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.

Let's examine the differences between the three main token types and their functions.

As Ethereum grew, the term "token" became a catch-all term for all assets built on the Ethereum blockchain. However, different tokens were grouped based on their applications and features, causing some confusion. Let's examine the modification of three main token types: security, utility, and non-fungible.

Utility tokens

They provide a specific utility benefit (or a number of such). A utility token is similar to a casino chip, a table game ticket, or a voucher. Depending on the terms of issuing, they can be earned and used in various ways. A utility token is a type of token that represents a tool or mechanism required to use the application in question. Like a service, a utility token's price is determined by supply and demand. Tokens can also be used as a bonus or reward mechanism in decentralized systems: for example, if you like someone's work, give them an upvote and they get a certain number of tokens. This is a way for authors or creators to earn money indirectly.

The most common way to use a utility token is to pay with them instead of cash for discounted goods or services.

Utility tokens are the most widely used by blockchain companies. Most cryptocurrency exchanges accept fees in native utility tokens.

Utility tokens can also be used as a reward. Companies tokenize their loyalty programs so that points can be bought and sold on blockchain exchanges. These tokens are widely used in decentralized companies as a bonus system. You can use utility tokens to reward creators for their contributions to a platform, for example. It also allows members to exchange tokens for specific bonuses and rewards on your site.

Unlike security tokens, which are subject to legal restrictions, utility tokens can be freely traded.

Security tokens

Security tokens are essentially traditional securities like shares, bonds, and investment fund units in a crypto token form.

The key distinction is that security tokens are typically issued by private firms (rather than public companies) that are not listed on stock exchanges and in which you can not invest right now. Banks and large venture funds used to be the only sources of funding. A person could only invest in private firms if they had millions of dollars in their bank account. Privately issued security tokens outperform traditional public stocks in terms of yield. Private markets grew 50% faster than public markets over the last decade, according to McKinsey Private Equity Research.

A security token is a crypto token whose value is derived from an external asset or company. So it is governed as security (read about the Howey test further in this article). That is, an ownership token derives its value from the company's valuation, assets on the balance sheet, or dividends paid to token holders.

Why are Security Tokens Important?

Cryptocurrency is a lucrative investment. Choosing from thousands of crypto assets can mean the difference between millionaire and bankrupt. Without security tokens, crypto investing becomes riskier and generating long-term profits becomes difficult. These tokens have lower risk than other cryptocurrencies because they are backed by real assets or business cash flows. So having them helps to diversify a portfolio and preserve the return on investment in riskier assets.

Security tokens open up new funding avenues for businesses. As a result, investors can invest in high-profit businesses that are not listed on the stock exchange.

The distinction between utility and security tokens isn't as clear as it seems. However, this increases the risk for token issuers, especially in the USA. The Howey test is the main pillar regulating judicial precedent in this area.

What is a Howey Test?

An "investment contract" is determined by the Howey Test, a lawsuit settled by the US Supreme Court. If it does, it's a security and must be disclosed and registered under the Securities Act of 1933 and the Securities Exchange Act of 1934.

If the SEC decides that a cryptocurrency token is a security, a slew of issues arise. In practice, this ensures that the SEC will decide when a token can be offered to US investors and if the project is required to file a registration statement with the SEC.

Due to the Howey test's extensive wording, most utility tokens will be classified as securities, even if not intended to be. Because of these restrictions, most ICOs are not available to US investors. When asked about ICOs in 2018, then-SEC Chairman Jay Clayton said they were securities. The given statement adds to the risk. If a company issues utility tokens without registering them as securities, the regulator may impose huge fines or even criminal charges.

What other documents regulate tokens?

Securities Act (1993) or Securities Exchange Act (1934) in the USA; MiFID directive and Prospectus Regulation in the EU. These laws require registering the placement of security tokens, limiting their transfer, but protecting investors.

Utility tokens have much less regulation. The Howey test determines whether a given utility token is a security. Tokens recognized as securities are now regulated as such. Having a legal opinion that your token isn't makes the implementation process much easier. Most countries don't have strict regulations regarding utility tokens except KYC (Know Your Client) and AML (Anti Money-Laundering).

