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

Protos
3 years ago
StableGains lost $42M in Anchor Protocol.
StableGains lost millions of dollars in customer funds in Anchor Protocol without telling its users. The Anchor Protocol offered depositors 19-20% APY before its parent ecosystem, Terra LUNA, lost tens of billions of dollars in market capitalization as LUNA fell below $0.01 and its stablecoin (UST) collapsed.
A Terra Research Forum member raised the alarm. StableGains changed its homepage and Terms and Conditions to reflect how it mitigates risk, a tacit admission that it should have done so from the start.
StableGains raised $600,000 in YCombinator's W22 batch. Moonfire, Broom Ventures, and Goodwater Capital invested $3 million more.
StableGains' 15% yield product attracted $42 million in deposits. StableGains kept most of its deposits in Anchor's UST pool earning 19-20% APY, kept one-quarter of the interest as a management fee, and then gave customers their promised 15% APY. It lost almost all customer funds when UST melted down. It changed withdrawal times, hurting customers.
- StableGains said de-pegging was unlikely. According to its website, 1 UST can be bought and sold for $1 of LUNA. LUNA became worthless, and Terra shut down its blockchain.
- It promised to diversify assets across several stablecoins to reduce the risk of one losing its $1 peg, but instead kept almost all of them in one basket.
- StableGains promised withdrawals in three business days, even if a stablecoin needed time to regain its peg. StableGains uses Coinbase for deposits and withdrawals, and customers receive the exact amount of USDC requested.
StableGains scrubs its website squeaky clean
StableGains later edited its website to say it only uses the "most trusted and tested stablecoins" and extended withdrawal times from three days to indefinite time "in extreme cases."
Previously, USDC, TerraUST (UST), and Dai were used (DAI). StableGains changed UST-related website content after the meltdown. It also removed most references to DAI.
Customers noticed a new clause in the Terms and Conditions denying StableGains liability for withdrawal losses. This new clause would have required customers to agree not to sue before withdrawing funds, avoiding a class-action lawsuit.
Customers must sign a waiver to receive a refund.
Erickson Kramer & Osborne law firm has asked StableGains to preserve all internal documents on customer accounts, marketing, and TerraUSD communications. The firm has not yet filed a lawsuit.
Thousands of StableGains customers lost an estimated $42 million.
Celsius Network customers also affected
CEL used Terra LUNA's Anchor Protocol. Celsius users lost money in the crypto market crash and UST meltdown. Many held CEL and LUNA as yielding deposits.
CEO Alex Mashinsky accused "unknown malefactors" of targeting Celsius Network without evidence. Celsius has not publicly investigated this claim as of this article's publication.
CEL fell before UST de-pegged. On June 2, 2021, it reached $8.01. May 19's close: $0.82.
When some Celsius Network users threatened to leave over token losses, Mashinsky replied, "Leave if you don't think I'm sincere and working harder than you, seven days a week."
Celsius Network withdrew $500 million from Anchor Protocol, but smaller holders had trouble.
Read original article here
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.
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Deon Ashleigh
2 years ago
You can dominate your daily productivity with these 9 little-known Google Calendar tips.
Calendars are great unpaid employees.
After using Notion to organize my next three months' goals, my days were a mess.
I grew very chaotic afterward. I was overwhelmed, unsure of what to do, and wasting time attempting to plan the day after it had started.
Imagine if our skeletons were on the outside. Doesn’t work.
The goals were too big; I needed to break them into smaller chunks. But how?
Enters Google Calendar
RescueTime’s recommendations took me seven hours to make a daily planner. This epic narrative begins with a sheet of paper and concludes with a daily calendar that helps me focus and achieve more goals. Ain’t nobody got time for “what’s next?” all day.
Onward!
Return to the Paleolithic Era
Plan in writing.
Not on the list, but it helped me plan my day. Physical writing boosts creativity and recall.
Find My Heart
i.e. prioritize
RescueTime suggested I prioritize before planning. Personal and business goals were proposed.
My top priorities are to exercise, eat healthily, spend time in nature, and avoid stress.
Priorities include writing and publishing Medium articles, conducting more freelance editing and Medium outreach, and writing/editing sci-fi books.
These eight things will help me feel accomplished every day.
Make a baby calendar.
Create daily calendar templates.
Make family, pleasure, etc. calendars.
Google Calendar instructions:
Other calendars
Press the “+” button
Create a new calendar
Create recurring events for each day
My calendar, without the template:
Empty, so I can fill it with vital tasks.
With the template:
My daily skeleton corresponds with my priorities. I've been overwhelmed for years because I lack daily, weekly, monthly, and yearly structure.
Google Calendars helps me reach my goals and focus my energy.
Get your colored pencils ready
Time-block color-coding.
Color labeling lets me quickly see what's happening. Maybe you are too.
Google Calendar instructions:
Determine which colors correspond to each time block.
When establishing new events, select a color.
