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
(Edited)
Hackernoon
3 years ago
👏 Awesome post! When is part 3 coming?
Trent Lapinski
3 years ago
Very complex topic, great explanation
More on Web3 & Crypto
CNET
3 years ago
How a $300K Bored Ape Yacht Club NFT was accidentally sold for $3K
The Bored Ape Yacht Club is one of the most prestigious NFT collections in the world. A collection of 10,000 NFTs, each depicting an ape with different traits and visual attributes, Jimmy Fallon, Steph Curry and Post Malone are among their star-studded owners. Right now the price of entry is 52 ether, or $210,000.
Which is why it's so painful to see that someone accidentally sold their Bored Ape NFT for $3,066.
Unusual trades are often a sign of funny business, as in the case of the person who spent $530 million to buy an NFT from themselves. In Saturday's case, the cause was a simple, devastating "fat-finger error." That's when people make a trade online for the wrong thing, or for the wrong amount. Here the owner, real name Max or username maxnaut, meant to list his Bored Ape for 75 ether, or around $300,000. Instead he accidentally listed it for 0.75. One hundredth the intended price.
It was bought instantaneously. The buyer paid an extra $34,000 to speed up the transaction, ensuring no one could snap it up before them. The Bored Ape was then promptly listed for $248,000. The transaction appears to have been done by a bot, which can be coded to immediately buy NFTs listed below a certain price on behalf of their owners in order to take advantage of these exact situations.
"How'd it happen? A lapse of concentration I guess," Max told me. "I list a lot of items every day and just wasn't paying attention properly. I instantly saw the error as my finger clicked the mouse but a bot sent a transaction with over 8 eth [$34,000] of gas fees so it was instantly sniped before I could click cancel, and just like that, $250k was gone."
"And here within the beauty of the Blockchain you can see that it is both honest and unforgiving," he added.
Fat finger trades happen sporadically in traditional finance -- like the Japanese trader who almost bought 57% of Toyota's stock in 2014 -- but most financial institutions will stop those transactions if alerted quickly enough. Since cryptocurrency and NFTs are designed to be decentralized, you essentially have to rely on the goodwill of the buyer to reverse the transaction.
Fat finger errors in cryptocurrency trades have made many a headline over the past few years. Back in 2019, the company behind Tether, a cryptocurrency pegged to the US dollar, nearly doubled its own coin supply when it accidentally created $5 billion-worth of new coins. In March, BlockFi meant to send 700 Gemini Dollars to a set of customers, worth roughly $1 each, but mistakenly sent out millions of dollars worth of bitcoin instead. Last month a company erroneously paid a $24 million fee on a $100,000 transaction.
Similar incidents are increasingly being seen in NFTs, now that many collections have accumulated in market value over the past year. Last month someone tried selling a CryptoPunk NFT for $19 million, but accidentally listed it for $19,000 instead. Back in August, someone fat finger listed their Bored Ape for $26,000, an error that someone else immediately capitalized on. The original owner offered $50,000 to the buyer to return the Bored Ape -- but instead the opportunistic buyer sold it for the then-market price of $150,000.
"The industry is so new, bad things are going to happen whether it's your fault or the tech," Max said. "Once you no longer have control of the outcome, forget and move on."
The Bored Ape Yacht Club launched back in April 2021, with 10,000 NFTs being sold for 0.08 ether each -- about $190 at the time. While NFTs are often associated with individual digital art pieces, collections like the Bored Ape Yacht Club, which allow owners to flaunt their NFTs by using them as profile pictures on social media, are becoming increasingly prevalent. The Bored Ape Yacht Club has since become the second biggest NFT collection in the world, second only to CryptoPunks, which launched in 2017 and is considered the "original" NFT collection.
Jonathan Vanian
3 years ago
What is Terra? Your guide to the hot cryptocurrency
With cryptocurrencies like Bitcoin, Ether, and Dogecoin gyrating in value over the past few months, many people are looking at so-called stablecoins like Terra to invest in because of their more predictable prices.
Terraform Labs, which oversees the Terra cryptocurrency project, has benefited from its rising popularity. The company said recently that investors like Arrington Capital, Lightspeed Venture Partners, and Pantera Capital have pledged $150 million to help it incubate various crypto projects that are connected to Terra.
Terraform Labs and its partners have built apps that operate on the company’s blockchain technology that helps keep a permanent and shared record of the firm’s crypto-related financial transactions.
