More on Web3 & Crypto

Vitalik
4 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

Elnaz Sarraf
3 years ago
Why Bitcoin's Crash Could Be Good for Investors

The crypto market crashed in June 2022. Bitcoin and other cryptocurrencies hit their lowest prices in over a year, causing market panic. Some believe this crash will benefit future investors.
Before I discuss how this crash might help investors, let's examine why it happened. Inflation in the U.S. reached a 30-year high in 2022 after Russia invaded Ukraine. In response, the U.S. Federal Reserve raised interest rates by 0.5%, the most in almost 20 years. This hurts cryptocurrencies like Bitcoin. Higher interest rates make people less likely to invest in volatile assets like crypto, so many investors sold quickly.

The crypto market collapsed. Bitcoin, Ethereum, and Binance dropped 40%. Other cryptos crashed so hard they were delisted from almost every exchange. Bitcoin peaked in April 2022 at $41,000, but after the May interest rate hike, it crashed to $28,000. Bitcoin investors were worried. Even in bad times, this crash is unprecedented.
Bitcoin wasn't "doomed." Before the crash, LUNA was one of the top 5 cryptos by market cap. LUNA was trading around $80 at the start of May 2022, but after the rate hike?
Less than 1 cent. LUNA lost 99.99% of its value in days and was removed from every crypto exchange. Bitcoin's "crash" isn't as devastating when compared to LUNA.
Many people said Bitcoin is "due" for a LUNA-like crash and that the only reason it hasn't crashed is because it's bigger. Still false. If so, Bitcoin should be worth zero by now. We didn't. Instead, Bitcoin reached 28,000, then 29k, 30k, and 31k before falling to 18k. That's not the world's greatest recovery, but it shows Bitcoin's safety.
Bitcoin isn't falling constantly. It fell because of the initial shock of interest rates, but not further. Now, Bitcoin's value is more likely to rise than fall. Bitcoin's low price also attracts investors. They know what prices Bitcoin can reach with enough hype, and they want to capitalize on low prices before it's too late.

Bitcoin's crash was bad, but in a way it wasn't. To understand, consider 2021. In March 2021, Bitcoin surpassed $60k for the first time. Elon Musk's announcement in May that he would no longer support Bitcoin caused a massive crash in the crypto market. In May 2017, Bitcoin's price hit $29,000. Elon Musk's statement isn't worth more than the Fed raising rates. Many expected this big announcement to kill Bitcoin.

Not so. Bitcoin crashed from $58k to $31k in 2021. Bitcoin fell from $41k to $28k in 2022. This crash is smaller. Bitcoin's price held up despite tensions and stress, proving investors still believe in it. What happened after the initial crash in the past?
Bitcoin fell until mid-July. This is also something we’re not seeing today. After a week, Bitcoin began to improve daily. Bitcoin's price rose after mid-July. Bitcoin's price fluctuated throughout the rest of 2021, but it topped $67k in November. Despite no major changes, the peak occurred after the crash. Elon Musk seemed uninterested in crypto and wasn't likely to change his mind soon. What triggered this peak? Nothing, really. What really happened is that people got over the initial statement. They forgot.
Internet users have goldfish-like attention spans. People quickly forgot the crash's cause and were back investing in crypto months later. Despite the market's setbacks, more crypto investors emerged by the end of 2017. Who gained from these peaks? Bitcoin investors who bought low. Bitcoin not only recovered but also doubled its ROI. It was like a movie, and it shows us what to expect from Bitcoin in the coming months.
The current Bitcoin crash isn't as bad as the last one. LUNA is causing market panic. LUNA and Bitcoin are different cryptocurrencies. LUNA crashed because Terra wasn’t able to keep its peg with the USD. Bitcoin is unanchored. It's one of the most decentralized investments available. LUNA's distrust affected crypto prices, including Bitcoin, but it won't last forever.
This is why Bitcoin will likely rebound in the coming months. In 2022, people will get over the rise in interest rates and the crash of LUNA, just as they did with Elon Musk's crypto stance in 2021. When the world moves on to the next big controversy, Bitcoin's price will soar.
Bitcoin may recover for another reason. Like controversy, interest rates fluctuate. The Russian invasion caused this inflation. World markets will stabilize, prices will fall, and interest rates will drop.
Next, lower interest rates could boost Bitcoin's price. Eventually, it will happen. The U.S. economy can't sustain such high interest rates. Investors will put every last dollar into Bitcoin if interest rates fall again.
Bitcoin has proven to be a stable investment. This boosts its investment reputation. Even if Ethereum dethrones Bitcoin as crypto king one day (or any other crypto, for that matter). Bitcoin may stay on top of the crypto ladder for a while. We'll have to wait a few months to see if any of this is true.
This post is a summary. Read the full article here.

