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
The Verge
3 years ago
Bored Ape Yacht Club creator raises $450 million at a $4 billion valuation.
Yuga Labs, owner of three of the biggest NFT brands on the market, announced today a $450 million funding round. The money will be used to create a media empire based on NFTs, starting with games and a metaverse project.
The team's Otherside metaverse project is an MMORPG meant to connect the larger NFT universe. They want to create “an interoperable world” that is “gamified” and “completely decentralized,” says Wylie Aronow, aka Gordon Goner, co-founder of Bored Ape Yacht Club. “We think the real Ready Player One experience will be player run.”
Just a few weeks ago, Yuga Labs announced the acquisition of CryptoPunks and Meebits from Larva Labs. The deal brought together three of the most valuable NFT collections, giving Yuga Labs more IP to work with when developing games and metaverses. Last week, ApeCoin was launched as a cryptocurrency that will be governed independently and used in Yuga Labs properties.
Otherside will be developed by “a few different game studios,” says Yuga Labs CEO Nicole Muniz. The company plans to create development tools that allow NFTs from other projects to work inside their world. “We're welcoming everyone into a walled garden.”
However, Yuga Labs believes that other companies are approaching metaverse projects incorrectly, allowing the startup to stand out. People won't bond spending time in a virtual space with nothing going on, says Yuga Labs co-founder Greg Solano, aka Gargamel. Instead, he says, people bond when forced to work together.
In order to avoid getting smacked, Solano advises making friends. “We don't think a Zoom chat and walking around saying ‘hi' creates a deep social experience.” Yuga Labs refused to provide a release date for Otherside. Later this year, a play-to-win game is planned.
The funding round was led by Andreessen Horowitz, a major investor in the Web3 space. It previously backed OpenSea and Coinbase. Animoca Brands, Coinbase, and MoonPay are among those who have invested. Andreessen Horowitz general partner Chris Lyons will join Yuga Labs' board. The Financial Times broke the story last month.
"META IS A DOMINANT DIGITAL EXPERIENCE PROVIDER IN A DYSTOPIAN FUTURE."
This emerging [Web3] ecosystem is important to me, as it is to companies like Meta,” Chris Dixon, head of Andreessen Horowitz's crypto arm, tells The Verge. “In a dystopian future, Meta is the dominant digital experience provider, and it controls all the money and power.” (Andreessen Horowitz co-founder Marc Andreessen sits on Meta's board and invested early in Facebook.)
Yuga Labs has been profitable so far. According to a leaked pitch deck, the company made $137 million last year, primarily from its NFT brands, with a 95% profit margin. (Yuga Labs declined to comment on deck figures.)
But the company has built little so far. According to OpenSea data, it has only released one game for a limited time. That means Yuga Labs gets hundreds of millions of dollars to build a gaming company from scratch, based on a hugely lucrative art project.
Investors fund Yuga Labs based on its success. That's what they did, says Dixon, “they created a culture phenomenon”. But ultimately, the company is betting on the same thing that so many others are: that a metaverse project will be the next big thing. Now they must construct it.
Olga Kharif
3 years ago
A month after freezing customer withdrawals, Celsius files for bankruptcy.
Alex Mashinsky, CEO of Celsius, speaks at Web Summit 2021 in Lisbon.
Celsius Network filed for Chapter 11 bankruptcy a month after freezing customer withdrawals, joining other crypto casualties.
Celsius took the step to stabilize its business and restructure for all stakeholders. The filing was done in the Southern District of New York.
The company, which amassed more than $20 billion by offering 18% interest on cryptocurrency deposits, paused withdrawals and other functions in mid-June, citing "extreme market conditions."
As the Fed raises interest rates aggressively, it hurts risk sentiment and squeezes funding costs. Voyager Digital Ltd. filed for Chapter 11 bankruptcy this month, and Three Arrows Capital has called in liquidators.
Celsius called the pause "difficult but necessary." Without the halt, "the acceleration of withdrawals would have allowed certain customers to be paid in full while leaving others to wait for Celsius to harvest value from illiquid or longer-term asset deployment activities," it said.
Celsius declined to comment. CEO Alex Mashinsky said the move will strengthen the company's future.
The company wants to keep operating. It's not requesting permission to allow customer withdrawals right now; Chapter 11 will handle customer claims. The filing estimates assets and liabilities between $1 billion and $10 billion.
Celsius is advised by Kirkland & Ellis, Centerview Partners, and Alvarez & Marsal.
Yield-promises
Celsius promised 18% returns on crypto loans. It lent those coins to institutional investors and participated in decentralized-finance apps.