As cryptocurrency and blockchain technologies evolve, more countries create UT regulations. If your company is based in the US, be aware of the Howey test and the Bank Secrecy Act. It classifies UTs and their issuance as money transmission services in most states, necessitating a license and strict regulations. Due to high regulatory demands, UT issuers try to avoid the United States as a whole. A new law separating utility tokens from bank secrecy act will be introduced in the near future, giving hope to American issuers.

The rest of the world has much simpler rules requiring issuers to create basic investor disclosures. For example, the latest European legislation (MiCA) allows businesses to issue utility tokens without regulator approval. They must also prepare a paper with all the necessary information for the investors.

A payment token is a utility token that is used to make a payment. They may be subject to electronic money laws. 

Because non-fungible tokens are a new instrument, there is no regulating paper yet. However, if the NFT is fractionalized, the smaller tokens acquired may be seen as securities.

NFT Tokens

Collectible tokens are also known as non-fungible tokens. Their distinctive feature is that they denote unique items such as artwork, merch, or ranks. Unlike utility tokens, which are fungible, meaning that two of the same tokens are identical, NFTs represent a unit of possession that is strictly one of a kind. In a way, NFTs are like baseball cards, each one unique and valuable.

As for today, the most recognizable NFT function is to preserve the fact of possession. Owning an NFT with a particular gif, meme, or sketch does not transfer the intellectual right to the possessor, but is analogous to owning an original painting signed by the author.

Collectible tokens can also be used as digital souvenirs, so to say. Businesses can improve their brand image by issuing their own branded NFTs, which represent ranks or achievements within the corporate ecosystem. Gamifying business ecosystems would allow people to connect with a brand and feel part of a community. 

Which type of tokens is right for you as a business to raise capital?

For most businesses, it's best to raise capital with security tokens by selling existing shares to global investors. Utility tokens aren't meant to increase in value over time, so leave them for gamification and community engagement. In a blockchain-based business, however, a utility token is often the lifeblood of the operation, and its appreciation potential is directly linked to the company's growth. You can issue multiple tokens at once, rather than just one type. It exposes you to various investors and maximizes the use of digital assets.

Which tokens should I buy?

There are no universally best tokens. Their volatility, industry, and risk-reward profile vary. This means evaluating tokens in relation to your overall portfolio and personal preferences: what industries do you understand best, what excites you, how do you approach taxes, and what is your planning horizon? To build a balanced portfolio, you need to know these factors.

Conclusion

The three most common types of tokens today are security, utility, and NFT. Security tokens represent stocks, mutual funds, and bonds. Utility tokens can be perceived as an inside-product "currency" or "ignition key" that grants you access to goods and services or empowers with other perks. NFTs are unique collectible units that identify you as the owner of something.

Creating 10,000 auto-generated artworks, deploying a smart contract to the Ethereum / Polygon blockchain, setting up some tools, etc.

There is so much to do from launching to running an NFT project. Creating parts for artworks, generating 10,000 unique artworks and metadata, creating a smart contract and deploying it to a blockchain network, creating a website, creating a Twitter account, setting up a Discord server, setting up an OpenSea collection. In addition, you need to have MetaMask installed in your browser and have some ETH / MATIC. Did you get tired of doing all this? Don’t worry, once you know what you need to do, all you have to do is do it one by one.

To be honest, it’s best to run an NFT project in a team of three or more, including artists, developers, and marketers. However, depending on your motivation, you can do it by yourself. Some people might come later to offer help with your project. The most important thing is to take a step as soon as possible.

Creating Parts for Artworks

There are lots of free/paid software for drawing, but after all, I think Adobe Illustrator or Photoshop is the best. The images of Skulls In Love are a composite of 48x48 pixel parts created using Photoshop.

How Many Parts Should You Create?

Are you wondering how many parts you should create to avoid duplication as much as possible when generating your artworks? My friend Stephane, a developer, has created a great tool to help with that.

Generating 10,000 Unique Artworks and Metadata

I highly recommend using the HashLips Art Engine to generate your artworks and metadata. Perhaps there is no better artworks generation tool at the moment.