Save
My calendar is color-coded as follows:
Yellow — passive income or other future-related activities
Red — important activities, like my monthly breast exam
Flamingo — shallow work, like emails, Twitter, etc.
Blue — all my favorite activities, like walking, watching comedy, napping, and sleeping. Oh, and eating.
Green — money-related events required for this adulting thing
Purple — writing-related stuff
Associating a time block with a color helps me stay focused. Less distractions mean faster work.
Open My Email
aka receive a daily email from Google Calendar.
Google Calendar sends a daily email feed of your calendars. I sent myself the template calendar in this email.
Google Calendar instructions:
Access settings
Select the calendar that you want to send (left side)
Go down the page to see more alerts
Under the daily agenda area, click Email.
Get in Touch With Your Red Bull Wings — Naturally
aka audit your energy levels.
My daily planner has arrows. These indicate how much energy each activity requires or how much I have.
Rightward arrow denotes medium energy.
I do my Medium and professional editing in the morning because it's energy-intensive.
Niharikaa Sodhi recommends morning Medium editing.
I’m a morning person. As long as I go to bed at a reasonable time, 5 a.m. is super wild GO-TIME. It’s like the world was just born, and I marvel at its wonderfulness.
Freelance editing lets me do what I want. An afternoon snooze will help me finish on time.
Ditch Schedule View
aka focus on the weekly view.
RescueTime advocated utilizing the weekly view of Google Calendar, so I switched.
When you launch the phone app or desktop calendar, a red line shows where you are in the day.
I'll follow the red line's instructions. My digital supervisor is easy to follow.
In the image above, it's almost 3 p.m., therefore the red line implies it's time to snooze.
I won't forget this block ;).
Reduce the Lighting
aka dim previous days.
This is another Google Calendar feature I didn't know about. Once the allotted time passes, the time block dims. This keeps me present.
Google Calendar instructions:
Access settings
remaining general
To view choices, click.
Check Diminish the glare of the past.
Bonus
Two additional RescueTimes hacks:
Maintain a space between tasks
I left 15 minutes between each time block to transition smoothly. This relates to my goal of less stress. If I set strict start and end times, I'll be stressed.
With a buffer, I can breathe, stroll around, and start the following time block fresh.
Find a time is related to the buffer.
This option allows you conclude small meetings five minutes early and longer ones ten. Before the next meeting, relax or go wild.
Decide on a backup day.
This productivity technique is amazing.
Spend this excess day catching up on work. It helps reduce tension and clutter.
That's all I can say about Google Calendar's functionality.

Aldric Chen
3 years ago
Jack Dorsey's Meeting Best Practice was something I tried. It Performs Exceptionally Well in Consulting Engagements.
Yes, client meetings are difficult. Especially when I'm alone.
Clients must tell us their problems so we can help.
In-meeting challenges contribute nothing to our work. Consider this:
Clients are unprepared.
Clients are distracted.
Clients are confused.
Introducing Jack Dorsey's Google Doc approach
I endorse his approach to meetings.
Not Google Doc-related. Jack uses it for meetings.
This is what his meetings look like.
Prior to the meeting, the Chair creates the agenda, structure, and information using Google Doc.
Participants in the meeting would have 5-10 minutes to read the Google Doc.
They have 5-10 minutes to type their comments on the document.
In-depth discussion begins
There is elegance in simplicity. Here's how Jack's approach is fantastic.
Unprepared clients are given time to read.
During the meeting, they think and work on it.
They can see real-time remarks from others.
Discussion ensues.
Three months ago, I fell for this strategy. After trying it with a client, I got good results.
I conducted social control experiments in a few client workshops.
Context matters.
I am sure Jack Dorsey’s method works well in meetings. What about client workshops?
So, I tested Enterprise of the Future with a consulting client.
I sent multiple emails to client stakeholders describing the new approach.
No PowerPoints that day. I spent the night setting up the Google Doc with conversation topics, critical thinking questions, and a Before and After section.
The client was shocked. First, a Google Doc was projected. Second surprise was a verbal feedback.
“No pre-meeting materials?”
“Don’t worry. I know you are not reading it before our meeting, anyway.”
We laughed. The experiment started.
Observations throughout a 90-minute engagement workshop from beginning to end
For 10 minutes, the workshop was silent.
People read the Google Doc. For some, the silence was unnerving.
“Are you not going to present anything to us?”
I said everything's in Google Doc. I asked them to read, remark, and add relevant paragraphs.
As they unlocked their laptops, they were annoyed.
Ten client stakeholders are typing on the Google Doc. My laptop displays comment bubbles, red lines, new paragraphs, and strikethroughs.
The first 10 minutes were productive. Everyone has seen and contributed to the document.
I was silent.
The move to a classical workshop was smooth. I didn't stimulate dialogue. They did.
Stephanie asked Joe why a blended workforce hinders company productivity. She questioned his comments and additional paragraphs.
That is when a light bulb hit my head. Yes, you want to speak to the right person to resolve issues!
