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
Isobel Asher Hamilton
3 years ago
$181 million in bitcoin buried in a dump. $11 million to get them back
James Howells lost 8,000 bitcoins. He has $11 million to get them back.
His life altered when he threw out an iPhone-sized hard drive.
Howells, from the city of Newport in southern Wales, had two identical laptop hard drives squirreled away in a drawer in 2013. One was blank; the other had 8,000 bitcoins, currently worth around $181 million.
He wanted to toss out the blank one, but the drive containing the Bitcoin went to the dump.
He's determined to reclaim his 2009 stash.
Howells, 36, wants to arrange a high-tech treasure hunt for bitcoins. He can't enter the landfill.
Newport's city council has rebuffed Howells' requests to dig for his hard drive for almost a decade, stating it would be expensive and environmentally destructive.
I got an early look at his $11 million idea to search 110,000 tons of trash. He expects submitting it to the council would convince it to let him recover the hard disk.
110,000 tons of trash, 1 hard drive
Finding a hard disk among heaps of trash may seem Herculean.
Former IT worker Howells claims it's possible with human sorters, robot dogs, and an AI-powered computer taught to find hard drives on a conveyor belt.
His idea has two versions, depending on how much of the landfill he can search.
His most elaborate solution would take three years and cost $11 million to sort 100,000 metric tons of waste. Scaled-down version costs $6 million and takes 18 months.
He's created a team of eight professionals in AI-powered sorting, landfill excavation, garbage management, and data extraction, including one who recovered Columbia's black box data.
The specialists and their companies would be paid a bonus if they successfully recovered the bitcoin stash.
Howells: "We're trying to commercialize this project."
Howells claimed rubbish would be dug up by machines and sorted near the landfill.
Human pickers and a Max-AI machine would sort it. The machine resembles a scanner on a conveyor belt.
Remi Le Grand of Max-AI told us it will train AI to recognize Howells-like hard drives. A robot arm would select candidates.
Howells has added security charges to his scheme because he fears people would steal the hard drive.
He's budgeted for 24-hour CCTV cameras and two robotic "Spot" canines from Boston Dynamics that would patrol at night and look for his hard drive by day.
Howells said his crew met in May at the Celtic Manor Resort outside Newport for a pitch rehearsal.
Richard Hammond's narrative swings from banal to epic.
Richard Hammond filmed the meeting and created a YouTube documentary on Howells.
Hammond said of Howells' squad, "They're committed and believe in him and the idea."
Hammond: "It goes from banal to gigantic." "If I were in his position, I wouldn't have the strength to answer the door."
Howells said trash would be cleaned and repurposed after excavation. Reburying the rest.
"We won't pollute," he declared. "We aim to make everything better."
After the project is finished, he hopes to develop a solar or wind farm on the dump site. The council is unlikely to accept his vision soon.
A council representative told us, "Mr. Howells can't convince us of anything." "His suggestions constitute a significant ecological danger, which we can't tolerate and are forbidden by our permit."
Will the recovered hard drive work?
The "platter" is a glass or metal disc that holds the hard drive's data. Howells estimates 80% to 90% of the data will be recoverable if the platter isn't damaged.
Phil Bridge, a data-recovery expert who consulted Howells, confirmed these numbers.
If the platter is broken, Bridge adds, data recovery is unlikely.
Bridge says he was intrigued by the proposal. "It's an intriguing case," he added. Helping him get it back and proving everyone incorrect would be a great success story.
Who'd pay?
Swiss and German venture investors Hanspeter Jaberg and Karl Wendeborn told us they would fund the project if Howells received council permission.
Jaberg: "It's a needle in a haystack and a high-risk investment."
Howells said he had no contract with potential backers but had discussed the proposal in Zoom meetings. "Until Newport City Council gives me something in writing, I can't commit," he added.
Suppose he finds the bitcoins.
Howells said he would keep 30% of the data, worth $54 million, if he could retrieve it.
A third would go to the recovery team, 30% to investors, and the remainder to local purposes, including gifting £50 ($61) in bitcoin to each of Newport's 150,000 citizens.
Howells said he opted to spend extra money on "professional firms" to help convince the council.
What if the council doesn't approve?
If Howells can't win the council's support, he'll sue, claiming its actions constitute a "illegal embargo" on the hard drive. "I've avoided that path because I didn't want to cause complications," he stated. I wanted to cooperate with Newport's council.
Howells never met with the council face-to-face. He mentioned he had a 20-minute Zoom meeting in May 2021 but thought his new business strategy would help.
He met with Jessica Morden on June 24. Morden's office confirmed meeting.
After telling the council about his proposal, he can only wait. "I've never been happier," he said. This is our most professional operation, with the best employees.
The "crypto proponent" buys bitcoin every month and sells it for cash.
Howells tries not to think about what he'd do with his part of the money if the hard disk is found functional. "Otherwise, you'll go mad," he added.
This post is a summary. Read the full article here.
Trent Lapinski
3 years ago
What The Hell Is A Crypto Punk?
We are Crypto Punks, and we are changing your world.
A “Crypto Punk” is a new generation of entrepreneurs who value individual liberty and collective value creation and co-creation through decentralization. While many Crypto Punks were born and raised in a digital world, some of the early pioneers in the crypto space are from the Oregon Trail generation. They were born to an analog world, but grew up simultaneously alongside the birth of home computing, the Internet, and mobile computing.
A Crypto Punk’s world view is not the same as previous generations. By the time most Crypto Punks were born everything from fiat currency, the stock market, pharmaceuticals, the Internet, to advanced operating systems and microprocessing were already present or emerging. Crypto Punks were born into pre-existing conditions and systems of control, not governed by logic or reason but by greed, corporatism, subversion, bureaucracy, censorship, and inefficiency.