Here’s what you need to know about Terra and the company behind it.
What is Terra?
Terra is a blockchain project developed by Terraform Labs that powers the startup’s cryptocurrencies and financial apps. These cryptocurrencies include the Terra U.S. Dollar, or UST, that is pegged to the U.S. dollar through an algorithm.
Terra is a stablecoin that is intended to reduce the volatility endemic to cryptocurrencies like Bitcoin. Some stablecoins, like Tether, are pegged to more conventional currencies, like the U.S. dollar, through cash and cash equivalents as opposed to an algorithm and associated reserve token.
To mint new UST tokens, a percentage of another digital token and reserve asset, Luna, is “burned.” If the demand for UST rises with more people using the currency, more Luna will be automatically burned and diverted to a community pool. That balancing act is supposed to help stabilize the price, to a degree.
“Luna directly benefits from the economic growth of the Terra economy, and it suffers from contractions of the Terra coin,” Terraform Labs CEO Do Kwon said.
Each time someone buys something—like an ice cream—using UST, that transaction generates a fee, similar to a credit card transaction. That fee is then distributed to people who own Luna tokens, similar to a stock dividend.
Who leads Terra?
The South Korean firm Terraform Labs was founded in 2018 by Daniel Shin and Kwon, who is now the company’s CEO. Kwon is a 29-year-old former Microsoft employee; Shin now heads the Chai online payment service, a Terra partner. Kwon said many Koreans have used the Chai service to buy goods like movie tickets using Terra cryptocurrency.
Terraform Labs does not make money from transactions using its crypto and instead relies on outside funding to operate, Kwon said. It has raised $57 million in funding from investors like HashKey Digital Asset Group, Divergence Digital Currency Fund, and Huobi Capital, according to deal-tracking service PitchBook. The amount raised is in addition to the latest $150 million funding commitment announced on July 16.
What are Terra’s plans?
Terraform Labs plans to use Terra’s blockchain and its associated cryptocurrencies—including one pegged to the Korean won—to create a digital financial system independent of major banks and fintech-app makers. So far, its main source of growth has been in Korea, where people have bought goods at stores, like coffee, using the Chai payment app that’s built on Terra’s blockchain. Kwon said the company’s associated Mirror trading app is experiencing growth in China and Thailand.
Meanwhile, Kwon said Terraform Labs would use its latest $150 million in funding to invest in groups that build financial apps on Terra’s blockchain. He likened the scouting and investing in other groups as akin to a “Y Combinator demo day type of situation,” a reference to the popular startup pitch event organized by early-stage investor Y Combinator.
The combination of all these Terra-specific financial apps shows that Terraform Labs is “almost creating a kind of bank,” said Ryan Watkins, a senior research analyst at cryptocurrency consultancy Messari.
In addition to cryptocurrencies, Terraform Labs has a number of other projects including the Anchor app, a high-yield savings account for holders of the group’s digital coins. Meanwhile, people can use the firm’s associated Mirror app to create synthetic financial assets that mimic more conventional ones, like “tokenized” representations of corporate stocks. These synthetic assets are supposed to be helpful to people like “a small retail trader in Thailand” who can more easily buy shares and “get some exposure to the upside” of stocks that they otherwise wouldn’t have been able to obtain, Kwon said. But some critics have said the U.S. Securities and Exchange Commission may eventually crack down on synthetic stocks, which are currently unregulated.
What do critics say?
Terra still has a long way to go to catch up to bigger cryptocurrency projects like Ethereum.
Most financial transactions involving Terra-related cryptocurrencies have originated in Korea, where its founders are based. Although Terra is becoming more popular in Korea thanks to rising interest in its partner Chai, it’s too early to say whether Terra-related currencies will gain traction in other countries.
Terra’s blockchain runs on a “limited number of nodes,” said Messari’s Watkins, referring to the computers that help keep the system running. That helps reduce latency that may otherwise slow processing of financial transactions, he said.
But the tradeoff is that Terra is less “decentralized” than other blockchain platforms like Ethereum, which is powered by thousands of interconnected computing nodes worldwide. That could make Terra less appealing to some blockchain purists.
Sam Hickmann
3 years ago
A quick guide to formatting your text on INTΞGRITY
[06/20/2022 update] We have now implemented a powerful text editor, but you can still use markdown.
