More on Personal Growth

Glorin Santhosh
3 years ago
In his final days, Steve Jobs sent an email to himself. What It Said Was This
An email capturing Steve Jobs's philosophy.
Steve Jobs may have been the most inspired and driven entrepreneur.
He worked on projects because he wanted to leave a legacy.
Steve Jobs' final email to himself encapsulated his philosophy.
After his death from pancreatic cancer in October 2011, Laurene Powell Jobs released the email. He was 56.
Read: Steve Jobs by Walter Isaacson (#BestSeller)
The Email:
September 2010 Steve Jobs email:
“I grow little of the food I eat, and of the little I do grow, I do not breed or perfect the seeds.” “I do not make my own clothing. I speak a language I did not invent or refine,” he continued. “I did not discover the mathematics I use… I am moved by music I did not create myself.”
Jobs ended his email by reflecting on how others created everything he uses.
He wrote:
“When I needed medical attention, I was helpless to help myself survive.”
The Apple co-founder concluded by praising humanity.
“I did not invent the transistor, the microprocessor, object-oriented programming, or most of the technology I work with. I love and admire my species, living and dead, and am totally dependent on them for my life and well-being,” he concluded.
The email was made public as a part of the Steve Jobs Archive, a website that was launched in tribute to his legacy.
Steve Jobs' widow founded the internet archive. Apple CEO Tim Cook and former design leader Jony Ive were prominent guests.
Steve Jobs has always inspired because he shows how even the best can be improved.
High expectations were always there, and they were consistently met.
We miss him because he was one of the few with lifelong enthusiasm and persona.

Khyati Jain
3 years ago
By Engaging in these 5 Duplicitous Daily Activities, You Rapidly Kill Your Brain Cells
No, it’s not smartphones, overeating, or sugar.
Everyday practices affect brain health. Good brain practices increase memory and cognition.
Bad behaviors increase stress, which destroys brain cells.
Bad behaviors can reverse evolution and diminish the brain. So, avoid these practices for brain health.
1. The silent assassin
Introverts appreciated quarantine.
Before the pandemic, they needed excuses to remain home; thereafter, they had enough.
I am an introvert, and I didn’t hate quarantine. There are billions of people like me who avoid people.
Social relationships are important for brain health. Social anxiety harms your brain.
Antisocial behavior changes brains. It lowers IQ and increases drug abuse risk.
What you can do is as follows:
Make a daily commitment to engage in conversation with a stranger. Who knows, you might turn out to be your lone mate.
Get outside for at least 30 minutes each day.
Shop for food locally rather than online.
Make a call to a friend you haven't spoken to in a while.
2. Try not to rush things.
People love hustle culture. This economy requires a side gig to save money.
Long hours reduce brain health. A side gig is great until you burn out.
Work ages your wallet and intellect. Overworked brains age faster and lose cognitive function.
Working longer hours can help you make extra money, but it can harm your brain.
Side hustle but don't overwork.
What you can do is as follows:
Decide what hour you are not permitted to work after.
Three hours prior to night, turn off your laptop.
Put down your phone and work.
Assign due dates to each task.
3. Location is everything!
The environment may cause brain fog. High pollution can cause brain damage.
Air pollution raises Alzheimer's risk. Air pollution causes cognitive and behavioral abnormalities.
Polluted air can trigger early development of incurable brain illnesses, not simply lung harm.
Your city's air quality is uncontrollable. You may take steps to improve air quality.
In Delhi, schools and colleges are closed to protect pupils from polluted air. So I've adapted.
What you can do is as follows:
To keep your mind healthy and young, make an investment in a high-quality air purifier.
Enclose your windows during the day.
Use a N95 mask every day.
4. Don't skip this meal.
Fasting intermittently is trendy. Delaying breakfast to finish fasting is frequent.
Some skip breakfast and have a hefty lunch instead.
Skipping breakfast might affect memory and focus. Skipping breakfast causes low cognition, delayed responsiveness, and irritation.
Breakfast affects mood and productivity.
Intermittent fasting doesn't prevent healthy breakfasts.
What you can do is as follows:
Try to fast for 14 hours, then break it with a nutritious breakfast.
