More on Web3 & Crypto
Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
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? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
Sam Bourgi
3 years ago
DAOs are legal entities in Marshall Islands.
The Pacific island state recognizes decentralized autonomous organizations.
The Republic of the Marshall Islands has recognized decentralized autonomous organizations (DAOs) as legal entities, giving collectively owned and managed blockchain projects global recognition.
The Marshall Islands' amended the Non-Profit Entities Act 2021 that now recognizes DAOs, which are blockchain-based entities governed by self-organizing communities. Incorporating Admiralty LLC, the island country's first DAO, was made possible thanks to the amendement. MIDAO Directory Services Inc., a domestic organization established to assist DAOs in the Marshall Islands, assisted in the incorporation.
The new law currently allows any DAO to register and operate in the Marshall Islands.
“This is a unique moment to lead,” said Bobby Muller, former Marshall Islands chief secretary and co-founder of MIDAO. He believes DAOs will help create “more efficient and less hierarchical” organizations.
A global hub for DAOs, the Marshall Islands hopes to become a global hub for DAO registration, domicile, use cases, and mass adoption. He added:
"This includes low-cost incorporation, a supportive government with internationally recognized courts, and a technologically open environment."
According to the World Bank, the Marshall Islands is an independent island state in the Pacific Ocean near the Equator. To create a blockchain-based cryptocurrency that would be legal tender alongside the US dollar, the island state has been actively exploring use cases for digital assets since at least 2018.
In February 2018, the Marshall Islands approved the creation of a new cryptocurrency, Sovereign (SOV). As expected, the IMF has criticized the plan, citing concerns that a digital sovereign currency would jeopardize the state's financial stability. They have also criticized El Salvador, the first country to recognize Bitcoin (BTC) as legal tender.
Marshall Islands senator David Paul said the DAO legislation does not pose the same issues as a government-backed cryptocurrency. “A sovereign digital currency is financial and raises concerns about money laundering,” . This is more about giving DAOs legal recognition to make their case to regulators, investors, and consumers.
OnChain Wizard
3 years ago
How to make a >800 million dollars in crypto attacking the once 3rd largest stablecoin, Soros style
Everyone is talking about the $UST attack right now, including Janet Yellen. But no one is talking about how much money the attacker made (or how brilliant it was). Lets dig in.
Our story starts in late March, when the Luna Foundation Guard (or LFG) starts buying BTC to help back $UST. LFG started accumulating BTC on 3/22, and by March 26th had a $1bn+ BTC position. This is leg #1 that made this trade (or attack) brilliant.
The second leg comes in the form of the 4pool Frax announcement for $UST on April 1st. This added the second leg needed to help execute the strategy in a capital efficient way (liquidity will be lower and then the attack is on).
We don't know when the attacker borrowed 100k BTC to start the position, other than that it was sold into Kwon's buying (still speculation). LFG bought 15k BTC between March 27th and April 11th, so lets just take the average price between these dates ($42k).
So you have a ~$4.2bn short position built. Over the same time, the attacker builds a $1bn OTC position in $UST. The stage is now set to create a run on the bank and get paid on your BTC short. In anticipation of the 4pool, LFG initially removes $150mm from 3pool liquidity.
The liquidity was pulled on 5/8 and then the attacker uses $350mm of UST to drain curve liquidity (and LFG pulls another $100mm of liquidity).
But this only starts the de-pegging (down to 0.972 at the lows). LFG begins selling $BTC to defend the peg, causing downward pressure on BTC while the run on $UST was just getting started.
With the Curve liquidity drained, the attacker used the remainder of their $1b OTC $UST position ($650mm or so) to start offloading on Binance. As withdrawals from Anchor turned from concern into panic, this caused a real de-peg as people fled for the exits
So LFG is selling $BTC to restore the peg while the attacker is selling $UST on Binance. Eventually the chain gets congested and the CEXs suspend withdrawals of $UST, fueling the bank run panic. $UST de-pegs to 60c at the bottom, while $BTC bleeds out.