rekt
4 years ago
LCX is the latest CEX to have suffered a private key exploit.
The attack began around 10:30 PM +UTC on January 8th.
Peckshield spotted it first, then an official announcement came shortly after.
We’ve said it before; if established companies holding millions of dollars of users’ funds can’t manage their own hot wallet security, what purpose do they serve?
The Unique Selling Proposition (USP) of centralised finance grows smaller by the day.
The official incident report states that 7.94M USD were stolen in total, and that deposits and withdrawals to the platform have been paused.
LCX hot wallet: 0x4631018f63d5e31680fb53c11c9e1b11f1503e6f
Hacker’s wallet: 0x165402279f2c081c54b00f0e08812f3fd4560a05
Stolen funds:
- 162.68 ETH (502,671 USD)
- 3,437,783.23 USDC (3,437,783 USD)
- 761,236.94 EURe (864,840 USD)
- 101,249.71 SAND Token (485,995 USD)
- 1,847.65 LINK (48,557 USD)
- 17,251,192.30 LCX Token (2,466,558 USD)
- 669.00 QNT (115,609 USD)
- 4,819.74 ENJ (10,890 USD)
- 4.76 MKR (9,885 USD)
**~$1M worth of $LCX remains in the address, along with 611k EURe which has been frozen by Monerium.
The rest, a total of 1891 ETH (~$6M) was sent to Tornado Cash.**
Why can’t they keep private keys private?
Is it really that difficult for a traditional corporate structure to maintain good practice?
CeFi hacks leave us with little to say - we can only go on what the team chooses to tell us.
Next time, they can write this article themselves.
See below for a template.
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Hunter Walk
2 years ago
Is it bad of me to want our portfolio companies to generate greater returns for outside investors than they did for us as venture capitalists?
Wishing for Lasting Companies, Not Penny Stocks or Goodwill Write-Downs
Get me a NASCAR-style company-logoed cremation urn (notice to the executor of my will, theres gonna be a lot of weird requests). I believe in working on projects that would be on your tombstone. As the Homebrew logo is tattooed on my shoulder, expanding the portfolio to my posthumous commemoration is easy. But this isn't an IRR victory lap; it's a hope that the firms we worked for would last beyond my lifetime.
Venture investors too often take credit or distance themselves from startups based on circumstances. Successful companies tell stories of crucial introductions, strategy conversations, and other value. Defeats Even whether our term involves Board service or systematic ethical violations, I'm just a little investment, so there's not much I can do. Since I'm guilty, I'm tossing stones from within the glass home (although we try to own our decisions through the lifecycle).
Post-exit company trajectories are usually unconfounded. Off the cap table, no longer a shareholder (or a diminishing one as you sell off/distribute), eventually leaving the Board. You can cheer for the squad or forget about it, but you've freed the corporation and it's back to portfolio work.
As I look at the downward track of most SPACs and other tarnished IPOs from the last few years, I wonder how I would feel if those were my legacy. Is my job done? Yes. When investing in a business, the odds are against it surviving, let alone thriving and being able to find sunlight. SPAC sponsors, institutional buyers, retail investments. Free trade in an open market is their right. Risking and losing capital is the system working! But
We were lead or co-lead investors in our first three funds, but as additional VCs joined the company, we were pushed down the cap table. Voting your shares rarely matters; supporting the firm when they need it does. Being valuable, consistent, and helping the company improve builds trust with the founders.
I hope every startup we sponsor becomes a successful public company before, during, and after we benefit. My perspective of American capitalism. Well, a stock ticker has a lot of garbage, and I support all types of regulation simplification (in addition to being a person investor in the Long-Term Stock Exchange). Yet being owned by a large group of investors and making actual gains for them is great. Likewise does seeing someone you met when they were just starting out become a public company CEO without losing their voice, leadership, or beliefs.
I'm just thinking about what we can do from the start to realize value from our investments and build companies with bright futures. Maybe seed venture financing shouldn't impact those outcomes, but I'm not comfortable giving up that obligation.