When TerraUSD (UST) and Luna collapsed in May, Celsius pulled its funds from Terra's Anchor Protocol, which offered 20% returns on UST deposits. Recently, another large holding, staked ETH, or stETH, which is tied to Ether, became illiquid and discounted to Ether.
The lender is one of many crypto companies hurt by risky bets in the bear market. Also, Babel halted withdrawals. Voyager Digital filed for bankruptcy, and crypto hedge fund Three Arrows Capital filed for Chapter 15 bankruptcy.
According to blockchain data and tracker Zapper, Celsius repaid all of its debt in Aave, Compound, and MakerDAO last month.
Celsius charged Symbolic Capital Partners Ltd. 2,000 Ether as collateral for a cash loan on June 13. According to company filings, Symbolic was charged 2,545.25 Ether on June 11.
In July 6 filings, it said it reshuffled its board, appointing two new members and firing others.
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.
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Aldric Chen
3 years ago
Jack Dorsey's Meeting Best Practice was something I tried. It Performs Exceptionally Well in Consulting Engagements.
Yes, client meetings are difficult. Especially when I'm alone.
Clients must tell us their problems so we can help.
In-meeting challenges contribute nothing to our work. Consider this:
Clients are unprepared.
Clients are distracted.
Clients are confused.
Introducing Jack Dorsey's Google Doc approach
I endorse his approach to meetings.
Not Google Doc-related. Jack uses it for meetings.
This is what his meetings look like.
Prior to the meeting, the Chair creates the agenda, structure, and information using Google Doc.
Participants in the meeting would have 5-10 minutes to read the Google Doc.
They have 5-10 minutes to type their comments on the document.
In-depth discussion begins
There is elegance in simplicity. Here's how Jack's approach is fantastic.
Unprepared clients are given time to read.
During the meeting, they think and work on it.
They can see real-time remarks from others.
Discussion ensues.
Three months ago, I fell for this strategy. After trying it with a client, I got good results.
I conducted social control experiments in a few client workshops.
Context matters.
I am sure Jack Dorsey’s method works well in meetings. What about client workshops?
So, I tested Enterprise of the Future with a consulting client.
I sent multiple emails to client stakeholders describing the new approach.
No PowerPoints that day. I spent the night setting up the Google Doc with conversation topics, critical thinking questions, and a Before and After section.
The client was shocked. First, a Google Doc was projected. Second surprise was a verbal feedback.
“No pre-meeting materials?”
“Don’t worry. I know you are not reading it before our meeting, anyway.”
We laughed. The experiment started.
Observations throughout a 90-minute engagement workshop from beginning to end
For 10 minutes, the workshop was silent.
People read the Google Doc. For some, the silence was unnerving.
“Are you not going to present anything to us?”
I said everything's in Google Doc. I asked them to read, remark, and add relevant paragraphs.
As they unlocked their laptops, they were annoyed.
Ten client stakeholders are typing on the Google Doc. My laptop displays comment bubbles, red lines, new paragraphs, and strikethroughs.
The first 10 minutes were productive. Everyone has seen and contributed to the document.
I was silent.
The move to a classical workshop was smooth. I didn't stimulate dialogue. They did.
Stephanie asked Joe why a blended workforce hinders company productivity. She questioned his comments and additional paragraphs.
That is when a light bulb hit my head. Yes, you want to speak to the right person to resolve issues!
Not only that was discussed. Others discussed their remark bubbles with neighbors. Debate circles sprung up one after the other.
The best part? I asked everyone to add their post-discussion thoughts on a Google Doc.
After the workshop, I have:
An agreement-based working document
A post-discussion minutes that are prepared for publication
A record of the discussion points that were brought up, argued, and evaluated critically
It showed me how stakeholders viewed their Enterprise of the Future. It allowed me to align with them.
Finale Keynotes
Client meetings are a hit-or-miss. I know that.
Jack Dorsey's meeting strategy works for consulting. It promotes session alignment.
It relieves clients of preparation.
I get the necessary information to advance this consulting engagement.
It is brilliant.
Alex Mathers
2 years ago
400 articles later, nobody bothered to read them.
Writing for readers:
14 years of daily writing.
I post practically everything on social media. I authored hundreds of articles, thousands of tweets, and numerous volumes to almost no one.
Tens of thousands of readers regularly praise me.
I despised writing. I'm stuck now.
I've learned what readers like and what doesn't.
Here are some essential guidelines for writing with impact:
Readers won't understand your work if you can't.