So that you can have breakfast in the morning, eat dinner early.
Make sure your breakfast is heavy in fiber and protein.
5. The quickest way to damage the health of your brain
Brain health requires water. 1% dehydration can reduce cognitive ability by 5%.
Cerebral fog and mental clarity might result from 2% brain dehydration. Dehydration shrinks brain cells.
Dehydration causes midday slumps and unproductivity. Water improves work performance.
Dehydration can harm your brain, so drink water throughout the day.
What you can do is as follows:
Always keep a water bottle at your desk.
Enjoy some tasty herbal teas.
With a big glass of water, begin your day.
Bring your own water bottle when you travel.
Conclusion
Bad habits can harm brain health. Low cognition reduces focus and productivity.
Unproductive work leads to procrastination, failure, and low self-esteem.
Avoid these harmful habits to optimize brain health and function.

Jari Roomer
3 years ago
After 240 articles and 2.5M views on Medium, 9 Raw Writing Tips
Late in 2018, I published my first Medium article, but I didn't start writing seriously until 2019. Since then, I've written more than 240 articles, earned over $50,000 through Medium's Partner Program, and had over 2.5 million page views.
Write A Lot
Most people don't have the patience and persistence for this simple writing secret:
Write + Write + Write = possible success
Writing more improves your skills.
The more articles you publish, the more likely one will go viral.
If you only publish once a month, you have no views. If you publish 10 or 20 articles a month, your success odds increase 10- or 20-fold.
Tim Denning, Ayodeji Awosika, Megan Holstein, and Zulie Rane. Medium is their jam. How are these authors alike? They're productive and consistent. They're prolific.
80% is publishable
Many writers battle perfectionism.
To succeed as a writer, you must publish often. You'll never publish if you aim for perfection.
Adopt the 80 percent-is-good-enough mindset to publish more. It sounds terrible, but it'll boost your writing success.
Your work won't be perfect. Always improve. Waiting for perfection before publishing will take a long time.
Second, readers are your true critics, not you. What you consider "not perfect" may be life-changing for the reader. Don't let perfectionism hinder the reader.
Don't let perfectionism hinder the reader. ou don't want to publish mediocre articles. When the article is 80% done, publish it. Don't spend hours editing. Realize it. Get feedback. Only this will work.
Make Your Headline Irresistible
We all judge books by their covers, despite the saying. And headlines. Readers, including yourself, judge articles by their titles. We use it to decide if an article is worth reading.
Make your headlines irresistible. Want more article views? Then, whether you like it or not, write an attractive article title.
Many high-quality articles are collecting dust because of dull, vague headlines. It didn't make the reader click.
As a writer, you must do more than produce quality content. You must also make people click on your article. This is a writer's job. How to create irresistible headlines:
Curiosity makes readers click. Here's a tempting example...
Example: What Women Actually Look For in a Guy, According to a Huge Study by Luba Sigaud
Use Numbers: Click-bait lists. I mean, which article would you click first? ‘Some ways to improve your productivity’ or ’17 ways to improve your productivity.’ Which would I click?
Example: 9 Uncomfortable Truths You Should Accept Early in Life by Sinem Günel
Most headlines are dull. If you want clicks, get 'sexy'. Buzzword-ify. Invoke emotion. Trendy words.
Example: 20 Realistic Micro-Habits To Live Better Every Day by Amardeep Parmar
Concise paragraphs
Our culture lacks focus. If your headline gets a click, keep paragraphs short to keep readers' attention.
Some writers use 6–8 lines per paragraph, but I prefer 3–4. Longer paragraphs lose readers' interest.
A writer should help the reader finish an article, in my opinion. I consider it a job requirement. You can't force readers to finish an article, but you can make it 'snackable'
Help readers finish an article with concise paragraphs, interesting subheadings, exciting images, clever formatting, or bold attention grabbers.
Work And Move On
I've learned over the years not to get too attached to my articles. Many writers report a strange phenomenon:
The articles you're most excited about usually bomb, while the ones you're not tend to do well.
This isn't always true, but I've noticed it in my own writing. My hopes for an article usually make it worse. The more objective I am, the better an article does.
Let go of a finished article. 40 or 40,000 views, whatever. Now let the article do its job. Onward. Next story. Start another project.
