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
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.
Onchain Wizard
3 years ago
Three Arrows Capital & Celsius Updates
I read 1k+ page 3AC liquidation documentation so you don't have to. Also sharing revised Celsius recovery plans.
3AC's liquidation documents:
Someone disclosed 3AC liquidation records in the BVI courts recently. I'll discuss the leak's timeline and other highlights.
Three Arrows Capital began trading traditional currencies in emerging markets in 2012. They switched to equities and crypto, then purely crypto in 2018.
By 2020, the firm had $703mm in net assets and $1.8bn in loans (these guys really like debt).
The firm's net assets under control reached $3bn in April 2022, according to the filings. 3AC had $600mm of LUNA/UST exposure before May 9th 2022, which put them over.
LUNA and UST go to zero quickly (I wrote about the mechanics of the blowup here). Kyle Davies, 3AC co-founder, told Blockchain.com on May 13 that they have $2.4bn in assets and $2.3bn NAV vs. $2bn in borrowings. As BTC and ETH plunged 33% and 50%, the company became insolvent by mid-2022.
3AC sent $32mm to Tai Ping Shen, a Cayman Islands business owned by Su Zhu and Davies' partner, Kelly Kaili Chen (who knows what is going on here).
3AC had borrowed over $3.5bn in notional principle, with Genesis ($2.4bn) and Voyager ($650mm) having the most exposure.
Genesis demanded $355mm in further collateral in June.
Deribit (another 3AC investment) called for $80 million in mid-June.
Even in mid-June, the corporation was trying to borrow more money to stay afloat. They approached Genesis for another $125mm loan (to pay another lender) and HODLnauts for BTC & ETH loans.
Pretty crazy. 3AC founders used borrowed money to buy a $50 million boat, according to the leak.
Su requesting for $5m + Chen Kaili Kelly asserting they loaned $65m unsecured to 3AC are identified as creditors.
Celsius:
This bankruptcy presentation shows the Celsius breakdown from March to July 14, 2022. From $22bn to $4bn, crypto assets plummeted from $14.6bn to $1.8bn (ouch). $16.5bn in user liabilities dropped to $4.72bn.
In my recent post, I examined if "forced selling" is over, with Celsius' crypto assets being a major overhang. In this presentation, it looks that Chapter 11 will provide clients the opportunity to accept cash at a discount or remain long crypto. Provided that a fresh source of money is unlikely to enter the Celsius situation, cash at a discount or crypto given to customers will likely remain a near-term market risk - cash at a discount will likely come from selling crypto assets, while customers who receive crypto could sell at any time. I'll share any Celsius updates I find.
Conclusion
Only Celsius and the Mt Gox BTC unlock remain as forced selling catalysts. While everything went through a "relief" pump, with ETH up 75% from the bottom and numerous alts multiples higher, there are still macro dangers to equities + risk assets. There's a lot of wealth waiting to be deployed in crypto ($153bn in stables), but fund managers are risk apprehensive (lower than 2008 levels).
We're hopefully over crypto's "bottom," with peak anxiety and forced selling behind us, but we may chop around.
To see the full article, click here.
You might also like
Sukhad Anand
3 years ago
How Do Discord's Trillions Of Messages Get Indexed?
They depend heavily on open source..
Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?
Let’s find out.
Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.
4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.
Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.
6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.
Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?
8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.
Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.
Paul DelSignore
2 years ago
The stunning new free AI image tool is called Leonardo AI.
Leonardo—The New Midjourney?
Users are comparing the new cowboy to Midjourney.
Leonardo.AI creates great photographs and has several unique capabilities I haven't seen in other AI image systems.
Midjourney's quality photographs are evident in the community feed.
Create Pictures Using Models
You can make graphics using platform models when you first enter the app (website):
Luma, Leonardo creative, Deliberate 1.1.
Clicking a model displays its description and samples:
Click Generate With This Model.
Then you can add your prompt, alter models, photos, sizes, and guide scale in a sleek UI.
Changing Pictures
Leonardo's Canvas editor lets you change created images by hovering over them:
The editor opens with masking, erasing, and picture download.
Develop Your Own Models
I've never seen anything like Leonardo's model training feature.
Upload a handful of similar photographs and save them as a model for future images. Share your model with the community.