Though obvious, this slipped me up. Share your truths.
Stories engage human brains.
Showing the journey of a person from worm to butterfly inspires the human spirit.
Overthinking hinders powerful writing.
The best ideas come from inner understanding in between thoughts.
Avoid writing to find it. Write.
Writing a masterpiece isn't motivating.
Write for five minutes to simplify. Step-by-step, entertaining, easy steps.
Good writing requires a willingness to make mistakes.
So write loads of garbage that you can edit into a good piece.
Courageous writing.
A courageous story will move readers. Personal experience is best.
Go where few dare.
Templates, outlines, and boundaries help.
Limitations enhance writing.
Excellent writing is straightforward and readable, removing all the unnecessary fat.
Use five words instead of nine.
Use ordinary words instead of uncommon ones.
Readers desire relatability.
Too much perfection will turn it off.
Write to solve an issue if you can't think of anything to write.
Instead, read to inspire. Best authors read.
Every tweet, thread, and novel must have a central idea.
What's its point?
This can make writing confusing.
️ Don't direct your reader.
Readers quit reading. Demonstrate, describe, and relate.
Even if no one responds, have fun. If you hate writing it, the reader will too.
Thomas Tcheudjio
3 years ago
If you don't crush these 3 metrics, skip the Series A.
I recently wrote about getting VCs excited about Marketplace start-ups. SaaS founders became envious!
Understanding how people wire tens of millions is the only Series A hack I recommend.
Few people understand the intellectual process behind investing.
VC is risk management.
Series A-focused VCs must cover two risks.
1. Market risk
You need a large market to cross a threshold beyond which you can build defensibilities. Series A VCs underwrite market risk.
They must see you have reached product-market fit (PMF) in a large total addressable market (TAM).
2. Execution risk
When evaluating your growth engine's blitzscaling ability, execution risk arises.
When investors remove operational uncertainty, they profit.
Series A VCs like businesses with derisked revenue streams. Don't raise unless you have a predictable model, pipeline, and growth.
Please beat these 3 metrics before Series A:
Achieve $1.5m ARR in 12-24 months (Market risk)
Above 100% Net Dollar Retention. (Market danger)
Lead Velocity Rate supporting $10m ARR in 2–4 years (Execution risk)
Hit the 3 and you'll raise $10M in 4 months. Discussing 2/3 may take 6–7 months.
If none, don't bother raising and focus on becoming a capital-efficient business (Topics for other posts).
Let's examine these 3 metrics for the brave ones.
1. Lead Velocity Rate supporting €$10m ARR in 2 to 4 years
Last because it's the least discussed. LVR is the most reliable data when evaluating a growth engine, in my opinion.
SaaS allows you to see the future.
Monthly Sales and Sales Pipelines, two predictive KPIs, have poor data quality. Both are lagging indicators, and minor changes can cause huge modeling differences.
Analysts and Associates will trash your forecasts if they're based only on Monthly Sales and Sales Pipeline.
LVR, defined as month-over-month growth in qualified leads, is rock-solid. There's no lag. You can See The Future if you use Qualified Leads and a consistent formula and process to qualify them.
With this metric in your hand, scaling your company turns into an execution play on which VCs are able to perform calculations risk.
2. Above-100% Net Dollar Retention.
Net Dollar Retention is a better-known SaaS health metric than LVR.
Net Dollar Retention measures a SaaS company's ability to retain and upsell customers. Ask what $1 of net new customer spend will be worth in years n+1, n+2, etc.
Depending on the business model, SaaS businesses can increase their share of customers' wallets by increasing users, selling them more products in SaaS-enabled marketplaces, other add-ons, and renewing them at higher price tiers.
If a SaaS company's annualized Net Dollar Retention is less than 75%, there's a problem with the business.
Slack's ARR chart (below) shows how powerful Net Retention is. Layer chart shows how existing customer revenue grows. Slack's S1 shows 171% Net Dollar Retention for 2017–2019.
Slack S-1
3. $1.5m ARR in the last 12-24 months.
According to Point 9, $0.5m-4m in ARR is needed to raise a $5–12m Series A round.
Target at least what you raised in Pre-Seed/Seed. If you've raised $1.5m since launch, don't raise before $1.5m ARR.
Capital efficiency has returned since Covid19. After raising $2m since inception, it's harder to raise $1m in ARR.
P9's 2016-2021 SaaS Funding Napkin
In summary, less than 1% of companies VCs meet get funded. These metrics can help you win.
If there’s demand for it, I’ll do one on direct-to-consumer.
Cheers!