Markdown:
Headers
SYNTAX:
# This is a heading 1
## This is a heading 2
### This is a heading 3
#### This is a heading 4
RESULT:
This is a heading 1
This is a heading 2
This is a heading 3
This is a heading 4
Emphasis
SYNTAX:
**This text will be bold**
~~Strikethrough~~
*You **can** combine them*
RESULT:
This text will be italic
This text will be bold
You can combine them
Images
SYNTAX:
RESULT:
Videos
SYNTAX:
https://www.youtube.com/watch?v=7KXGZAEWzn0
RESULT:
Links
SYNTAX:
[Int3grity website](https://www.int3grity.com)
RESULT:
Tweets
SYNTAX:
https://twitter.com/samhickmann/status/1503800505864130561
RESULT:
Blockquotes
SYNTAX:
> Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. \- Doug Engelbart, 1961
RESULT:
Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. - Doug Engelbart, 1961
Inline code
SYNTAX:
Text inside `backticks` on a line will be formatted like code.
RESULT:
Text inside backticks on a line will be formatted like code.
Code blocks
SYNTAX:
'''js
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
'''
RESULT:
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
Maths
We support LaTex to typeset math. We recommend reading the full documentation on the official website
SYNTAX:
$$[x^n+y^n=z^n]$$
RESULT:
[x^n+y^n=z^n]
Tables
SYNTAX:
| header a | header b |
| ---- | ---- |
| row 1 col 1 | row 1 col 2 |
RESULT:
| header a | header b | header c |
|---|---|---|
| row 1 col 1 | row 1 col 2 | row 1 col 3 |
You might also like
Grace Huang
3 years ago
I sold 100 copies of my book when I had anticipated selling none.
After a decade in large tech, I know how software engineers were interviewed. I've seen outstanding engineers fail interviews because their responses were too vague.
So I wrote Nail A Coding Interview: Six-Step Mental Framework. Give candidates a mental framework for coding questions; help organizations better prepare candidates so they can calibrate traits.
Recently, I sold more than 100 books, something I never expected.
In this essay, I'll describe my publication journey, which included self-doubt and little triumphs. I hope this helps if you want to publish.
It was originally a Medium post.
How did I know to develop a coding interview book? Years ago, I posted on Medium.
Six steps to ace a coding interview Inhale. blog.devgenius.io
This story got a lot of attention and still gets a lot of daily traffic. It indicates this domain's value.
Converted the Medium article into an ebook
The Medium post contains strong bullet points, but it is missing the “flesh”. How to use these strategies in coding interviews, for example. I filled in the blanks and made a book.
I made the book cover for free. It's tidy.
Shared the article with my close friends on my social network WeChat.
I shared the book on Wechat's Friend Circle (朋友圈) after publishing it on Gumroad. Many friends enjoyed my post. It definitely triggered endorphins.
In Friend Circle, I presented a 100% off voucher. No one downloaded the book. Endorphins made my heart sink.
Several days later, my Apple Watch received a Gumroad notification. A friend downloaded it. I majored in finance, he subsequently said. My brother-in-law can get it? He downloaded it to cheer me up.
I liked him, but was disappointed that he didn't read it.
The Tipping Point: Reddit's Free Giving
I trusted the book. It's based on years of interviewing. I felt it might help job-hunting college students. If nobody wants it, it can still have value.
I posted the book's link on /r/leetcode. I told them to DM me for a free promo code.
Momentum shifted everything. Gumroad notifications kept coming when I was out with family. Following orders.
As promised, I sent DMs a promo code. Some consumers ordered without asking for a promo code. Some readers finished the book and posted reviews.
My book was finally on track.
A 5-Star Review, plus More
A reader afterwards DMed me and inquired if I had another book on system design interviewing. I said that was a good idea, but I didn't have one. If you write one, I'll be your first reader.
Later, I asked for a book review. Yes, but how? That's when I learned readers' reviews weren't easy. I built up an email pipeline to solicit customer reviews. Since then, I've gained credibility through ratings.
Learnings
I wouldn't have gotten 100 if I gave up when none of my pals downloaded. Here are some lessons.
Your friends are your allies, but they are not your clients.
Be present where your clients are
Request ratings and testimonials
gain credibility gradually
I did it, so can you. Follow me on Twitter @imgracehuang for my publishing and entrepreneurship adventure.
Antonio Neto
3 years ago
What's up with tech?
Massive Layoffs, record low VC investment, debate over crash... why is it happening and what’s the endgame?