The crypto community panics as they wonder how much $BTC will be sold to keep the peg. There are liquidations across the board and LUNA pukes because of its redemption mechanism (the attacker very well could have shorted LUNA as well). BTC fell 25% from $42k on 4/11 to $31.3k
So how much did our attacker make? There aren't details on where they covered obviously, but if they are able to cover (or buy back) the entire position at ~$32k, that means they made $952mm on the short.
On the $350mm of $UST curve dumps I don't think they took much of a loss, lets assume 3% or just $11m. And lets assume that all the Binance dumps were done at 80c, thats another $125mm cost of doing business. For a grand total profit of $815mm (bf borrow cost).
BTC was the perfect playground for the trade, as the liquidity was there to pull it off. While having LFG involved in BTC, and foreseeing they would sell to keep the peg (and prevent LUNA from dying) was the kicker.
Lastly, the liquidity being low on 3pool in advance of 4pool allowed the attacker to drain it with only $350mm, causing the broader panic in both BTC and $UST. Any shorts on LUNA would've added a lot of P&L here as well, with it falling -65% since 5/7.
And for the reply guys, yes I know a lot of this involves some speculation & assumptions. But a lot of money was made here either way, and I thought it would be cool to dive into how they did it.
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Alex Mathers
3 years ago
8 guidelines to help you achieve your objectives 5x fast
If you waste time every day, even though you're ambitious, you're not alone.
Many of us could use some new time-management strategies, like these:
Focus on the following three.
You're thinking about everything at once.
You're overpowered.
It's mental. We just have what's in front of us. So savor the moment's beauty.
Prioritize 1-3 things.
To be one of the most productive people you and I know, follow these steps.
Get along with boredom.
Many of us grow bored, sweat, and turn on Netflix.
We shout, "I'm rarely bored!" Look at me! I'm happy.
Shut it, Sally.
You're not making wonderful things for the world. Boredom matters.
If you can sit with it for a second, you'll get insight. Boredom? Breathe.
Go blank.
Then watch your creativity grow.
Check your MacroVision once more.
We don't know what to do with our time, which contributes to time-wasting.
Nobody does, either. Jeff Bezos won't hand-deliver that crap to you.
Daily vision checks are required.
Also:
What are 5 things you'd love to create in the next 5 years?
You're soul-searching. It's food.
Return here regularly, and you'll adore the high you get from doing valuable work.
Improve your thinking.
What's Alex's latest nonsense?
I'm talking about overcoming our own thoughts. Worrying wastes so much time.
Too many of us are assaulted by lies, myths, and insecurity.
Stop letting your worries massage you into a worried coma like a Thai woman.
Optimizing your thoughts requires accepting what you can't control.
It means letting go of unhelpful thoughts and returning to the moment.
Keep your blood sugar level.
I gave up gluten, donuts, and sweets.
This has really boosted my energy.
Blood-sugar-spiking carbs make us irritable and tired.
These day-to-day ups and downs aren't productive. It's crucial.
Know how your diet affects insulin levels. Now I have more energy and can do more without clenching my teeth.
Reduce harmful carbs to boost energy.
Create a focused setting for yourself.
When we optimize the mind, we have more energy and use our time better because we're not tense.
Changing our environment can also help us focus. Disabling alerts is one example.
Too hot makes me procrastinate and irritable.
List five items that hinder your productivity.
You may be amazed at how much you may improve by removing distractions.
Be responsible.
Accountability is a time-saver.
Creating an emotional pull to finish things.
Writing down our goals makes us accountable.
We can engage a coach or work with an accountability partner to feel horrible if we don't show up and finish on time.
‘Hey Jake, I’m going to write 1000 words every day for 30 days — you need to make sure I do.’ ‘Sure thing, Nathan, I’ll be making sure you check in daily with me.’
Tick.
You might also blog about your ambitions to show your dedication.
Now you can't hide when you promised to appear.
Acquire a liking for bravery.
Boldness changes everything.
I sometimes feel lazy and wonder why. If my food and sleep are in order, I should assess my footing.
Most of us live backward. Doubtful. Uncertain. Feelings govern us.