GitHub: https://github.com/HashLips/hashlips_art_engine
YouTube:

Storing Artworks and Metadata

Ideally, the generated artworks and metadata should be stored on-chain, but if you want to store them off-chain, you should use IPFS. Do not store in centralized storage. This is because data will be lost if the server goes down or if the company goes down. On the other hand, IPFS is a more secure way to find data because it utilizes a distributed, decentralized system.

Storing to IPFS is easy with Pinata, NFT.Storage, and so on. The Skulls In Love uses Pinata. It’s very easy to use, just upload the folder containing your artworks.

Creating and Deploying a Smart Contract

You don’t have to create a smart contract from scratch. There are many great NFT projects, many of which publish their contract source code on Etherscan / PolygonScan. You can choose the contract you like and reuse it. Of course, that requires some knowledge of Solidity, but it depends on your efforts. If you don’t know which contract to choose, use the HashLips smart contract. It’s very simple, but it has almost all the functions you need.

GitHub: https://github.com/HashLips/hashlips_nft_contract

Creating a Website

The website here is not just a static site to showcase your project, it’s a so-called dApp that allows you to access your smart contract and mint NFTs. In fact, this level of dApp is not too difficult for anyone who has ever created a website. Because the ethers.js / web3.js libraries make it easy to interact with your smart contract. There’s also no problem connecting wallets, as MetaMask has great documentation.

The Skulls In Love uses a simple, fast, and modern dApp that I built from scratch using Next.js. It is published on GitHub, so feel free to use it.

Why do people mint NFTs on a website?

Ethereum’s gas fees are high, so if you mint all your NFTs, there will be a huge initial cost. So it makes sense to get the buyers to help with the gas fees for minting.
What about Polygon? Polygon’s gas fees are super cheap, so even if you mint 10,000 NFTs, it’s not a big deal. But we don’t do that. Since NFT projects are a kind of game, it involves the fun of not knowing what will come out after minting.

Creating a Twitter Account

I highly recommend creating a Twitter account. Twitter is an indispensable tool for announcing giveaways and reaching more people. It’s better to announce your project and your artworks little by little, 1–2 weeks before launching your project.

Creating and Setting Up a Discord Server

I highly recommend creating a Discord server as well as a Twitter account. The Discord server is a community and its home. Fans of your NFT project will want to join your community and interact with many other members. So, carefully create each channel on your Discord server to make it a cozy place for your community members.

If you are unfamiliar with Discord, you may be particularly confused by the following:
What bots should I use?
How should I set roles and permissions?
But don’t worry. There are lots of great YouTube videos and blog posts about these.
It’s also a good idea to join the Discord servers of some NFT projects and see how they’re made. Our Discord server is so simple that even beginners will find it easy to understand. Please join us and see it!

UPDATED: As your Discord server grows, you cannot manage it on your own. In this case, you will be hiring several moderators, but choose carefully before hiring. And don’t give them important role permissions right after hiring. Initially, the same permissions as other members are sufficient. After a while, you can add permissions as needed, such as kicking/banning, using the “@every” tag, and adding roles. Again, don’t immediately give significant permissions to your Mod role. Your server can be messed up by fake moderators.

Setting Up Your OpenSea Collection

Before you start selling your NFTs, you need to reserve some for airdrops, giveaways, staff, and more. It’s up to you whether it’s 100, 500, or how many.

After minting some of your NFTs, your account and collection should have been created in OpenSea. Go to OpenSea, connect to your wallet, and set up your collection. Just set your logo, banner image, description, links, royalties, and more. It’s not that difficult.

Promoting Your Project

After all, promotion is the most important thing. In fact, almost every successful NFT project spends a lot of time and effort on it.

In addition to Twitter and Discord, it’s even better to use Instagram, Reddit, and Medium. Also, register your project in NFTCalendar and DISBOARD

About Promoters

You’ll probably get lots of contacts from promoters on your Discord, Twitter, Instagram, and more. But most of them are scams, so don’t pay right away. If you have a promoter that looks attractive to you, be sure to check the promoter’s social media accounts or website to see who he/she is. They basically charge in dollars. The amount they charge isn’t cheap, but promoters with lots of followers may have some temporary effect on your project. Some promoters accept 50% prepaid and 50% postpaid. If you can afford it, it might be worth a try. I never ask them, though.

When Should the Promotion Activities Start?