This article generalizes a diverse industry. For objectivity, specific tech company challenges like growing competition within named segments won't be considered. Please comment on the posts.
According to Layoffs.fyi, nearly 120.000 people have been fired from startups since March 2020. More than 700 startups have fired 1% to 100% of their workforce. "The tech market is crashing"
Venture capital investment dropped 19% QoQ in the first four months of 2022, a 2018 low. Since January 2022, Nasdaq has dropped 27%. Some believe the tech market is collapsing.
It's bad, but nothing has crashed yet. We're about to get super technical, so buckle up!
I've written a follow-up article about what's next. For a more optimistic view of the crisis' aftermath, see: Tech Diaspora and Silicon Valley crisis
What happened?
Insanity reigned. Last decade, everyone became a unicorn. Seed investments can be made without a product or team. While the "real world" economy suffered from the pandemic for three years, tech companies enjoyed the "new normal."
COVID sped up technology adoption on several fronts, but this "new normal" wasn't so new after many restrictions were lifted. Worse, it lived with disrupted logistics chains, high oil prices, and WW3. The consumer market has felt the industry's boom for almost 3 years. Inflation, unemployment, mental distress...what looked like a fast economic recovery now looks like unfulfilled promises.
People rethink everything they eat. Paying a Netflix subscription instead of buying beef is moronic if you can watch it for free on your cousin’s account. No matter how great your real estate app's UI is, buying a house can wait until mortgage rates drop. PLGProduct Led Growth (PLG) isn't the go-to strategy when consumers have more basic expense priorities.
Exponential growth and investment
Until recently, tech companies believed that non-exponential revenue growth was fatal. Exponential growth entails doing more with less. From Salim Ismail words:
An Exponential Organization (ExO) has 10x the impact of its peers.
Many tech companies' theories are far from reality.
Investors have funded (sometimes non-exponential) growth. Scale-driven companies throw people at problems until they're solved. Need an entire closing team because you’ve just bought a TV prime time add? Sure. Want gold-weight engineers to colorize buttons? Why not?
Tech companies don't need cash flow to do it; they can just show revenue growth and get funding. Even though it's hard to get funding, this was the market's momentum until recently.
The graph at the beginning of this section shows how industry heavyweights burned money until 2020, despite being far from their market-share seed stage. Being big and being sturdy are different things, and a lot of the tech startups out there are paper tigers. Without investor money, they have no foundation.
A little bit about interest rates
Inflation-driven high interest rates are said to be causing tough times. Investors would rather leave money in the bank than spend it (I myself said it some days ago). It’s not wrong, but it’s also not that simple.
The USA central bank (FED) is a good proxy of global economics. Dollar treasury bonds are the safest investment in the world. Buying U.S. debt, the only country that can print dollars, guarantees payment.
The graph above shows that FED interest rates are low and 10+ year bond yields are near 2018 levels. Nobody was firing at 2018. What’s with that then?
Full explanation is too technical for this article, so I'll just summarize: Bond yields rise due to lack of demand or market expectations of longer-lasting inflation. Safe assets aren't a "easy money" tactic for investors. If that were true, we'd have seen the current scenario before.
Long-term investors are protecting their capital from inflation.
Not a crash, a landing
I bombarded you with info... Let's review:
Consumption is down, hurting revenue.
Tech companies of all ages have been hiring to grow revenue at the expense of profit.
Investors expect inflation to last longer, reducing future investment gains.
Inflation puts pressure on a wheel that was rolling full speed not long ago. Investment spurs hiring, growth, and more investment. Worried investors and consumers reduce the cycle, and hiring follows.
Long-term investors back startups. When the invested company goes public or is sold, it's ok to burn money. What happens when the payoff gets further away? What if all that money sinks? Investors want immediate returns.
Why isn't the market crashing? Technology is not losing capital. It’s expecting change. The market realizes it threw moderation out the window and is reversing course. Profitability is back on the menu.
People solve problems and make money, but they also cost money. Huge cost for the tech industry. Engineers, Product Managers, and Designers earn up to 100% more than similar roles. Businesses must be careful about who they keep and in what positions to avoid wasting money.
What the future holds
From here on, it's all speculation. I found many great articles while researching this piece. Some are cited, others aren't (like this and this). We're in an adjustment period that may or may not last long.
Big companies aren't laying off many workers. Netflix firing 100 people makes headlines, but it's only 1% of their workforce. The biggest seem to prefer not hiring over firing.