Backfooting isn't living. It's lame, and you'll soon melt. Live boldly now.
Be assertive.
Get disgustingly into everything. Expand.
Even if it's hard, stop being a b*tch.
Those that make Mr. Bold Bear their spirit animal benefit. Save time to maximize your effect.
Leon Ho
3 years ago
Digital Brainbuilding (Your Second Brain)
The human brain is amazing. As more scientists examine the brain, we learn how much it can store.
The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]
What if you could store and access more info, freeing up brain space for problem-solving and creativity?
Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.
Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.
How to construct a second brain to organize information and achieve goals.
What Is a Second Brain?
How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?
If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.
This is when the second brain comes in.
Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.
Digital tools are preferable to analog for building a second brain.
Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.
Brainware
Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult.
Memory has three components in computing:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
For example:
Due to rigorous security settings, many websites need you to create complicated passwords with special characters.
You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).
Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.
It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.
It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.
Why You Need a Digital Brain
Dual minds are best. Birth brain is limited.
The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]
Building a second brain improves learning and memory.
Learn and store information effectively
Faster information recall
Organize information to see connections and patterns
Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings.
Why you need a Digital Brain:
1. Use Brainpower Effectively
Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.
Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.
2. Staying Organized
Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.
Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.
You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.
3. Creativity Process
Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.
Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.
4. Transforming Your Knowledge Into Opportunities
This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.
Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.
5. Improving Thinking and Uncovering Connections
Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.
This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]
Your ability to recognize trends will help you stay ahead of the pack.
6. Credibility for a New Job or Business
Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.
This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.
7. Using Learning Resources
Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.
These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.
How does a second brain feel?
Digital Brain has helped me arrange my job and family life for years.
No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.
Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.
No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.
How to Develop Your Digital Brain (Your Second Brain)
It's cheap but requires work.
Digital Brain development requires:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
1. Decide what information matters before recording.
To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.
What information do you need to achieve your goals?
You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.
2. Use the Right Tool
We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.
This information isn't used. You must store information in a central location.
Different information needs different instruments.
Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.
Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design
Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.
To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.
3. Organize data for easy retrieval
How should you organize collected data?
When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.
Choosing the correct tools helps organize data. Here are some tools selection criteria:
Can the tool sync across devices?
Personal or team?
Has a search function for easy information retrieval?
Does it provide easy data categorization?
Can users create lists or collections?
Does it offer easy idea-information connections?
Does it mind map and visually organize thoughts?
Conclusion
Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.
People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength.
Reference
[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?
[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?
[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery
Sean Bloomfield
3 years ago
How Jeff Bezos wins meetings over
We've all been there: You propose a suggestion to your team at a meeting, and most people appear on board, but a handful or small minority aren't. How can we achieve collective buy-in when we need to go forward but don't know how to deal with some team members' perceived intransigence?
Steps:
Investigate the divergent opinions: Begin by sincerely attempting to comprehend the viewpoint of your disagreeing coworkers. Maybe it makes sense to switch horses in the middle of the race. Have you completely overlooked a blind spot, such as a political concern that could arise as an unexpected result of proceeding? This is crucial to ensure that the person or people feel heard as well as to advance the goals of the team. Sometimes all individuals need is a little affirmation before they fully accept your point of view.
It says a lot about you as a leader to be someone who always lets the perceived greatest idea win, regardless of the originating channel, if after studying and evaluating you see the necessity to align with the divergent position.
If, after investigation and assessment, you determine that you must adhere to the original strategy, we go to Step 2.
2. Disagree and Commit: Jeff Bezos, CEO of Amazon, has had this experience, and Julie Zhuo describes how he handles it in her book The Making of a Manager.
It's OK to disagree when the team is moving in the right direction, but it's not OK to accidentally or purposefully damage the team's efforts because you disagree. Let the team know your opinion, but then help them achieve company goals even if they disagree. Unknown. You could be wrong in today's ever-changing environment.
So next time you have a team member who seems to be dissenting and you've tried the previous tactics, you may ask the individual in the meeting I understand you but I don't want us to leave without you on board I need your permission to commit to this approach would you give us your commitment?