Disregard Haters
Online content creators will encounter haters, whether on YouTube, Instagram, or Medium. More views equal more haters. Fun, right?
As a web content creator, I learned:
Don't debate haters. Never.
It's a mistake I've made several times. It's tempting to prove haters wrong, but they'll always find a way to be 'right'. Your response is their fuel.
I smile and ignore hateful comments. I'm indifferent. I won't enter a negative environment. I have goals, money, and a life to build. "I'm not paid to argue," Drake once said.
Use Grammarly
Grammarly saves me as a non-native English speaker. You know Grammarly. It shows writing errors and makes article suggestions.
As a writer, you need Grammarly. I have a paid plan, but their free version works. It improved my writing greatly.
Put The Reader First, Not Yourself
Many writers write for themselves. They focus on themselves rather than the reader.
Ask yourself:
This article teaches what? How can they be entertained or educated?
Personal examples and experiences improve writing quality. Don't focus on yourself.
It's not about you, the content creator. Reader-focused. Putting the reader first will change things.
Extreme ownership: Stop blaming others
I remember writing a lot on Medium but not getting many views. I blamed Medium first. Poor algorithm. Poor publishing. All sucked.
Instead of looking at what I could do better, I blamed others.
When you blame others, you lose power. Owning your results gives you power.
As a content creator, you must take full responsibility. Extreme ownership means 100% responsibility for work and results.
You don’t blame others. You don't blame the economy, president, platform, founders, or audience. Instead, you look for ways to improve. Few people can do this.
Blaming is useless. Zero. Taking ownership of your work and results will help you progress. It makes you smarter, better, and stronger.
Instead of blaming others, you'll learn writing, marketing, copywriting, content creation, productivity, and other skills. Game-changer.
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Isaac Benson
3 years ago
What's the difference between Proof-of-Time and Proof-of-History?

Blockchain validates transactions with consensus algorithms. Bitcoin and Ethereum use Proof-of-Work, while Polkadot and Cardano use Proof-of-Stake.
Other consensus protocols are used to verify transactions besides these two. This post focuses on Proof-of-Time (PoT), used by Analog, and Proof-of-History (PoH), used by Solana as a hybrid consensus protocol.
PoT and PoH may seem similar to users, but they are actually very different protocols.
Proof-of-Time (PoT)
Analog developed Proof-of-Time (PoT) based on Delegated Proof-of-Stake (DPoS). Users select "delegates" to validate the next block in DPoS. PoT uses a ranking system, and validators stake an equal amount of tokens. Validators also "self-select" themselves via a verifiable random function."
The ranking system gives network validators a performance score, with trustworthy validators with a long history getting higher scores. System also considers validator's fixed stake. PoT's ledger is called "Timechain."
Voting on delegates borrows from DPoS, but there are changes. PoT's first voting stage has validators (or "time electors" putting forward a block to be included in the ledger).
Validators are chosen randomly based on their ranking score and fixed stake. One validator is chosen at a time using a Verifiable Delay Function (VDF).
Validators use a verifiable delay function to determine if they'll propose a Timechain block. If chosen, they validate the transaction and generate a VDF proof before submitting both to other Timechain nodes.
This leads to the second process, where the transaction is passed through 1,000 validators selected using the same method. Each validator checks the transaction to ensure it's valid.
If the transaction passes, validators accept the block, and if over 2/3 accept it, it's added to the Timechain.
Proof-of-History (PoH)
Proof-of-History is a consensus algorithm that proves when a transaction occurred. PoH uses a VDF to verify transactions, like Proof-of-Time. Similar to Proof-of-Work, VDFs use a lot of computing power to calculate but little to verify transactions, similar to (PoW).
This shows users and validators how long a transaction took to verify.
PoH uses VDFs to verify event intervals. This process uses cryptography to prevent determining output from input.
The outputs of one transaction are used as inputs for the next. Timestamps record the inputs' order. This checks if data was created before an event.
PoT vs. PoH
PoT and PoH differ in that:
PoT uses VDFs to select validators (or time electors), while PoH measures time between events.
PoH uses a VDF to validate transactions, while PoT uses a ranking system.