Gareth Willey
3 years ago
I've had these five apps on my phone for a long time.
TOP APPS
Who survives spring cleaning?
Relax. Notion is off-limits. This topic is popular.
(I wrote about it 2 years ago, before everyone else did.) So).
These apps are probably new to you. I hope you find a new phone app after reading this.
Outdooractive
ViewRanger is Google Maps for outdoor enthusiasts.
This app has been so important to me as a freedom-loving long-distance walker and hiker.
This app shows nearby trails and right-of-ways on top of an Open Street Map.
Helpful detail and data. Any route's distance,
You can download and follow tons of routes planned by app users.
This has helped me find new routes and places a fellow explorer has tried.
Free with non-intrusive ads. Years passed before I subscribed. Pro costs £2.23/month.
This app is for outdoor lovers.
Google Files
New phones come with bloatware. These rushed apps are frustrating.
We must replace these apps. 2017 was Google's year.
Files is a file manager. It's quick, innovative, and clean. They've given people what they want.
It's easy to organize files, clear space, and clear cache.
I recommend Gallery by Google as a gallery app alternative. It's quick and easy.
Trainline
App for trains, buses, and coaches.
I've used this app for years. It did the basics well when I first used it.
Since then, it's improved. It's constantly adding features to make traveling easier and less stressful.
Split-ticketing helps me save hundreds a year on train fares. This app is only available in the UK and Europe.
This service doesn't link to a third-party site. Their app handles everything.
Not all train and coach companies use this app. All the big names are there, though.
Here's more on the app.
Battlefield: Mobile
Play Store has 478,000 games. Few can turn my phone into a console.
Call of Duty Mobile and Asphalt 8/9 are examples.
Asphalt's loot boxes and ads make it unplayable. Call of Duty opens with a few ads. Close them to play without hassle.
This game uses all your phone's features to provide a high-quality, seamless experience. If my internet connection is good, I never experience lag or glitches.
The gameplay is energizing and intense, just like on consoles. Sometimes I'm too involved. I've thrown my phone in anger. I'm totally absorbed.
Customizability is my favorite. Since phones have limited screen space, we should only have the buttons we need, placed conveniently.
Size, opacity, and position are modifiable. Adjust audio, graphics, and textures. It's customizable.
This game has been on my phone for three years. It began well and has gotten better. When I think the creators can't do more, they do.
If you play, read my tips for winning a Battle Royale.
Lightroom
As a photographer, I believe your best camera is on you. The phone.
2017 was a big year for this app. I've tried many photo-editing apps since then. This always wins.
The app is dull. I've never seen better photo editing on a phone.
Adjusting settings and sliders doesn't damage or compress photos. It's detailed.
This is important for phone photos, which are lower quality than professional ones.
Some tools are behind a £4.49/month paywall. Adobe must charge a subscription fee instead of selling licenses. (I'm still bitter about Creative Cloud's price)
Snapseed is my pick. Lightroom is where I do basic editing before moving to Snapseed. Snapseed review:
These apps are great. They cover basic and complex editing needs while traveling.
Final Reflections
I hope you downloaded one of these. Share your favorite apps. These apps are scarce.