Smaller startups beyond the seeding stage may be hardest hit. Without structure or product maturity, many will die.
I expect layoffs to continue for some time, even at Meta or Amazon. I don't see any industry names falling like they did during the .com crisis, but the market will shrink.
If you are currently employed, think twice before moving out and where to.
If you've been fired, hurry, there are still many opportunities.
If you're considering a tech career, wait.
If you're starting a business, I respect you. Good luck.
Jano le Roux
3 years ago
Apple Quietly Introduces A Revolutionary Savings Account That Kills Banks
Would you abandon your bank for Apple?
Banks are struggling.
not as a result of inflation
not due to the economic downturn.
not due to the conflict in Ukraine.
But because they’re underestimating Apple.
Slowly but surely, Apple is looking more like a bank.
An easy new savings account like Apple
Apple has a new savings account.
Apple says Apple Card users may set up and manage savings straight in Wallet.
No more charges
Colorfully high yields
With no minimum balance
No minimal down payments
Most consumer-facing banks will have to match Apple's offer or suffer disruption.
Users may set it up from their iPhones without traveling to a bank or filling out paperwork.
It’s built into the iPhone in your pocket.
So now more waiting for slow approval processes.
Once the savings account is set up, Apple will automatically transfer all future Daily Cash into it. Users may also add these cash to an Apple Cash card in their Apple Wallet app and adjust where Daily Cash is paid at any time.
Apple Pay and Apple Wallet VP Jennifer Bailey:
Savings enables Apple Card users to grow their Daily Cash rewards over time, while also saving for the future.
Bailey says Savings adds value to Apple Card's Daily Cash benefit and offers another easy-to-use tool to help people lead healthier financial lives.
Transfer money from a linked bank account or Apple Cash to a Savings account. Users can withdraw monies to a connected bank account or Apple Cash card without costs.
Once set up, Apple Card customers can track their earnings via Wallet's Savings dashboard. This dashboard shows their account balance and interest.
This product targets younger people as the easiest way to start a savings account on the iPhone.
Why would a Gen Z account holder travel to the bank if their iPhone could be their bank?
Using this concept, Apple will transform the way we think about banking by 2030.
Two other nightmares keep bankers awake at night
Apple revealed two new features in early 2022 that banks and payment gateways hated.
Tap to Pay with Apple
Late Apple Pay
They startled the industry.
Tap To Pay converts iPhones into mobile POS card readers. Apple Pay Later is pushing the BNPL business in a consumer-friendly direction, hopefully ending dodgy lending practices.
Tap to Pay with Apple
iPhone POS
Millions of US merchants, from tiny shops to huge establishments, will be able to accept Apple Pay, contactless credit and debit cards, and other digital wallets with a tap.
No hardware or payment terminal is needed.
Revolutionary!
Stripe has previously launched this feature.
Tap to Pay on iPhone will provide companies with a secure, private, and quick option to take contactless payments and unleash new checkout experiences, said Bailey.
Apple's solution is ingenious. Brilliant!
Bailey says that payment platforms, app developers, and payment networks are making it easier than ever for businesses of all sizes to accept contactless payments and thrive.
I admire that Apple is offering this up to third-party services instead of closing off other functionalities.
Slow POS terminals, farewell.
Late Apple Pay
Pay Apple later.
Apple Pay Later enables US consumers split Apple Pay purchases into four equal payments over six weeks with no interest or fees.
The Apple ecosystem integration makes this BNPL scheme unique. Nonstick. No dumb forms.
Frictionless.
Just double-tap the button.
Apple Pay Later was designed with users' financial well-being in mind. Apple makes it easy to use, track, and pay back Apple Pay Later from Wallet.
Apple Pay Later can be signed up in Wallet or when using Apple Pay. Apple Pay Later can be used online or in an app that takes Apple Pay and leverages the Mastercard network.
Apple Pay Order Tracking helps consumers access detailed receipts and order tracking in Wallet for Apple Pay purchases at participating stores.
Bad BNPL suppliers, goodbye.
Most bankers will be caught in Apple's eye playing mini golf in high-rise offices.
The big problem:
Banks still think about features and big numbers just like other smartphone makers did not too long ago.
Apple thinks about effortlessness, seamlessness, and frictionlessness that just work through integrated hardware and software.
Let me know what you think Apple’s next power moves in the banking industry could be.