PoT's VDF-elected validators verify transactions proposed by a previous validator. PoH uses a VDF to validate transactions and data.
Conclusion
Both Proof-of-Time (PoT) and Proof-of-History (PoH) validate blockchain transactions differently. PoT uses a ranking system to randomly select validators to verify transactions.
PoH uses a Verifiable Delay Function to validate transactions, verify how much time has passed between two events, and allow validators to quickly verify a transaction without malicious actors knowing the input.
Scott Duke Kominers
3 years ago
NFT Creators Go Creative Commons Zero (cc0)
On January 1, "Public Domain Day," thousands of creative works immediately join the public domain. The original creator or copyright holder loses exclusive rights to reproduce, adapt, or publish the work, and anybody can use it. It happens with movies, poems, music, artworks, books (where creative rights endure 70 years beyond the author's death), and sometimes source code.
Public domain creative works open the door to new uses. 400,000 sound recordings from before 1923, including Winnie-the-Pooh, were released this year. With most of A.A. Milne's 1926 Winnie-the-Pooh characters now available, we're seeing innovative interpretations Milne likely never planned. The ancient hyphenated version of the honey-loving bear is being adapted for a horror movie: "Winnie-the-Pooh: Blood and Honey"... with Pooh and Piglet as the baddies.
Counterintuitively, experimenting and recombination can occasionally increase IP value. Open source movements allow the public to build on (or fork and duplicate) existing technologies. Permissionless innovation helps Android, Linux, and other open source software projects compete. Crypto's success at attracting public development is also due to its support of open source and "remix culture," notably in NFT forums.
Production memes
NFT projects use several IP strategies to establish brands, communities, and content. Some preserve regular IP protections; others offer NFT owners the opportunity to innovate on connected IP; yet others have removed copyright and other IP safeguards.
By using the "Creative Commons Zero" (cc0) license, artists can intentionally select for "no rights reserved." This option permits anyone to benefit from derivative works without legal repercussions. There's still a lot of confusion between copyrights and NFTs, so nothing here should be considered legal, financial, tax, or investment advice. Check out this post for an overview of copyright vulnerabilities with NFTs and how authors can protect owners' rights. This article focuses on cc0.
Nouns, a 2021 project, popularized cc0 for NFTs. Others followed, including: A Common Place, Anonymice, Blitmap, Chain Runners, Cryptoadz, CryptoTeddies, Goblintown, Gradis, Loot, mfers, Mirakai, Shields, and Terrarium Club are cc0 projects.
Popular crypto artist XCOPY licensed their 1-of-1 NFT artwork "Right-click and Save As Guy" under cc0 in January, exactly one month after selling it. cc0 has spawned many derivatives.
"Right-click Save As Guy" by XCOPY (1)/derivative works (2)
XCOPY said Monday he would apply cc0 to "all his existing art." "We haven't seen a cc0 summer yet, but I think it's approaching," said the artist. - predicting a "DeFi summer" in 2020, when decentralized finance gained popularity.
Why do so many NFT authors choose "no rights"?
Promoting expansions of the original project to create a more lively and active community is one rationale. This makes sense in crypto, where many value open sharing and establishing community.
Creativity depends on cultural significance. NFTs may allow verifiable ownership of any digital asset, regardless of license, but cc0 jumpstarts "meme-ability" by actively, not passively, inviting derivative works. As new derivatives are made and shared, attention might flow back to the original, boosting its reputation. This may inspire new interpretations, leading in a flywheel effect where each derivative adds to the original's worth - similar to platform network effects, where platforms become more valuable as more users join them.
cc0 licence allows creators "seize production memes."
Physical items are also using cc0 NFT assets, thus it's not just a digital phenomenon. The Nouns Vision initiative turned the square-framed spectacles shown on each new NounsDAO NFT ("one per day, forever") into luxury sunglasses. Blitmap's pixel-art has been used on shoes, apparel, and caps. In traditional IP regimes, a single owner controls creation, licensing, and production.
