More on Web3 & Crypto
Scott Hickmann
4 years ago
YouTube
This is a YouTube video:
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
Isaac Benson
3 years ago
What's the difference between Proof-of-Time and Proof-of-History?
Blockchain validates transactions with consensus algorithms. Bitcoin and Ethereum use Proof-of-Work, while Polkadot and Cardano use Proof-of-Stake.
Other consensus protocols are used to verify transactions besides these two. This post focuses on Proof-of-Time (PoT), used by Analog, and Proof-of-History (PoH), used by Solana as a hybrid consensus protocol.
PoT and PoH may seem similar to users, but they are actually very different protocols.
Proof-of-Time (PoT)
Analog developed Proof-of-Time (PoT) based on Delegated Proof-of-Stake (DPoS). Users select "delegates" to validate the next block in DPoS. PoT uses a ranking system, and validators stake an equal amount of tokens. Validators also "self-select" themselves via a verifiable random function."
The ranking system gives network validators a performance score, with trustworthy validators with a long history getting higher scores. System also considers validator's fixed stake. PoT's ledger is called "Timechain."
Voting on delegates borrows from DPoS, but there are changes. PoT's first voting stage has validators (or "time electors" putting forward a block to be included in the ledger).
Validators are chosen randomly based on their ranking score and fixed stake. One validator is chosen at a time using a Verifiable Delay Function (VDF).
Validators use a verifiable delay function to determine if they'll propose a Timechain block. If chosen, they validate the transaction and generate a VDF proof before submitting both to other Timechain nodes.
This leads to the second process, where the transaction is passed through 1,000 validators selected using the same method. Each validator checks the transaction to ensure it's valid.
If the transaction passes, validators accept the block, and if over 2/3 accept it, it's added to the Timechain.
Proof-of-History (PoH)
Proof-of-History is a consensus algorithm that proves when a transaction occurred. PoH uses a VDF to verify transactions, like Proof-of-Time. Similar to Proof-of-Work, VDFs use a lot of computing power to calculate but little to verify transactions, similar to (PoW).
This shows users and validators how long a transaction took to verify.
PoH uses VDFs to verify event intervals. This process uses cryptography to prevent determining output from input.
The outputs of one transaction are used as inputs for the next. Timestamps record the inputs' order. This checks if data was created before an event.
PoT vs. PoH
PoT and PoH differ in that:
PoT uses VDFs to select validators (or time electors), while PoH measures time between events.
PoH uses a VDF to validate transactions, while PoT uses a ranking system.
PoT's VDF-elected validators verify transactions proposed by a previous validator. PoH uses a VDF to validate transactions and data.
Conclusion
Both Proof-of-Time (PoT) and Proof-of-History (PoH) validate blockchain transactions differently. PoT uses a ranking system to randomly select validators to verify transactions.
PoH uses a Verifiable Delay Function to validate transactions, verify how much time has passed between two events, and allow validators to quickly verify a transaction without malicious actors knowing the input.
You might also like
KonstantinDr
3 years ago
Early Adopters And the Fifth Reason WHY
Product management wizardry.
Early adopters buy a product even if it hasn't hit the market or has flaws.
Who are the early adopters?
Early adopters try a new technology or product first. Early adopters are interested in trying or buying new technologies and products before others. They're risk-tolerant and can provide initial cash flow and product reviews. They help a company's new product or technology gain social proof.
Early adopters are most common in the technology industry, but they're in every industry. They don't follow the crowd. They seek innovation and report product flaws before mass production. If the product works well, the first users become loyal customers, and colleagues value their opinion.
What to do with early adopters?
They can be used to collect feedback and initial product promotion, first sales, and product value validation.
How to find early followers?
Start with your immediate environment and target audience. Communicate with them to see if they're interested in your value proposition.
1) Innovators (2.5% of the population) are risk-takers seeking novelty. These people are the first to buy new and trendy items and drive social innovation. However, these people are usually elite;
Early adopters (13.5%) are inclined to accept innovations but are more cautious than innovators; they start using novelties when innovators or famous people do;
3) The early majority (34%) is conservative; they start using new products when many people have mastered them. When the early majority accepted the innovation, it became ingrained in people's minds.
4) Attracting 34% of the population later means the novelty has become a mass-market product. Innovators are using newer products;
5) Laggards (16%) are the most conservative, usually elderly people who use the same products.
Stages of new information acceptance
1. The information is strange and rejected by most. Accepted only by innovators;
2. When early adopters join, more people believe it's not so bad; when a critical mass is reached, the novelty becomes fashionable and most people use it.
3. Fascination with a novelty peaks, then declines; the majority and laggards start using it later; novelty becomes obsolete; innovators master something new.
Problems with early implementation
Early adopter sales have disadvantages.
