius Network without evidence. Celsius has not publicly investigated this claim as of this article's publication.
CEL fell before UST de-pegged. On June 2, 2021, it reached $8.01. May 19's close: $0.82.
When some Celsius Network users threatened to leave over token losses, Mashinsky replied, "Leave if you don't think I'm sincere and working harder than you, seven days a week."
Celsius Network withdrew $500 million from Anchor Protocol, but smaller holders had trouble.
Read original article here

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.
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DC Palter
3 years ago
How Will You Generate $100 Million in Revenue? The Startup Business Plan
A top-down company plan facilitates decision-making and impresses investors.
A startup business plan starts with the product, the target customers, how to reach them, and how to grow the business.
Bottom-up is terrific unless venture investors fund it.
If it can prove how it can exceed $100M in sales, investors will invest. If not, the business may be wonderful, but it's not venture capital-investable.
As a rule, venture investors only fund firms that expect to reach $100M within 5 years.
Investors get nothing until an acquisition or IPO. To make up for 90% of failed investments and still generate 20% annual returns, portfolio successes must exit with a 25x return. A $20M-valued company must be acquired for $500M or more.
This requires $100M in sales (or being on a nearly vertical trajectory to get there). The company has 5 years to attain that milestone and create the requisite ROI.
This motivates venture investors (venture funds and angel investors) to hunt for $100M firms within 5 years. When you pitch investors, you outline how you'll achieve that aim.
I'm wary of pitches after seeing a million hockey sticks predicting $5M to $100M in year 5 that never materialized. Doubtful.
Startups fail because they don't have enough clients, not because they don't produce a great product. That jump from $5M to $100M never happens. The company reaches $5M or $10M, growing at 10% or 20% per year. That's great, but not enough for a $500 million deal.
Once it becomes clear the company won’t reach orbit, investors write it off as a loss. When a corporation runs out of money, it's shut down or sold in a fire sale. The company can survive if expenses are trimmed to match revenues, but investors lose everything.
When I hear a pitch, I'm not looking for bright income projections but a viable plan to achieve them. Answer these questions in your pitch.
Is the market size sufficient to generate $100 million in revenue?
Will the initial beachhead market serve as a springboard to the larger market or as quicksand that hinders progress?
What marketing plan will bring in $100 million in revenue? Is the market diffuse and will cost millions of dollars in advertising, or is it one, focused market that can be tackled with a team of salespeople?
Will the business be able to bridge the gap from a small but fervent set of early adopters to a larger user base and avoid lock-in with their current solution?
Will the team be able to manage a $100 million company with hundreds of people, or will hypergrowth force the organization to collapse into chaos?
Once the company starts stealing market share from the industry giants, how will it deter copycats?
The requirement to reach $100M may be onerous, but it provides a context for difficult decisions: What should the product be? Where should we concentrate? who should we hire? Every strategic choice must consider how to reach $100M in 5 years.
Focusing on $100M streamlines investor pitches. Instead of explaining everything, focus on how you'll attain $100M.
As an investor, I know I'll lose my money if the startup doesn't reach this milestone, so the revenue prediction is the first thing I look at in a pitch deck.
Reaching the $100M goal needs to be the first thing the entrepreneur thinks about when putting together the business plan, the central story of the pitch, and the criteria for every important decision the company makes.

Pat Vieljeux
3 years ago
Your entrepreneurial experience can either be a beautiful adventure or a living hell with just one decision.
Choose.
DNA makes us distinct.
We act alike. Most people follow the same road, ignoring differences. We remain quiet about our uniqueness for fear of exclusion (family, social background, religion). We live a more or less imposed life.
Off the beaten path, we stand out from the others. We obey without realizing we're sewing a shroud. We're told to do as everyone else and spend 40 years dreaming of a golden retirement and regretting not living.
“One of the greatest regrets in life is being what others would want you to be, rather than being yourself.” - Shannon L. Alder
Others dare. Again, few are creative; most follow the example of those who establish a business for the sake of entrepreneurship. To live.
They pick a potential market and model their MVP on an existing solution. Most mimic others, alter a few things, appear to be original, and end up with bland products, adding to an already crowded market.
SaaS, PaaS, etc. followed suit. It's reduced pricing, profitability, and product lifespan.
As competitors become more aggressive, their profitability diminishes, making life horrible for them and their employees. They fail to innovate, cut costs, and close their company.
Few of them look happy and fulfilled.
How did they do it?
The answer is unsettlingly simple.
They are themselves.
They start their company, propelled at first by a passion or maybe a calling.
Then, at their own pace, they create it with the intention of resolving a dilemma.
They assess what others are doing and consider how they might improve it.
In contrast to them, they respond to it in their own way by adding a unique personal touch. Therefore, it is obvious.
Originals, like their DNA, can't be copied. Or if they are, they're poorly printed. Originals are unmatched. Artist-like. True collectors only buy Picasso paintings by the master, not forgeries, no matter how good.
