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

Nitin Sharma
2 years ago
Web3 Terminology You Should Know
The easiest online explanation.
Web3 is growing. Crypto companies are growing.
Instagram, Adidas, and Stripe adopted cryptocurrency.
Bitcoin and other cryptocurrencies made web3 famous.
Most don't know where to start. Cryptocurrency, DeFi, etc. are investments.
Since we don't understand web3, I'll help you today.
Let’s go.
1. Web3
It is the third generation of the web, and it is built on the decentralization idea which means no one can control it.
There are static webpages that we can only read on the first generation of the web (i.e. Web 1.0).
Web 2.0 websites are interactive. Twitter, Medium, and YouTube.
Each generation controlled the website owner. Simply put, the owner can block us. However, data breaches and selling user data to other companies are issues.
They can influence the audience's mind since they have control.
Assume Twitter's CEO endorses Donald Trump. Result? Twitter would have promoted Donald Trump with tweets and graphics, enhancing his chances of winning.
We need a decentralized, uncontrollable system.
And then there’s Web3.0 to consider. As Bitcoin and Ethereum values climb, so has its popularity. Web3.0 is uncontrolled web evolution. It's good and bad.
Dapps, DeFi, and DAOs are here. It'll all be explained afterwards.
2. Cryptocurrencies:
No need to elaborate.
Bitcoin, Ethereum, Cardano, and Dogecoin are cryptocurrencies. It's digital money used for payments and other uses.
Programs must interact with cryptocurrencies.
3. Blockchain:
Blockchain facilitates bitcoin transactions, investments, and earnings.
This technology governs Web3. It underpins the web3 environment.
Let us delve much deeper.
Blockchain is simple. However, the name expresses the meaning.
Blockchain is a chain of blocks.
Let's use an image if you don't understand.
The graphic above explains blockchain. Think Blockchain. The block stores related data.
Here's more.
4. Smart contracts
Programmers and developers must write programs. Smart contracts are these blockchain apps.
That’s reasonable.
Decentralized web3.0 requires immutable smart contracts or programs.
5. NFTs
Blockchain art is NFT. Non-Fungible Tokens.
Explaining Non-Fungible Token may help.
Two sorts of tokens:
These tokens are fungible, meaning they can be changed. Think of Bitcoin or cash. The token won't change if you sell one Bitcoin and acquire another.
Non-Fungible Token: Since these tokens cannot be exchanged, they are exclusive. For instance, music, painting, and so forth.
Right now, Companies and even individuals are currently developing worthless NFTs.
The concept of NFTs is much improved when properly handled.
6. Dapp
Decentralized apps are Dapps. Instagram, Twitter, and Medium apps in the same way that there is a lot of decentralized blockchain app.
Curve, Yearn Finance, OpenSea, Axie Infinity, etc. are dapps.
7. DAOs
DAOs are member-owned and governed.
Consider it a company with a core group of contributors.
8. DeFi
We all utilize centrally regulated financial services. We fund these banks.
If you have $10,000 in your bank account, the bank can invest it and retain the majority of the profits.
We only get a penny back. Some banks offer poor returns. To secure a loan, we must trust the bank, divulge our information, and fill out lots of paperwork.
DeFi was built for such issues.
Decentralized banks are uncontrolled. Staking, liquidity, yield farming, and more can earn you money.
Web3 beginners should start with these resources.

CyberPunkMetalHead
3 years ago
195 countries want Terra Luna founder Do Kwon
Interpol has issued a red alert on Terraform Labs' CEO, South Korean prosecutors said.
After the May crash of Terra Luna revealed tax evasion issues, South Korean officials filed an arrest warrant for Do Kwon, but he is missing.
Do Kwon is now a fugitive in 195 countries after Seoul prosecutors placed him to Interpol's red list. Do Kwon hasn't commented since then. The red list allows any country's local authorities to apprehend Do Kwon.
