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
Robert Kim
3 years ago
Crypto Legislation Might Progress Beyond Talk in 2022
Financial regulators have for years attempted to apply existing laws to the multitude of issues created by digital assets. In 2021, leading federal regulators and members of Congress have begun to call for legislation to address these issues. As a result, 2022 may be the year when federal legislation finally addresses digital asset issues that have been growing since the mining of the first Bitcoin block in 2009.
Digital Asset Regulation in the Absence of Legislation
So far, Congress has left the task of addressing issues created by digital assets to regulatory agencies. Although a Congressional Blockchain Caucus formed in 2016, House and Senate members introduced few bills addressing digital assets until 2018. As of October 2021, Congress has not amended federal laws on financial regulation, which were last significantly revised by the Dodd-Frank Act in 2010, to address digital asset issues.
In the absence of legislation, issues that do not fit well into existing statutes have created problems. An example is the legal status of digital assets, which can be considered to be either securities or commodities, and can even shift from one to the other over time. Years after the SEC’s 2017 report applying the definition of a security to digital tokens, the SEC and the CFTC have yet to clarify the distinction between securities and commodities for the thousands of digital assets in existence.
SEC Chair Gary Gensler has called for Congress to act, stating in August, “We need additional Congressional authorities to prevent transactions, products, and platforms from falling between regulatory cracks.” Gensler has reached out to Sen. Elizabeth Warren (D-Ma.), who has expressed her own concerns about the need for legislation.
Legislation on Digital Assets in 2021
While regulators and members of Congress talked about the need for legislation, and the debate over cryptocurrency tax reporting in the 2021 infrastructure bill generated headlines, House and Senate bills proposing specific solutions to various issues quietly started to emerge.
Digital Token Sales
Several House bills attempt to address securities law barriers to digital token sales—some of them by building on ideas proposed by regulators in past years.
Exclusion from the definition of a security. Congressional Blockchain Caucus members have been introducing bills to exclude digital tokens from the definition of a security since 2018, and they have revived those bills in 2021. They include the Token Taxonomy Act of 2021 (H.R. 1628), successor to identically named bills in 2018 and 2019, and the Securities Clarity Act (H.R. 4451), successor to a 2020 namesake.
Safe harbor. SEC Commissioner Hester Peirce proposed a regulatory safe harbor for token sales in 2020, and two 2021 bills have proposed statutory safe harbors. Rep. Patrick McHenry (R-N.C.), Republican leader of the House Financial Services Committee, introduced a Clarity for Digital Tokens Act of 2021 (H.R. 5496) that would amend the Securities Act to create a safe harbor providing a grace period of exemption from Securities Act registration requirements. The Digital Asset Market Structure and Investor Protection Act (H.R. 4741) from Rep. Don Beyer (D-Va.) would amend the Securities Exchange Act to define a new type of security—a “digital asset security”—and add issuers of digital asset securities to an existing provision for delayed registration of securities.
Stablecoins
Stablecoins—digital currencies linked to the value of the U.S. dollar or other fiat currencies—have not yet been the subject of regulatory action, although Treasury Secretary Janet Yellen and Federal Reserve Chair Jerome Powell have each underscored the need to create a regulatory framework for them. The Beyer bill proposes to create a regulatory regime for stablecoins by amending Title 31 of the U.S. Code. Treasury Department approval would be required for any “digital asset fiat-based stablecoin” to be issued or used, under an application process to be established by Treasury in consultation with the Federal Reserve, the SEC, and the CFTC.
Serious consideration for any of these proposals in the current session of Congress may be unlikely. A spate of autumn bills on crypto ransom payments (S. 2666, S. 2923, S. 2926, H.R. 5501) shows that Congress is more inclined to pay attention first to issues that are more spectacular and less arcane. Moreover, the arcaneness of digital asset regulatory issues is likely only to increase further, now that major industry players such as Coinbase and Andreessen Horowitz are starting to roll out their own regulatory proposals.
Digital Dollar vs. Digital Yuan
Impetus to pass legislation on another type of digital asset, a central bank digital currency (CBDC), may come from a different source: rivalry with China.