Imaginative people are constantly ahead. Copycats fall behind unless they innovate. They watch their competition continuously. Their solution or product isn't sexy. They hope to cash in on their copied product by flooding the market.
They're mostly pirates. They're short-sighted, unlike creators.
Creators see further ahead and have no rivals. They use copiers to confirm a necessity. To maintain their individuality, creators avoid copying others. They find copying boring. It's boring. They oppose plagiarism.
It's thrilling and inspiring.
It will also make them more able to withstand their opponents' tension. Not to mention roadblocks. For creators, impediments are games.
Others fear it. They race against the clock and fear threats that could interrupt their momentum since they lack inventiveness and their product has a short life cycle.
Creators have time on their side. They're dedicated. Clearly. Passionate booksellers will have their own bookstore. Their passion shows in their book choices. Only the ones they love.
The copier wants to display as many as possible, including mediocre authors, and will cut costs. All this to dominate the market. They're digging their own grave.
The bookseller is just one example. I could give you tons of them.
Closing remarks
Entrepreneurs might follow others or be themselves. They risk exhaustion trying to predict what their followers will do.
It's true.
Life offers choices.
Being oneself or doing as others do, with the possibility of regretting not expressing our uniqueness and not having lived.
“Be yourself; everyone else is already taken”. Oscar Wilde
The choice is yours.
Evgenii Nelepko
3 years ago
My 3 biggest errors as a co-founder and CEO
Reflections on the closed company Hola! Dating app
I'll discuss my fuckups as an entrepreneur and CEO. All of them refer to the dating app Hola!, which I co-founded and starred in.
Spring 2021 was when we started. Two techies and two non-techies created a dating app. Pokemon Go and Tinder were combined.
Online dating is a business, and it takes two weeks from a like to a date. We questioned online dating app users if they met anyone offline last year.
75% replied yes, 50% sometimes, 25% usually.
Offline dating is popular, yet people have concerns.
Men are reluctant to make mistakes in front of others.
Women are curious about the background of everyone who approaches them.
We designed unique mechanics that let people date after a match. No endless chitchat. Women would be safe while men felt like cowboys.
I wish to emphasize three faults that lead to founders' estrangement.
This detachment ultimately led to us shutting down the company.
The wrong technology stack
Situation
Instead of generating a faster MVP and designing an app in a universal stack for iOS and Android, I argued we should pilot the app separately for iOS and Android. Technical founders' expertise made this possible.
Self-reflection
Mistaken strategy. We lost time and resources developing two apps at once. We chose iOS since it's more profitable. Apple took us out after the release, citing Guideline 4.3 Spam. After 4 months, we had nothing. We had a long way to go to get the app on Android and the Store.
I suggested creating a uniform platform for the company's growth. This makes parallel product development easier. The strategist's lack of experience and knowledge made it a piece of crap.
What would I have changed if I could?
We should have designed an Android universal stack. I expected Apple to have issues with a dating app.
Our approach should have been to launch something and subsequently improve it, but prejudice won.
The lesson
Discuss the IT stack with your CTO. It saves time and money. Choose the easiest MVP method.
2. A tardy search for investments
Situation
Though the universe and other founders encouraged me to locate investors first, I started pitching when we almost had an app.
When angels arrived, it was time to close. The app was banned, war broke out, I left the country, and the other co-founders stayed. We had no savings.
Self-reflection
I loved interviewing users. I'm proud of having done 1,000 interviews. I wanted to understand people's pain points and improve the product.
Interview results no longer affected the product. I was terrified to start pitching. I filled out accelerator applications and redid my presentation. You must go through that so you won't be terrified later.
What would I have changed if I could?
Get an external or internal mentor to help me with my first pitch as soon as possible. I'd be supported if criticized. He'd cheer with me if there was enthusiasm.
In 99% of cases, I'm comfortable jumping into the unknown, but there are exceptions. The mentor's encouragement would have prompted me to act sooner.
The lesson
Begin fundraising immediately. Months may pass. Show investors your pre-MVP project. Draw inferences from feedback.
3. Role ambiguity
Situation
My technical co-founders were also part-time lead developers, which produced communication issues. As co-founders, we communicated well and recognized the problems. Stakes, vesting, target markets, and approach were agreed upon.
We were behind schedule. Technical debt and strategic gap grew.
Bi-daily and weekly reviews didn't help. Each time, there were explanations. Inside, I was freaking out.
Self-reflection
I am a fairly easy person to talk to. I always try to stick to agreements; otherwise, my head gets stuffed with unnecessary information, interpretations, and emotions.
Sit down -> talk -> decide -> do -> evaluate the results. Repeat it.
If I don't get detailed comments, I start ruining everyone's mood. If there's a systematic violation of agreements without a good justification, I won't join the project or I'll end the collaboration.
What would I have done otherwise?
This is where it’s scariest to draw conclusions. Probably the most logical thing would have been not to start the project as we started it. But that was already a completely different project. So I would not have done anything differently and would have failed again.
But I drew conclusions for the future.
The lesson
First-time founders should find an adviser or team coach for a strategic session. It helps split the roles and responsibilities.