Do Dwon and Terraform Labs were believed to have moved to Singapore days before the $40 billion wipeout, but Singapore authorities said he fled the country on September 17. Do Kwon tweeted that he wasn't on the run and cited privacy concerns.
Do Kwon was not on the red list at the time and said he wasn't "running," only to reply to his own tweet saying he hasn't jogged in a while and needed to trim calories.
Whether or not it makes sense to read too much into this, the reality is that Do Kwon is now on Interpol red list, despite the firmly asserts on twitter that he does absolutely nothing to hide.
UPDATE:
South Korean authorities are investigating alleged withdrawals of over $60 million U.S. and seeking to freeze these assets. Korean authorities believe a new wallet exchanged over 3000 BTC through OKX and Kucoin.
Do Kwon and the Luna Foundation Guard (of whom Do Kwon is a key member of) have declined all charges and dubbed this disinformation.
Singapore's Luna Foundation Guard (LFG) manages the Terra Ecosystem.
The Legal Situation
Multiple governments are searching for Do Kwon and five other Terraform Labs employees for financial markets legislation crimes.
South Korean authorities arrested a man suspected of tax fraud and Ponzi scheme.
The U.S. SEC is also examining Terraform Labs on how UST was advertised as a stablecoin. No legal precedent exists, so it's unclear what's illegal.
The future of Terraform Labs, Terra, and Terra 2 is unknown, and despite what Twitter shills say about LUNC, the company remains in limbo awaiting a decision that will determine its fate. This project isn't a wise investment.

joyce shen
3 years ago
Framework to Evaluate Metaverse and Web3
Everywhere we turn, there's a new metaverse or Web3 debut. Microsoft recently announced a $68.7 BILLION cash purchase of Activision.
Like AI in 2013 and blockchain in 2014, NFT growth in 2021 feels like this year's metaverse and Web3 growth. We are all bombarded with information, conflicting signals, and a sensation of FOMO.
How can we evaluate the metaverse and Web3 in a noisy, new world? My framework for evaluating upcoming technologies and themes is shown below. I hope you will also find them helpful.
Understand the “pipes” in a new space.
Whatever people say, Metaverse and Web3 will have to coexist with the current Internet. Companies who host, move, and store data over the Internet have a lot of intriguing use cases in Metaverse and Web3, whether in infrastructure, data analytics, or compliance. Hence the following point.
## Understand the apps layer and their infrastructure.
Gaming, crypto exchanges, and NFT marketplaces would not exist today if not for technology that enables rapid app creation. Yes, according to Chainalysis and other research, 30–40% of Ethereum is self-hosted, with the rest hosted by large cloud providers. For Microsoft to acquire Activision makes strategic sense. It's not only about the games, but also the infrastructure that supports them.
Follow the money
Understanding how money and wealth flow in a complex and dynamic environment helps build clarity. Unless you are exceedingly wealthy, you have limited ability to significantly engage in the Web3 economy today. Few can just buy 10 ETH and spend it in one day. You must comprehend who benefits from the process, and how that 10 ETH circulates now and possibly tomorrow. Major holders and players control supply and liquidity in any market. Today, most Web3 apps are designed to increase capital inflow so existing significant holders can utilize it to create a nascent Web3 economy. When you see a new Metaverse or Web3 application, remember how money flows.
What is the use case?
What does the app do? If there is no clear use case with clear makers and consumers solving a real problem, then the euphoria soon fades, and the only stakeholders who remain enthused are those who have too much to lose.
Time is a major competition that is often overlooked.
We're only busier, but each day is still 24 hours. Using new apps may mean that time is lost doing other things. The user must be eager to learn. Metaverse and Web3 vs. our time? I don't think we know the answer yet (at least for working adults whose cost of time is higher).
I don't think we know the answer yet (at least for working adults whose cost of time is higher).
People and organizations need security and transparency.