The physical "blitcap" (3rd level) is a descendant of the trait in the cc0 Chain Runners collection (2nd), which uses the "logo" from cc0 Blitmap (1st)! The Logo is Blitmap token #84 and has been used as a trait in various collections. The "Dom Rose" is another popular token. These homages reference Blitmap's influence as a cc0 leader, as one of the earliest NFT projects to proclaim public domain intents. A new collection, Citizens of Tajigen, emerged last week with a Blitcap characteristic.
These derivatives can be a win-win for everyone, not just the original inventors, especially when using NFT assets to establish unique brands. As people learn about the derivative, they may become interested in the original. If you see someone wearing Nouns glasses on the street (or in a Super Bowl ad), you may desire a pair, but you may also be interested in buying an original NounsDAO NFT or related derivative.
Blitmap Logo Hat (1), Chain Runners #780 ft. Hat (2), and Blitmap Original "Logo #87" (3)
Co-creating open source
NFTs' power comes from smart contract technology's intrinsic composability. Many smart contracts can be integrated or stacked to generate richer applications.
"Money Legos" describes how decentralized finance ("DeFi") smart contracts interconnect to generate new financial use cases. Yearn communicates with MakerDAO's stablecoin $DAI and exchange liquidity provider Curve by calling public smart contract methods. NFTs and their underlying smart contracts can operate as the base-layer framework for recombining and interconnecting culture and creativity.
cc0 gives an NFT's enthusiast community authority to develop new value layers whenever, wherever, and however they wish.
Multiple cc0 projects are playable characters in HyperLoot, a Loot Project knockoff.
Open source and Linux's rise are parallels. When the internet was young, Microsoft dominated the OS market with Windows. Linux (and its developer Linus Torvalds) championed a community-first mentality, freely available the source code without restrictions. This led to developers worldwide producing new software for Linux, from web servers to databases. As people (and organizations) created world-class open source software, Linux's value proposition grew, leading to explosive development and industry innovation. According to Truelist, Linux powers 96.3% of the top 1 million web servers and 85% of smartphones.
With cc0 licensing empowering NFT community builders, one might hope for long-term innovation. Combining cc0 with NFTs "turns an antagonistic game into a co-operative one," says NounsDAO cofounder punk4156. It's important on several levels. First, decentralized systems from open source to crypto are about trust and coordination, therefore facilitating cooperation is crucial. Second, the dynamics of this cooperation work well in the context of NFTs because giving people ownership over their digital assets allows them to internalize the results of co-creation through the value that accrues to their assets and contributions, which incentivizes them to participate in co-creation in the first place.
Licensed to create
If cc0 projects are open source "applications" or "platforms," then NFT artwork, metadata, and smart contracts provide the "user interface" and the underlying blockchain (e.g., Ethereum) is the "operating system." For these apps to attain Linux-like potential, more infrastructure services must be established and made available so people may take advantage of cc0's remixing capabilities.
These services are developing. Zora protocol and OpenSea's open source Seaport protocol enable open, permissionless NFT marketplaces. A pixel-art-rendering engine was just published on-chain to the Ethereum blockchain and integrated into OKPC and ICE64. Each application improves blockchain's "out-of-the-box" capabilities, leading to new apps created from the improved building blocks.
Web3 developer growth is at an all-time high, yet it's still a small fraction of active software developers globally. As additional developers enter the field, prospective NFT projects may find more creative and infrastructure Legos for cc0 and beyond.
Electric Capital Developer Report (2021), p. 122
Growth requires composability. Users can easily integrate digital assets developed on public standards and compatible infrastructure into other platforms. The Loot Project is one of the first to illustrate decentralized co-creation, worldbuilding, and more in NFTs. This example was low-fi or "incomplete" aesthetically, providing room for imagination and community co-creation.
Loot began with a series of Loot bag NFTs, each listing eight "adventure things" in white writing on a black backdrop (such as Loot Bag #5726's "Katana, Divine Robe, Great Helm, Wool Sash, Divine Slippers, Chain Gloves, Amulet, Gold Ring"). Dom Hofmann's free Loot bags served as a foundation for the community.
Several projects have begun metaphorical (lore) and practical (game development) world-building in a short time, with artists contributing many variations to the collective "Lootverse." They've produced games (Realms & The Crypt), characters (Genesis Project, Hyperloot, Loot Explorers), storytelling initiatives (Banners, OpenQuill), and even infrastructure (The Rift).