Higher risk of defects
Selling to first-time users increases the risk of defects. Early adopters are often influential, so this can affect the brand's and its products' long-term perception.
Not what was expected
First-time buyers may be disappointed by the product. Marketing messages can mislead consumers, and if the first users believe the company misrepresented the product, this will affect future sales.
Compatibility issues
Some technological advances cause compatibility issues. Consumers may be disappointed if new technology is incompatible with their electronics.
Method 5 WHY
Let's talk about 5 why, a good tool for finding project problems' root causes. This method is also known as the five why rule, method, or questions.
The 5 why technique came from Toyota's lean manufacturing and helps quickly determine a problem's root cause.
On one, two, and three, you simply do this:
We identify and frame the issue for which a solution is sought.
We frequently ponder this question. The first 2-3 responses are frequently very dull, making you want to give up on this pointless exercise. However, after that, things get interesting. And occasionally it's so fascinating that you question whether you really needed to know.
We consider the final response, ponder it, and choose a course of action.
Always do the 5 whys with the customer or team to have a reasonable discussion and better understand what's happening.
And the “five whys” is a wonderful and simplest tool for introspection. With the accumulated practice, it is used almost automatically in any situation like “I can’t force myself to work, the mood is bad in the morning” or “why did I decide that I have no life without this food processor for 20,000 rubles, which will take half of my rather big kitchen.”
An illustration of the five whys
A simple, but real example from my work practice that I think is very indicative, given the participants' low IT skills. Anonymized, of course.
Users spend too long looking for tender documents.
Why? Because they must search through many company tender documents.
Why? Because the system can't filter department-specific bids.
Why? Because our contract management system requirements didn't include a department-tender link. That's it, right? We'll add a filter and be happy. but still…
why? Because we based the system's requirements on regulations for working with paper tender documents (when they still had envelopes and autopsies), not electronic ones, and there was no search mechanism.
Why? We didn't consider how our work would change when switching from paper to electronic tenders when drafting the requirements.
Now I know what to do in the future. We add a filter, enter department data, and teach users to use it. This is tactical, but strategically we review the same forgotten requirements to make all the necessary changes in a package, plus we include it in the checklist for the acceptance of final requirements for the future.
Errors when using 5 why
Five whys seems simple, but it can be misused.
Popular ones:
The accusation of everyone and everything is then introduced. After all, the 5 why method focuses on identifying the underlying causes rather than criticizing others. As a result, at the third step, it is not a good idea to conclude that the system is ineffective because users are stupid and that we can therefore do nothing about it.
to fight with all my might so that the outcome would be exactly 5 reasons, neither more nor less. 5 questions is a typical number (it sounds nice, yes), but there could be 3 or 7 in actuality.
Do not capture in-between responses. It is difficult to overestimate the power of the written or printed word, so the result is so-so when the focus is lost. That's it, I suppose. Simple, quick, and brilliant, like other project management tools.
Conclusion
Today we analyzed important study elements:
Early adopters and 5 WHY We've analyzed cases and live examples of how these methods help with product research and growth point identification. Next, consider the HADI cycle.
Sam Hickmann
3 years ago
Donor-Advised Fund Tax Benefits (DAF)
Giving through a donor-advised fund can be tax-efficient. Using a donor-advised fund can reduce your tax liability while increasing your charitable impact.
Grow Your Donations Tax-Free.
Your DAF's charitable dollars can be invested before being distributed. Your DAF balance can grow with the market. This increases grantmaking funds. The assets of the DAF belong to the charitable sponsor, so you will not be taxed on any growth.
Avoid a Windfall Tax Year.
DAFs can help reduce tax burdens after a windfall like an inheritance, business sale, or strong market returns. Contributions to your DAF are immediately tax deductible, lowering your taxable income. With DAFs, you can effectively pre-fund years of giving with assets from a single high-income event.
Make a contribution to reduce or eliminate capital gains.
One of the most common ways to fund a DAF is by gifting publicly traded securities. Securities held for more than a year can be donated at fair market value and are not subject to capital gains tax. If a donor liquidates assets and then donates the proceeds to their DAF, capital gains tax reduces the amount available for philanthropy. Gifts of appreciated securities, mutual funds, real estate, and other assets are immediately tax deductible up to 30% of Adjusted gross income (AGI), with a five-year carry-forward for gifts that exceed AGI limits.
Using Appreciated Stock as a Gift
Donating appreciated stock directly to a DAF rather than liquidating it and donating the proceeds reduces philanthropists' tax liability by eliminating capital gains tax and lowering marginal income tax.
In the example below, a donor has $100,000 in long-term appreciated stock with a cost basis of $10,000:
Using a DAF would allow this donor to give more to charity while paying less taxes. This strategy often allows donors to give more than 20% more to their favorite causes.