For new technologies or apps to be widely used, they must be safe, transparent, and trustworthy. What does secure Metaverse and Web3 mean? This is an intriguing subject for both the business and public sectors. Cloud adoption grew in part due to improved security and data protection regulations.
The following frameworks can help analyze and understand new technologies and emerging technological topics, unless you are a significant investment fund with the financial ability to gamble on numerous initiatives and essentially form your own “index fund”.
I write on VC, startups, and leadership.
More on https://www.linkedin.com/in/joycejshen/ and https://joyceshen.substack.com/
This writing is my own opinion and does not represent investment advice.
You might also like

Christianlauer
3 years ago
Looker Studio Pro is now generally available, according to Google.
Great News about the new Google Business Intelligence Solution
Google has renamed Data Studio to Looker Studio and Looker Studio Pro.
Now, Google releases Looker Studio Pro. Similar to the move from Data Studio to Looker Studio, Looker Studio Pro is basically what Looker was previously, but both solutions will merge. Google says the Pro edition will acquire new enterprise management features, team collaboration capabilities, and SLAs.
In addition to Google's announcements and sales methods, additional features include:
Looker Studio assets can now have organizational ownership. Customers can link Looker Studio to a Google Cloud project and migrate existing assets once. This provides:
Your users' created Looker Studio assets are all kept in a Google Cloud project.
When the users who own assets leave your organization, the assets won't be removed.
Using IAM, you may provide each Looker Studio asset in your company project-level permissions.
Other Cloud services can access Looker Studio assets that are owned by a Google Cloud project.
Looker Studio Pro clients may now manage report and data source access at scale using team workspaces.
Google announcing these features for the pro version is fascinating. Both products will likely converge, but Google may only release many features in the premium version in the future. Microsoft with Power BI and its free and premium variants already achieves this.
Sources and Further Readings
Google, Release Notes (2022)
Google, Looker (2022)

Dr Mehmet Yildiz
3 years ago
How I train my brain daily for clarity and productivity.
I use a conceptual and practical system I developed decades ago as an example.
Since childhood, I've been interested in the brain-mind connection, so I developed a system using scientific breakthroughs, experiments, and the experiences of successful people in my circles.
This story provides a high-level overview of a custom system to inform and inspire readers. Creating a mind gym was one of my best personal and professional investments.
Such a complex system may not be possible for everyone or appear luxurious at first. However, the process and approach may help you find more accessible and viable solutions.
Visualizing the brain as a muscle, I learned to stimulate it with physical and mental exercises, applying a new mindset and behavioral changes.
My methods and practices may not work for others because we're all different. I focus on the approach's principles and highlights so you can create your own program.
Some create a conceptual and practical system intuitively, and others intellectually. Both worked. I see intellect and intuition as higher selves.
The mental tools I introduce are based on lifestyle changes and can be personalized by anyone, barring physical constraints or underlying health conditions.
Some people can't meditate despite wanting to due to mental constraints. This story lacks exceptions.
People's systems may vary. Many have used my tools successfully. All have scientific backing because their benefits attracted scientists. None are unethical or controversial.
My focus is cognition, which is the neocortex's ability. These practices and tools can affect the limbic and reptilian brain regions.
A previous article discussed brain health's biological aspects. This article focuses on psychology.
Thinking, learning, and remembering are cognitive abilities. Cognitive abilities determine our health and performance.
Cognitive health is the ability to think, concentrate, learn, and remember. Cognitive performance boosting involves various tools and processes. My system and protocols address cognitive health and performance.
As a biological organ, the brain's abilities decline with age, especially if not used regularly. Older people have more neurodegenerative disorders like dementia.
As aging is inevitable, I focus on creating cognitive reserves to remain mentally functional as we age and face mental decline or cognitive impairment.
My protocols focus on neurogenesis, or brain growth and maintenance. Neurons and connections can grow at any age.
Metacognition refers to knowing our cognitive abilities, like thinking about thinking and learning how to learn.