China established itself as a world leader in developing a CBDC with a pilot project launched in 2020, and in 2021, the People’s Bank of China announced that its CBDC will be used at the Beijing Winter Olympics in February 2022. Republican Senators responded by calling for the U.S. Olympic Committee to forbid use of China’s CBDC by U.S. athletes in Beijing and introducing a bill (S. 2543) to require a study of its national security implications.
The Beijing Olympics could motivate a legislative mandate to accelerate implementation of a U.S. digital dollar, which the Federal Reserve has been in the process of considering in 2021. Antecedents to such legislation already exist. A House bill sponsored by 46 Republicans (H.R. 4792) has a provision that would require the Treasury Department to assess China’s CBDC project and report on the status of Federal Reserve work on a CBDC, and the Beyer bill includes a provision amending the Federal Reserve Act to authorize issuing a digital dollar.
Both parties are likely to support creating a digital dollar. The Covid-19 pandemic made a digital dollar for delivery of relief payments a popular idea in 2020, and House Democrats introduced bills with provisions for creating one in 2020 and 2021. Bipartisan support for a bill on a digital dollar, based on concerns both foreign and domestic in nature, could result.
International rivalry and bipartisan support may make the digital dollar a gateway issue for digital asset legislation in 2022. Legislative work on a digital dollar may open the door for considering further digital asset issues—including the regulatory issues that have been emerging for years—in 2022 and beyond.
Shan Vernekar
2 years ago
How the Ethereum blockchain's transactions are carried out
Overview
Ethereum blockchain is a network of nodes that validate transactions. Any network node can be queried for blockchain data for free. To write data as a transition requires processing and writing to each network node's storage. Fee is paid in ether and is also called as gas.
We'll examine how user-initiated transactions flow across the network and into the blockchain.
Flow of transactions
A user wishes to move some ether from one external account to another. He utilizes a cryptocurrency wallet for this (like Metamask), which is a browser extension.
The user enters the desired transfer amount and the external account's address. He has the option to choose the transaction cost he is ready to pay.
Wallet makes use of this data, signs it with the user's private key, and writes it to an Ethereum node. Services such as Infura offer APIs that enable writing data to nodes. One of these services is used by Metamask. An example transaction is shown below. Notice the “to” address and value fields.
var rawTxn = {
nonce: web3.toHex(txnCount),
gasPrice: web3.toHex(100000000000),
gasLimit: web3.toHex(140000),
to: '0x633296baebc20f33ac2e1c1b105d7cd1f6a0718b',
value: web3.toHex(0),
data: '0xcc9ab24952616d6100000000000000000000000000000000000000000000000000000000'
};The transaction is written to the target Ethereum node's local TRANSACTION POOL. It informed surrounding nodes of the new transaction, and those nodes reciprocated. Eventually, this transaction is received by and written to each node's local TRANSACTION pool.
The miner who finds the following block first adds pending transactions (with a higher gas cost) from the nearby TRANSACTION POOL to the block.
The transactions written to the new block are verified by other network nodes.
A block is added to the main blockchain after there is consensus and it is determined to be genuine. The local blockchain is updated with the new node by additional nodes as well.
Block mining begins again next.
The image above shows how transactions go via the network and what's needed to submit them to the main block chain.
References
ethereum.org/transactions How Ethereum transactions function, their data structure, and how to send them via app. ethereum.org
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Karthik Rajan
3 years ago
11 Cooking Hacks I Wish I Knew Earlier
Quick, easy and tasty (and dollops of parenting around food).
My wife and mom are both great mothers. They're super-efficient planners. They soak and ferment food. My 104-year-old grandfather loved fermented foods.
When I'm hungry and need something fast, I waffle to the pantry. Like most people, I like to improvise. I wish I knew these 11 hacks sooner.
1. The world's best pasta sauce only has 3 ingredients.
You watch recipe videos with prepped ingredients. In reality, prepping and washing take time. The food's taste isn't guaranteed. The raw truth at a sublime level is not talked about often.