All Systems Are Human Made
Crypto Punks understand that all systems were created by people and that previous generations did not have access to information technologies that we have today. This is why Crypto Punks have different values than their parents, and value liberty, decentralization, equality, social justice, and freedom over wealth, money, and power. They understand that the only path forward is to work together to build new and better systems that make the old world order obsolete.
Unlike the original cypher punks and cyber punks, Crypto Punks are a new iteration or evolution of these previous cultures influenced by cryptography, blockchain technology, crypto economics, libertarianism, holographics, democratic socialism, and artificial intelligence. They are tasked with not only undoing the mistakes of previous generations, but also innovating and creating new ways of solving complex problems with advanced technology and solutions.
Where Crypto Punks truly differ is in their understanding that computer systems can exist for more than just engagement and entertainment, but actually improve the human condition by automating bureaucracy and inefficiency by creating more efficient economic incentives and systems.
Crypto Punks Value Transparency and Do Not Trust Flawed, Unequal, and Corrupt Systems
Crypto Punks have a strong distrust for inherently flawed and corrupt systems. This why Crypto Punks value transparency, free speech, privacy, and decentralization. As well as arguably computer systems over human powered systems.
Crypto Punks are the children of the Great Recession, and will never forget the economic corruption that still enslaves younger generations.
Crypto Punks were born to think different, and raised by computers to view reality through an LED looking glass. They will not surrender to the flawed systems of economic wage slavery, inequality, censorship, and subjection. They will literally engineer their own unstoppable financial systems and trade in cryptography over fiat currency merely to prove that belief systems are more powerful than corruption.
Crypto Punks are here to help achieve freedom from world governments, corporations and bankers who monetizine our data to control our lives.
Crypto Punks Decentralize
Despite all the evils of the world today, Crypto Punks know they have the power to create change. This is why Crypto Punks are optimistic about the future despite all the indicators that humanity is destined for failure.
Crypto Punks believe in systems that prioritize people and the planet above profit. Even so, Crypto Punks still believe in capitalistic systems, but only capitalistic systems that incentivize good behaviors that do not violate the common good for the sake of profit.
Cyber Punks Are Co-Creators
We are Crypto Punks, and we will build a better world for all of us. For the true price of creation is not in US dollars, but through working together as equals to replace the unequal and corrupt greedy systems of previous generations.
Where they have failed, Crypto Punks will succeed. Not because we want to, but because we have to. The world we were born into is so corrupt and its systems so flawed and unequal we were never given a choice.
We have to be the change we seek.
We are Crypto Punks.
Either help us, or get out of our way.
Are you a Crypto Punk?
Scott Hickmann
3 years ago
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3 years ago
The Learning Habit
The Habit of Learning implies constantly learning something new. One daily habit will make you successful. Learning will help you succeed.
Most successful people continually learn. Success requires this behavior. Daily learning.
Success loves books. Books offer expert advice. Everything is online today. Most books are online, so you can skip the library. You must download it and study for 15-30 minutes daily. This habit changes your thinking.
Typical Successful People
Warren Buffett reads 500 pages of corporate reports and five newspapers for five to six hours each day.
Each year, Bill Gates reads 50 books.
Every two weeks, Mark Zuckerberg reads at least one book.
According to his brother, Elon Musk studied two books a day as a child and taught himself engineering and rocket design.
Learning & Making Money Online
No worries if you can't afford books. Everything is online. YouTube, free online courses, etc.
How can you create this behavior in yourself?
1) Consider what you want to know
Before learning, know what's most important. So, move together.
Set a goal and schedule learning.
After deciding what you want to study, create a goal and plan learning time.
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Get the most out of your learning resources. Online or offline.
Daniel Clery
3 years ago
Twisted device investigates fusion alternatives
German stellarator revamped to run longer, hotter, compete with tokamaks
Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.
If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.
The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.
W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.
Wendelstein 7-X's water-cooled inner surface allows for longer runs.
HOSAN/IPP
Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.
Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.
Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.
W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.
The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.
In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.
W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.
A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.
W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.
Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.
Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.
Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.
Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”
Jared Heyman
2 years ago
The survival and demise of Y Combinator startups
I've written a lot about Y Combinator's success, but as any startup founder or investor knows, many startups fail.
Rebel Fund invests in the top 5-10% of new Y Combinator startups each year, so we focus on identifying and supporting the most promising technology startups in our ecosystem. Given the power law dynamic and asymmetric risk/return profile of venture capital, we worry more about our successes than our failures. Since the latter still counts, this essay will focus on the proportion of YC startups that fail.
Since YC's launch in 2005, the figure below shows the percentage of active, inactive, and public/acquired YC startups by batch.
As more startups finish, the blue bars (active) decrease significantly. By 12 years, 88% of startups have closed or exited. Only 7% of startups reach resolution each year.
YC startups by status after 12 years:
Half the startups have failed, over one-third have exited, and the rest are still operating.
In venture investing, it's said that failed investments show up before successful ones. This is true for YC startups, but only in their early years.
Below, we only present resolved companies from the first chart. Some companies fail soon after establishment, but after a few years, the inactive vs. public/acquired ratio stabilizes around 55:45. After a few years, a YC firm is roughly as likely to quit as fail, which is better than I imagined.
I prepared this post because Rebel investors regularly question me about YC startup failure rates and how long it takes for them to exit or shut down.
Early-stage venture investors can overlook it because 100x investments matter more than 0x investments.
YC founders can ignore it because it shouldn't matter if many of their peers succeed or fail ;)