Not only that was discussed. Others discussed their remark bubbles with neighbors. Debate circles sprung up one after the other.
The best part? I asked everyone to add their post-discussion thoughts on a Google Doc.
After the workshop, I have:
An agreement-based working document
A post-discussion minutes that are prepared for publication
A record of the discussion points that were brought up, argued, and evaluated critically
It showed me how stakeholders viewed their Enterprise of the Future. It allowed me to align with them.
Finale Keynotes
Client meetings are a hit-or-miss. I know that.
Jack Dorsey's meeting strategy works for consulting. It promotes session alignment.
It relieves clients of preparation.
I get the necessary information to advance this consulting engagement.
It is brilliant.

Simon Ash
2 years ago
The Three Most Effective Questions for Ongoing Development
The Traffic Light Approach to Reviewing Personal, Team and Project Development
What needs improvement? If you want to improve, you need to practice your sport, musical instrument, habit, or work project. You need to assess your progress.
Continuous improvement is the foundation of focused practice and a growth mentality. Not just individually. High-performing teams pursue improvement. Right? Why is it hard?
As a leadership coach, senior manager, and high-level athlete, I've found three key questions that may unlock high performance in individuals and teams.
Problems with Reviews
Reviewing and improving performance is crucial, however I hate seeing review sessions in my diary. I rarely respond to questionnaire pop-ups or emails. Why?
Time constrains. Requests to fill out questionnaires often state they will take 10–15 minutes, but I can think of a million other things to do with that time. Next, review overload. Businesses can easily request comments online. No matter what you buy, someone will ask for your opinion. This bombardment might make feedback seem bad, which is bad.
The problem is that we might feel that way about important things like personal growth and work performance. Managers and team leaders face a greater challenge.
When to Conduct a Review
We must be wise about reviewing things that matter to us. Timing and duration matter. Reviewing the experience as quickly as possible preserves information and sentiments. Time must be brief. The review's importance and size will determine its length. We might only take a few seconds to review our morning coffee, but we might require more time for that six-month work project.
These post-event reviews should be supplemented by periodic reflection. Journaling can help with daily reflections, but I also like to undertake personal reviews every six months on vacation or at a retreat.
As an employee or line manager, you don't want to wait a year for a performance assessment. Little and frequently is best, with a more formal and in-depth assessment (typically with a written report) in 6 and 12 months.
The Easiest Method to Conduct a Review Session
I follow Einstein's review process:
“Make things as simple as possible but no simpler.”
Thus, it should be brief but deliver the necessary feedback. Quality critique is hard to receive if the process is overly complicated or long.
I have led or participated in many review processes, from strategic overhauls of big organizations to personal goal coaching. Three key questions guide the process at either end:
What ought to stop being done?
What should we do going forward?
What should we do first?
Following the Rule of 3, I compare it to traffic lights. Red, amber, and green lights:
Red What ought should we stop?
Amber What ought to we keep up?
Green Where should we begin?
This approach is easy to understand and self-explanatory, however below are some examples under each area.
Red What ought should we stop?
As a team or individually, we must stop doing things to improve.
Sometimes they're bad. If we want to lose weight, we should avoid sweets. If a team culture is bad, we may need to stop unpleasant behavior like gossiping instead of having difficult conversations.
Not all things we should stop are wrong. Time matters. Since it is finite, we sometimes have to stop nice things to focus on the most important. Good to Great author Jim Collins famously said:
“Don’t let the good be the enemy of the great.”
Prioritizing requires this idea. Thus, decide what to stop to prioritize.
Amber What ought to we keep up?
Should we continue with the amber light? It helps us decide what to keep doing during review. Many items fall into this category, so focus on those that make the most progress.
Which activities have the most impact? Which behaviors create the best culture? Success-building habits?
Use these questions to find positive momentum. These are the fly-wheel motions, according to Jim Collins. The Compound Effect author Darren Hardy says:
“Consistency is the key to achieving and maintaining momentum.”
What can you do consistently to reach your goal?
Green Where should we begin?
Finally, green lights indicate new beginnings. Red/amber difficulties may be involved. Stopping a red issue may give you more time to do something helpful (in the amber).
This green space inspires creativity. Kolbs learning cycle requires active exploration to progress. Thus, it's crucial to think of new approaches, try them out, and fail if required.
This notion underpins lean start-build, up's measure, learn approach and agile's trying, testing, and reviewing. Try new things until you find what works. Thomas Edison, the lighting legend, exclaimed:
“There is a way to do it better — find it!”
Failure is acceptable, but if you want to fail forward, look back on what you've done.
John Maxwell concurred with Edison:
“Fail early, fail often, but always fail forward”
A good review procedure lets us accomplish that. To avoid failure, we must act, experiment, and reflect.
Use the traffic light system to prioritize queries. Ask:
Red What needs to stop?
Amber What should continue to occur?
Green What might be initiated?
Take a moment to reflect on your day. Check your priorities with these three questions. Even if merely to confirm your direction, it's a terrific exercise!