Karo Wanner
3 years ago
This is how I started my Twitter account.
My 12-day results look good.
Twitter seemed for old people and politicians.
I thought the platform would die soon like Facebook.
The platform's growth stalled around 300m users between 2015 and 2019.
In 2020, Twitter grew and now has almost 400m users.
Niharikaa Kaur Sodhi built a business on Twitter while I was away, despite its low popularity.
When I read about the success of Twitter users in the past 2 years, I created an account and a 3-month strategy.
I'll see if it's worth starting Twitter in 2022.
Late or perfect? I'll update you. Track my Twitter growth. You can find me here.
My Twitter Strategy
My Twitter goal is to build a community and recruit members for Mindful Monday.
I believe mindfulness is the only way to solve problems like poverty, inequality, and the climate crisis.
The power of mindfulness is my mission.
Mindful Monday is your weekly reminder to live in the present moment. I send mindfulness tips every Monday.
My Twitter profile promotes Mindful Monday and encourages people to join.
What I paid attention to:
I designed a brand-appropriate header to promote Mindful Monday.
Choose a profile picture. People want to know who you are.
I added my name as I do on Medium, Instagram, and emails. To stand out and be easily recognized, add an emoji if appropriate. Add what you want to be known for, such as Health Coach, Writer, or Newsletter.
People follow successful, trustworthy people. Describe any results you have. This could be views, followers, subscribers, or major news outlets. Create!
Tell readers what they'll get by following you. Can you help?
Add CTA to your profile. Your Twitter account's purpose. Give instructions. I placed my sign-up link next to the CTA to promote Mindful Monday. Josh Spector recommended this. (Thanks! Bonus tip: If you don't want the category to show in your profile, e.g. Entrepreneur, go to edit profile, edit professional profile, and choose 'Other'
Here's my Twitter:
I'm no expert, but I tried. Please share any additional Twitter tips and suggestions in the comments.
To hide your Revue newsletter subscriber count:
Join Revue. Select 'Hide Subscriber Count' in Account settings > Settings > Subscriber Count. Voila!
How frequently should you tweet?
1 to 20 Tweets per day, but consistency is key.
Stick to a daily tweet limit. Start with less and be consistent than the opposite.
I tweet 3 times per day. That's my comfort zone. Larger accounts tweet 5–7 times daily.
Do what works for you and that is the right amount.
Twitter is a long-term game, so plan your tweets for a year.
How to Batch Your Tweets?
Sunday batchs.
Sunday evenings take me 1.5 hours to create all my tweets for the week.
Use a word document and write down your posts. Podcasts, books, my own articles inspire me.
When I have a good idea or see a catchy Tweet, I take a screenshot.
To not copy but adapt.
Two pillars support my content:
(90% ~ 29 tweets per week) Inspirational quotes, mindfulness tips, zen stories, mistakes, myths, book recommendations, etc.
(10% 2 tweets per week) I share how I grow Mindful Monday with readers. This pillar promotes MM and behind-the-scenes content.
Second, I schedule all my Tweets using TweetDeck. I tweet at 7 a.m., 5 p.m., and 6 p.m.
Include Twitter Threads in your content strategy
Tweets are blog posts. In your first tweet, you include a headline, then tweet your content.
That’s how you create a series of connected Tweets.
What’s the point? You have more room to convince your reader you're an expert.
Add a call-to-action to your thread.
Follow for more like this
Newsletter signup (share your link)
Ask for retweet
One thread per week is my goal.
I'll schedule threads with Typefully. In the free version, you can schedule one Tweet, but that's fine.
Pin a thread to the top of your profile if it leads to your newsletter. So new readers see your highest-converting content first.
Tweet Medium posts
I also tweet Medium articles.
I schedule 1 weekly repost for 5 weeks after each publication. I share the same article daily for 5 weeks.
Every time I tweet, I include a different article quote, so even if the link is the same, the quote adds value.
Engage Other Experts
When you first create your account, few people will see it. Normal.
If you comment on other industry accounts, you can reach their large audience.
First, you need 50 to 100 followers. Here's my beginner tip.
15 minutes a day or when I have downtime, I comment on bigger accounts in my niche.
My 12-Day Results
Now let's look at the first data.
I had 32 followers on March 29. 12 followers in 11 days. I have 52 now.
Not huge, but growing rapidly.
Let's examine impressions/views.
As a newbie, I gained 4,300 impressions/views in 12 days. On Medium, I got fewer views.
The 1,6k impressions per day spike comes from a larger account I mentioned the day before. First, I was shocked to see the spike and unsure of its origin.
These results are promising given the effort required to be consistent on Twitter.
Let's see how my journey progresses. I'll keep you posted.
Tweeters, Does this content strategy make sense? What's wrong? Comment below.
Let's support each other on Twitter. Here's me.
Which Twitter strategy works for you in 2022?
This post is a summary. Read the full article here