Why cc0 and composability? Because consumers own and control Loot bags, they may use them wherever they choose by connecting their crypto wallets. This allows users to participate in multiple derivative projects, such as Genesis Adventurers, whose characters appear in many others — creating a decentralized franchise not owned by any one corporation.
Genesis Project's Genesis Adventurer (1) with HyperLoot (2) and Loot Explorer (3) versions
When to go cc0
There are several IP development strategies NFT projects can use. When it comes to cc0, it’s important to be realistic. The public domain won't make a project a runaway success just by implementing the license. cc0 works well for NFT initiatives that can develop a rich, enlarged ecosystem.
Many of the most successful cc0 projects have introduced flexible intellectual property. The Nouns brand is as obvious for a beer ad as for real glasses; Loot bags are simple primitives that make sense in all adventure settings; and the Goblintown visual style looks good on dwarfs, zombies, and cranky owls as it does on Val Kilmer.
The ideal cc0 NFT project gives builders the opportunity to add value:
vertically, by stacking new content and features directly on top of the original cc0 assets (for instance, as with games built on the Loot ecosystem, among others), and
horizontally, by introducing distinct but related intellectual property that helps propagate the original cc0 project’s brand (as with various Goblintown derivatives, among others).
These actions can assist cc0 NFT business models. Because cc0 NFT projects receive royalties from secondary sales, third-party extensions and derivatives can boost demand for the original assets.
Using cc0 license lowers friction that could hinder brand-reinforcing extensions or lead to them bypassing the original. Robbie Broome recently argued (in the context of his cc0 project A Common Place) that giving away his IP to cc0 avoids bad rehashes down the line. If UrbanOutfitters wanted to put my design on a tee, they could use the actual work instead of hiring a designer. CC0 can turn competition into cooperation.
Community agreement about core assets' value and contribution can help cc0 projects. Cohesion and engagement are key. Using the above examples: Developers can design adventure games around whatever themes and item concepts they desire, but many choose Loot bags because of the Lootverse's community togetherness. Flipmap shared half of its money with the original Blitmap artists in acknowledgment of that project's core role in the community. This can build a healthy culture within a cc0 project ecosystem. Commentator NiftyPins said it was smart to acknowledge the people that constructed their universe. Many OG Blitmap artists have popped into the Flipmap discord to share information.
cc0 isn't a one-size-fits-all answer; NFTs formed around well-established brands may prefer more restrictive licenses to preserve their intellectual property and reinforce exclusivity. cc0 has some superficial similarities to permitting NFT owners to market the IP connected with their NFTs (à la Bored Ape Yacht Club), but there is a significant difference: cc0 holders can't exclude others from utilizing the same IP. This can make it tougher for holders to develop commercial brands on cc0 assets or offer specific rights to partners. Holders can still introduce enlarged intellectual property (such as backstories or derivatives) that they control.
Blockchain technologies and the crypto ethos are decentralized and open-source. This makes it logical for crypto initiatives to build around cc0 content models, which build on the work of the Creative Commons foundation and numerous open source pioneers.
NFT creators that choose cc0 must select how involved they want to be in building the ecosystem. Some cc0 project leaders, like Chain Runners' developers, have kept building on top of the initial cc0 assets, creating an environment derivative projects can plug into. Dom Hofmann stood back from Loot, letting the community lead. (Dom is also working on additional cc0 NFT projects for the company he formed to build Blitmap.) Other authors have chosen out totally, like sartoshi, who announced his exit from the cc0 project he founded, mfers, and from the NFT area by publishing a final edition suitably named "end of sartoshi" and then deactivating his Twitter account. A multi-signature wallet of seven mfers controls the project's smart contract.
cc0 licensing allows a robust community to co-create in ways that benefit all members, regardless of original creators' continuous commitment. We foresee more organized infrastructure and design patterns as NFT matures. Like open source software, value capture frameworks may see innovation. (We could imagine a variant of the "Sleepycat license," which requires commercial software to pay licensing fees when embedding open source components.) As creators progress the space, we expect them to build unique rights and licensing strategies. cc0 allows NFT producers to bootstrap ideas that may take off.

Vitalik
3 years ago
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