In the following sections, I provide an overview of my system, mental tools, and protocols.
This system summarizes my 50-year career. Some may find it too abstract, so I give examples.
First, explain the system. Section 2 introduces activities. Third, how to measure and maintain mental growth.
1 — Developed a practical mental gym.
The mental gym is a metaphor for the physical fitness gym to improve our mental muscles.
This concept covers brain and mind functionality. Integrated biological and psychological components.
I'll describe my mental gym so my other points make sense. My mental gym has physical and mental tools.
Mindfulness, meditation, visualization, self-conversations, breathing exercises, expressive writing, working in a flow state, reading, music, dance, isometric training, barefoot walking, cold/heat exposure, CBT, and social engagements are regular tools.
Dancing, walking, and thermogenesis are body-related tools. As the brain is part of the body and houses the mind, these tools can affect mental abilities such as attention, focus, memory, task switching, and problem-solving.
Different people may like different tools. I chose these tools based on my needs, goals, and lifestyle. They're just examples. You can choose tools that fit your goals and personality.
2 — Performed tasks regularly.
These tools gave me clarity. They became daily hobbies. Some I did alone, others with others.
Some examples: I meditate daily. Even though my overactive mind made daily meditation difficult at first, I now enjoy it. Meditation three times a day sharpens my mind.
Self-talk is used for self-therapy and creativity. Self-talk was initially difficult, but neurogenesis rewired my brain to make it a habit.
Cold showers, warm baths with Epsom salts, fasting, barefoot walks on the beach or grass, dancing, calisthenics, trampoline hopping, and breathing exercises increase my mental clarity, creativity, and productivity.
These exercises can increase BDNF, which promotes nervous system growth. They improve mental capacity and performance by increasing blood flow and brain oxygenation.
I use weekly and occasional activities like dry saunas, talking with others, and community activities.
These activities stimulate the brain and mind, improving performance and cognitive capacity.
3 — Measured progress, set growth goals.
Measuring progress helps us stay on track. Without data, it's hard to stay motivated. When we face inevitable setbacks, we may abandon our dreams.
I created a daily checklist for a spreadsheet with macros. I tracked how often and long I did each activity.
I measured my progress objectively and subjectively. In the progress spreadsheet, I noted my meditation hours and subjective feelings.
In another column, I used good, moderate, and excellent to get qualitative data. It took time and effort. Later, I started benefiting from this automated structure.
Creating a page for each activity, such as meditation, self-talk, cold showers, walking, expressive writing, personal interactions, etc., gave me empirical data I could analyze, modify, and graph to show progress.
Colored charts showed each area's strengths and weaknesses.
Strengths motivate me to continue them. Identifying weaknesses helped me improve them.
As the system matured, data recording became a habit and took less time. I saw the result immediately because I automated the charts when I entered daily data. Early time investment paid off later.
Mind Gym Benefits, Effective Use, and Progress Measuring
This concept helped me move from comfort to risk. I accept things as they are.
Turnarounds were made. I stopped feeling "Fight-Flight-Freeze" and maintained self-control.
I tamed my overactive amygdala by strengthening my brain. Stress and anxiety decreased. With these shifts, I accepted criticism and turned envy into admiration. Clarity improved.
When the cognitive part of the brain became stronger and the primitive part was tamed, managing thoughts and emotions became easier. My AQ increased. I learned to tolerate people, physical, mental, and emotional obstacles.
Accessing vast information sources in my subconscious mind through an improved RAS allowed me to easily tap into my higher self and recognize flaws in my lower self.
Summary
The brain loves patterns and routines, so habits help. Observing, developing, and monitoring habits mindfully can be beneficial. Mindfulness helps us achieve this goal systematically.
As body and mind are connected, we must consider both when building habits. Consistent and joyful practices can strengthen neurons and neural connections.