You can make photos using your own model and a community-shared set of fine-tuned models:
Obtain Leonardo access
Leonardo is currently free.
Visit Leonardo.ai and click "Get Early Access" to receive access.
Add your email to receive a link to join the discord channel. Simply describe yourself and fill out a form to join the discord channel.
Please go to 👑│introductions to make an introduction and ✨│priority-early-access will be unlocked, you must fill out a form and in 24 hours or a little more (due to demand), the invitation will be sent to you by email.
I got access in two hours, so hopefully you can too.
Last Words
I know there are many AI generative platforms, some free and some expensive, but Midjourney produces the most artistically stunning images and art.
Leonardo is the closest I've seen to Midjourney, but Midjourney is still the leader.
It's free now.
Leonardo's fine-tuned model selections, model creation, image manipulation, and output speed and quality make it a great AI image toolbox addition.
Steffan Morris Hernandez
2 years ago
10 types of cognitive bias to watch out for in UX research & design
10 biases in 10 visuals
Cognitive biases are crucial for UX research, design, and daily life. Our biases distort reality.
After learning about biases at my UX Research bootcamp, I studied Erika Hall's Just Enough Research and used the Nielsen Norman Group's wealth of information. 10 images show my findings.
1. Bias in sampling
Misselection of target population members causes sampling bias. For example, you are building an app to help people with food intolerances log their meals and are targeting adult males (years 20-30), adult females (ages 20-30), and teenage males and females (ages 15-19) with food intolerances. However, a sample of only adult males and teenage females is biased and unrepresentative.
2. Sponsor Disparity
Sponsor bias occurs when a study's findings favor an organization's goals. Beware if X organization promises to drive you to their HQ, compensate you for your time, provide food, beverages, discounts, and warmth. Participants may endeavor to be neutral, but incentives and prizes may bias their evaluations and responses in favor of X organization.
In Just Enough Research, Erika Hall suggests describing the company's aims without naming it.
Third, False-Consensus Bias
False-consensus bias is when a person thinks others think and act the same way. For instance, if a start-up designs an app without researching end users' needs, it could fail since end users may have different wants. https://www.nngroup.com/videos/false-consensus-effect/
Working directly with the end user and employing many research methodologies to improve validity helps lessen this prejudice. When analyzing data, triangulation can boost believability.
Bias of the interviewer
I struggled with this bias during my UX research bootcamp interviews. Interviewing neutrally takes practice and patience. Avoid leading questions that structure the story since the interviewee must interpret them. Nodding or smiling throughout the interview may subconsciously influence the interviewee's responses.
The Curse of Knowledge
The curse of knowledge occurs when someone expects others understand a subject as well as they do. UX research interviews and surveys should reduce this bias because technical language might confuse participants and harm the research. Interviewing participants as though you are new to the topic may help them expand on their replies without being influenced by the researcher's knowledge.
Confirmation Bias
Most prevalent bias. People highlight evidence that supports their ideas and ignore data that doesn't. The echo chamber of social media creates polarization by promoting similar perspectives.
A researcher with confirmation bias may dismiss data that contradicts their research goals. Thus, the research or product may not serve end users.
Design biases
UX Research design bias pertains to study construction and execution. Design bias occurs when data is excluded or magnified based on human aims, assumptions, and preferences.
The Hawthorne Impact
Remember when you behaved differently while the teacher wasn't looking? When you behaved differently without your parents watching? A UX research study's Hawthorne Effect occurs when people modify their behavior because you're watching. To escape judgment, participants may act and speak differently.
To avoid this, researchers should blend into the background and urge subjects to act alone.
The bias against social desire
People want to belong to escape rejection and hatred. Research interviewees may mislead or slant their answers to avoid embarrassment. Researchers should encourage honesty and confidentiality in studies to address this. Observational research may reduce bias better than interviews because participants behave more organically.
Relative Time Bias
Humans tend to appreciate recent experiences more. Consider school. Say you failed a recent exam but did well in the previous 7 exams. Instead, you may vividly recall the last terrible exam outcome.
If a UX researcher relies their conclusions on the most recent findings instead of all the data and results, recency bias might occur.
I hope you liked learning about UX design, research, and real-world biases.