For illustration purposes, this hypothetical example assumes a 35% income tax rate. All realized gains are subject to the federal long-term capital gains tax of 20% and the 3.8% Medicare surtax. No other state taxes are considered.
The information provided here is general and educational in nature. It is not intended to be, nor should it be construed as, legal or tax advice. NPT does not provide legal or tax advice. Furthermore, the content provided here is related to taxation at the federal level only. NPT strongly encourages you to consult with your tax advisor or attorney before making charitable contributions.
Charlie Brown
3 years ago
What Happens When You Sell Your House, Never Buying It Again, Reverse the American Dream
Homeownership isn't the only life pattern.
Want to irritate people?
My party trick is to say I used to own a house but no longer do.
I no longer wish to own a home, not because I lost it or because I'm moving.
It was a long-term plan. It was more deliberate than buying a home. Many people are committed for this reason.
Poppycock.
Anyone who told me that owning a house (or striving to do so) is a must is wrong.
Because, URGH.
One pattern for life is to own a home, but there are millions of others.
You can afford to buy a home? Go, buddy.
You think you need 1,000 square feet (or more)? You think it's non-negotiable in life?
Nope.
It's insane that society forces everyone to own real estate, regardless of income, wants, requirements, or situation. As if this trade brings happiness, stability, and contentment.
Take it from someone who thought this for years: drywall isn't happy. Living your way brings contentment.
That's in real estate. It may also be renting a small apartment in a city that makes your soul sing, but you can't afford the downpayment or mortgage payments.
Living or traveling abroad is difficult when your life savings are connected to something that eats your money the moment you sign.
#vanlife, which seems like torment to me, makes some people feel alive.
I've seen co-living, vacation rental after holiday rental, living with family, and more work.
Insisting that home ownership is the only path in life is foolish and reduces alternative options.
How little we question homeownership is a disgrace.
No one challenges a homebuyer's motives. We congratulate them, then that's it.
When you offload one, you must answer every question, even if you have a loose screw.
Why do you want to sell?
Do you have any concerns about leaving the market?
Why would you want to renounce what everyone strives for?
Why would you want to abandon a beautiful place like that?
Why would you mismanage your cash in such a way?
But surely it's only temporary? RIGHT??
Incorrect questions. Buying a property requires several inquiries.
The typical American has $4500 saved up. When something goes wrong with the house (not if, it’s never if), can you actually afford the repairs?
Are you certain that you can examine a home in less than 15 minutes before committing to buying it outright and promising to pay more than twice the asking price on a 30-year 7% mortgage?
Are you certain you're ready to leave behind friends, family, and the services you depend on in order to acquire something?
Have you thought about the connotation that moving to a suburb, which more than half of Americans do, means you will be dependent on a car for the rest of your life?
Plus:
Are you sure you want to prioritize home ownership over debt, employment, travel, raising kids, and daily routines?
Homeownership entails that. This ex-homeowner says it will rule your life from the time you put the key in the door.
This isn't questioned. We don't question enough. The holy home-ownership grail was set long ago, and we don't challenge it.
Many people question after signing the deeds. 70% of homeowners had at least one regret about buying a property, including the expense.
Exactly. Tragic.
Homes are different from houses
We've been fooled into thinking home ownership will make us happy.
Some may agree. No one.
Bricks and brick hindered me from living the version of my life that made me most comfortable, happy, and steady.
I'm spending the next month in a modest apartment in southern Spain. Even though it's late November, today will be 68 degrees. My spouse and I will soon meet his visiting parents. We'll visit a Sherry store. We'll eat, nap, walk, and drink Sherry. Writing. Jerez means flamenco.
That's my home. This is such a privilege. Living a fulfilling life brings me the contentment that buying a home never did.
I'm happy and comfortable knowing I can make almost all of my days good. Rejecting home ownership is partly to blame.
I'm broke like most folks. I had to choose between home ownership and comfort. I said, I didn't find them together.
Feeling at home trumps owning brick-and-mortar every day.
The following is the reality of what it's like to turn the American Dream around.
Leaving the housing market.
Sometimes I wish I owned a home.
I miss having my own yard and bed. My kitchen, cookbooks, and pizza oven are missed.
But I rarely do.
Someone else's life plan pushed home ownership on me. I'm grateful I figured it out at 35. Many take much longer, and some never understand homeownership stinks (for them).
It's confusing. People will think you're dumb or suicidal.
If you read what I write, you'll know. You'll realize that all you've done is choose to live intentionally. Find a home beyond four walls and a picket fence.
Miss? As I said, they're not home. If it were, a pizza oven, a good mattress, and a well-stocked kitchen would bring happiness.
No.
If you can afford a house and desire one, more power to you.
There are other ways to discover home. Find calm and happiness. For fun.
For it, look deeper than your home's foundation.