Habits help us accomplish more with less effort. Regularly using mental tools and processes can improve our cognitive health and performance as we age.
Creating daily habits to improve cognitive abilities can sharpen our minds and boost our well-being.
Some apps monitor our activities and behavior to help build habits. If you can't replicate my system, try these apps. Some smartwatches and fitness devices include them.
Set aside time each day for mental activities you enjoy. Regular scheduling and practice can strengthen brain regions and form habits. Once you form habits, tasks become easy.
Improving our minds is a lifelong journey. It's easier and more sustainable to increase our efforts daily, weekly, monthly, or annually.
Despite life's ups and downs, many want to remain calm and cheerful.
This valuable skill is unrelated to wealth or fame. It's about our mindset, fueled by our biological and psychological needs.
Here are some lessons I've learned about staying calm and composed despite challenges and setbacks.
1 — Tranquillity starts with observing thoughts and feelings.
2 — Clear the mental clutter and emotional entanglements with conscious breathing and gentle movements.
3 — Accept situations and events as they are with no resistance.
4 — Self-love can lead to loving others and increasing compassion.
5 — Count your blessings and cultivate gratitude.
Clear thinking can bring joy and satisfaction. It's a privilege to wake up with a healthy body and clear mind, ready to connect with others and serve them.
Thank you for reading my perspectives. I wish you a healthy and happy life.

Jenn Leach
3 years ago
This clever Instagram marketing technique increased my sales to $30,000 per month.
No Paid Ads Required
I had an online store. After a year of running the company alongside my 9-to-5, I made enough to resign.
That day was amazing.
This Instagram marketing plan helped the store succeed.
How did I increase my sales to five figures a month without using any paid advertising?
I used customer event marketing.
I'm not sure this term exists. I invented it to describe what I was doing.
Instagram word-of-mouth, fan engagement, and interaction drove sales.
If a customer liked or disliked a product, the buzz would drive attention to the store.
I used customer-based events to increase engagement and store sales.
Success!
Here are the weekly Instagram customer events I coordinated while running my business:
Be the Buyer Days
Flash sales
Mystery boxes
Be the Buyer Days: How do they work?
Be the Buyer Days are exactly that.
You choose a day to share stock selections with social media followers.
This is an easy approach to engaging customers and getting fans enthusiastic about new releases.
First, pick a handful of items you’re considering ordering. I’d usually pick around 3 for Be the Buyer Day.
Then I'd poll the crowd on Instagram to vote on their favorites.
This was before Instagram stories, polls, and all the other cool features Instagram offers today. I think using these tools now would make this event even better.
I'd ask customers their favorite back then.
The growing comments excited customers.
Then I'd declare the winner, acquire the products, and start selling it.
How do flash sales work?
I mostly ran flash sales.
You choose a limited number of itemsdd for a few-hour sale.
We wanted most sales to result in sold-out items.
When an item sells out, it contributes to the sensation of scarcity and can inspire customers to visit your store to buy a comparable product, join your email list, become a fan, etc.
We hoped they'd act quickly.
I'd hold flash deals twice a week, which generated scarcity and boosted sales.
The store had a few thousand Instagram followers when I started flash deals.
Each flash sale item would make $400 to $600.
$400 x 3= $1,200
That's $1,200 on social media!
Twice a week, you'll make roughly $10K a month from Instagram.
$1,200/day x 8 events/month=$9,600
Flash sales did great.
We held weekly flash deals and sent social media and email reminders. That’s about it!
How are mystery boxes put together?
All you do is package a box of store products and sell it as a mystery box on TikTok or retail websites.
A $100 mystery box would cost $30.
You're discounting high-value boxes.
This is a clever approach to get rid of excess inventory and makes customers happy.
It worked!
Be the Buyer Days, flash deals, and mystery boxes helped build my company without paid advertisements.
All companies can use customer event marketing. Involving customers and providing an engaging environment can boost sales.
Try it!