Sometimes a radical recipe comes along that's so easy and tasty, you're dumbfounded. The Classic Italian Cook Book has a pasta recipe.
One 28-ounce can of whole, peeled tomatoes, one medium peeled onion, and 5 tablespoons of butter. And salt to taste.
Combine everything in a single pot and simmer for 45 minutes, uncovered. Stir occasionally. Toss the onion halves after 45 minutes and pour the sauce over pasta. Finish!
This simple recipe fights our deepest fears.
Salt to taste! Customized to perfection, no frills.
2. Reheating rice with ice. Magical.
Most of the world eats rice. I was raised in south India. My grandfather farmed rice in the Cauvery river delta.
The problem with rice With growing kids, you can't cook just enough. Leftovers are a norm. Microwaves help most people. Ice cubes are the frosting.
Before reheating rice in the microwave, add an ice cube. The ice will steam the rice, making it fluffy and delicious again.
3. Pineapple leaf
if it comes off easy, it is ripe enough to cut. No rethinking.
My daughter loves pineapples like her dad. One daddy task is cutting them. Sharing immediate results is therapeutic.
Timing the cut has been the most annoying part over the years. The pineapple leaf tip reveals the fruitiness inside. Always loved it.
4. Magic knife words (rolling and curling)
Cutting hand: Roll the blade's back, not its tip, to cut.
Other hand: If you can’t see your finger tips, you can’t cut them. So curl your fingers.
I dislike that schools don't teach financial literacy or cutting skills.
My wife and I used scissors differently for 25 years. We both used the thumb. My index finger, her middle. We googled the difference when I noticed it and laughed. She's right.
This video teaches knifing skills:
5. Best advice about heat
If it's done in the pan, it's overdone on the plate.
This simple advice stands out when we worry about ingredients and proportions.
6. The truth about pasta water
Pasta water should be sea-salty.
Properly seasoning food separates good from great. Salt depends is a good line.
Want delicious pasta? Well, then kind of a lot, to be perfectly honest.
7. Clean as you go
Clean blender as you go by blending water and dish soap.
I find clean as you go easier than clean afterwords. This easy tip is gold.
8. Clean as you go (bis)
Microwave a bowl of water, vinegar, and a toothpick for 5 minutes.
2 cups water, 2 tablespoons vinegar, and a toothpick to prevent overflow.
5-minute microwave. Let the steam work for another 2 minutes. Sponge-off dirt and food. Simple.
9 and 10. Tools,tools, tools
Immersion blender and pressure cooker save time and money.
Narrative: I experienced fatherly pride. My middle-schooler loves science. We discussed boiling. I spoke. Water doesn't need 100°C to boil. She looked confused. 100 degrees assume something. The world around the water is a normal room. Changing water pressure affects its boiling point. This saves energy. Pressure cooker magic.
I captivated her. She's into science and sustainable living.
Whistling is a subliminal form of self-expression when done right. Pressure cookers remind me of simple pleasures.
Your handiness depends on your home tools. Immersion blenders are great for pre- and post-cooking. It eliminates chopping and washing. Second to the dishwasher, in my opinion.
11. One pepper is plenty
A story I share with my daughters.
Once, everyone thought about spice (not spicy). More valuable than silk. One of the three mighty oceans was named after a source country. Columbus sailed the wrong way and found America. The explorer called the natives after reaching his spice destination.
It was pre-internet days. His Google wasn't working.
My younger daughter listens in awe. Strong roots. Image cast. She can contextualize one of the ocean names.
I struggle with spices in daily life. Combinations are mind-boggling. I have more spices than Columbus. Flavor explosion has repercussions. You must closely follow the recipe without guarantees. Best aha. Double down on one spice and move on. If you like it, it's great.
I naturally gravitate towards cumin soups, fennel dishes, mint rice, oregano pasta, basil thai curry and cardamom pudding.
Variety enhances life. Each of my dishes is unique.
To each their own comfort food and nostalgic memories.
Happy living!
Jack Shepherd
3 years ago
A Dog's Guide to Every Type of Zoom Call Participant
Are you one of these Zoom dogs?
The Person Who Is Apparently Always on Mute
Waffles thinks he can overpower the mute button by shouting loudly.
The person who believed their camera to be off
Barkley's used to remote work, but he hasn't mastered the "Stop Video" button. Everyone is affected.
Who is driving for some reason, exactly?
Why is Pumpkin always late? Who knows? Shouldn't she be driving? If you could hear her over the freeway, she'd answer these questions.
The Person With the Amazing Bookcase
Cicero likes to use SAT-words like "leverage" and "robust" in Zoom sessions, presumably from all the books he wants you to see behind him.
The Individual Who Is Unnecessarily Dressed
We hope Bandit is going somewhere beautiful after this meeting, or else he neglected the quarterly earnings report and is overcompensating to distract us.
The person who works through lunch in between zoom calls
Barksworth has back-to-back meetings all day, so you can watch her eat while she talks.
The Person Who Is A Little Too Comfy
Hercules thinks Zoom meetings happen between sleeps. He'd appreciate everyone speaking more quietly.
The Person Who Answered the Phone Outside
Frisbee has a gorgeous backyard and lives in a place with great weather year-round, and she wants you to think about that during the daily team huddle.
Who Wants You to Pay Attention to Their Pet
Snickers hasn't listened to you in 20 minutes unless you tell her how cute her kitten is.
One who is, for some reason, positioned incorrectly on the screen
Nelson's meetings consist primarily of attempting to figure out how he positioned his laptop so absurdly.
The person who says too many goodbyes
Zeus waves farewell like it's your first day of school while everyone else searches for the "Leave Meeting" button. It's nice.
He who has a poor internet connection
Ziggy's connectivity problems continue... She gives a long speech as everyone waits awkwardly to inform her they missed it.
The Clearly Multitasking Person
Tinkerbell can play fetch during the monthly staff meeting if she works from home, but that's not a good idea.
The Person Using Zoom as a Makeup and Hair Mirror
If Gail and Bob knew Zoom had a "hide self view" option, they'd be distraught.
The person who feels at ease with simply leaving
Rusty bails when a Zoom conference is over. Rusty's concept is decent.
William Anderson
3 years ago
When My Remote Leadership Skills Took Off
4 Ways To Manage Remote Teams & Employees
The wheels hit the ground as I landed in Rochester.
Our six-person satellite office was now part of my team.
Their manager only reported to me the day before, but I had my ticket booked ahead of time.
I had managed remote employees before but this was different. Engineers dialed into headquarters for every meeting.
So when I learned about the org chart change, I knew a strong first impression would set the tone for everything else.
I was either their boss, or their boss's boss, and I needed them to know I was committed.
Managing a fleet of satellite freelancers or multiple offices requires treating others as more than just a face behind a screen.
You must comprehend each remote team member's perspective and daily interactions.
The good news is that you can start using these techniques right now to better understand and elevate virtual team members.
1. Make Visits To Other Offices
If budgeted, visit and work from offices where teams and employees report to you. Only by living alongside them can one truly comprehend their problems with communication and other aspects of modern life.
2. Have Others Come to You
• Having remote, distributed, or satellite employees and teams visit headquarters every quarter or semi-quarterly allows the main office culture to rub off on them.
When remote team members visit, more people get to meet them, which builds empathy.
If you can't afford to fly everyone, at least bring remote managers or leaders. Hopefully they can resurrect some culture.
3. Weekly Work From Home
No home office policy?
Make one.
WFH is a team-building, problem-solving, and office-viewing opportunity.
For dial-in meetings, I started working from home on occasion.
It also taught me which teams “forget” or “skip” calls.
As a remote team member, you experience all the issues first hand.
This isn't as accurate for understanding teams in other offices, but it can be done at any time.
4. Increase Contact Even If It’s Just To Chat
Don't underestimate office banter.
Sometimes it's about bonding and trust, other times it's about business.
If you get all this information in real-time, please forward it.
Even if nothing critical is happening, call remote team members to check in and chat.
I guarantee that building relationships and rapport will increase both their job satisfaction and yours.