You may be worried that if you promote your project before it starts, someone will copy your project (artworks). It is true that some projects have actually suffered such damage. I don’t have a clear answer to this question right now, but:

• Do not publish all the information about your project too early
• The information should be released little by little
• Creating artworks that no one can easily copy
  I think these are important.
  If anyone has a good idea, please share it!

About Giveaways

When hosting giveaways, you’ll probably use multiple social media platforms. You may want to grow your Discord server faster. But if joining the Discord server is included in the giveaway requirements, some people hate it. I recommend holding giveaways for each platform. On Twitter and Reddit, you should just add the words “Discord members-only giveaway is being held now! Please join us if you like!”.

If you want to easily pick a giveaway winner in your browser, I recommend Twitter Picker.

Precautions for Distributing Free NFTs

If you want to increase your Twitter followers and Discord members, you can actually get a lot of people by holding events such as giveaways and invite contests. However, distributing many free NFTs at once can be dangerous. Some people who want free NFTs, as soon as they get a free one, sell it at a very low price on marketplaces such as OpenSea. They don’t care about your project and are only thinking about replacing their own “free” NFTs with Ethereum. The lower the floor price of your NFTs, the lower the value of your NFTs (project). Try to think of ways to get people to “buy” your NFTs as much as possible.

Ethereum vs. Polygon

Even though Ethereum has high gas fees, NFT projects on the Ethereum network are still mainstream and popular. On the other hand, Polygon has very low gas fees and fast transaction processing, but NFT projects on the Polygon network are not very popular.

Why? There are several reasons, but the biggest one is that it’s a lot of work to get MATIC (on Polygon blockchain, use MATIC instead of ETH) ready to use. Simply put, you need to bridge your tokens to the Polygon chain. So people need to do this first before minting your NFTs on your website. It may not be a big deal for those who are familiar with crypto and blockchain, but it may be complicated for those who are not. I hope that the tedious work will be simplified in the near future.

If you are confident that your NFTs will be purchased even if they are expensive, or if the total supply of your NFTs is low, you may choose Ethereum. If you just want to save money, you should choose Polygon. Keep in mind that gas fees are incurred not only when minting, but also when performing some of your smart contract functions and when transferring your NFTs.
If I were to launch a new NFT project, I would probably choose Ethereum or Solana.

Conclusion

Some people may want to start an NFT project to make money, but don’t forget to enjoy your own project. Several months ago, I was playing with creating generative art by imitating the CryptoPunks. I found out that auto-generated artworks would be more interesting than I had imagined, and since then I’ve been completely absorbed in generative art.

This is one of the Skulls In Love artworks:

This character wears a cowboy hat, black slim sunglasses, and a kimono. If anyone looks like this, I can’t help laughing!

The Skulls In Love NFTs can be minted for a small amount of MATIC on the official website. Please give it a try to see what kind of unique characters will appear 💀💖

Thank you for reading to the end. I hope this article will be helpful to those who want to launch an NFT project in the future ✨

Quenched lava may have aided in the formation of long RNA strands required by primitive life.

It took a long time for life to emerge. Microbes were present 3.7 billion years ago, just a few hundred million years after the 4.5-billion-year-old Earth had cooled enough to sustain biochemistry, according to fossils, and many scientists believe RNA was the genetic material for these first species. RNA, while not as complicated as DNA, would be difficult to forge into the lengthy strands required to transmit genetic information, raising the question of how it may have originated spontaneously.

Researchers may now have a solution. They demonstrate how basaltic glasses assist individual RNA letters, also known as nucleoside triphosphates, join into strands up to 200 letters long in lab studies. The glasses are formed when lava is quenched in air or water, or when melted rock generated by asteroid strikes cools rapidly, and they would have been plentiful in the early Earth's fire and brimstone.

The outcome has caused a schism among top origin-of-life scholars. "This appears to be a great story that finally explains how nucleoside triphosphates react with each other to create RNA strands," says Thomas Carell, a scientist at Munich's Ludwig Maximilians University. However, Harvard University's Jack Szostak, an RNA expert, says he won't believe the results until the study team thoroughly describes the RNA strands.

Researchers interested in the origins of life like the idea of a primordial "RNA universe" since the molecule can perform two different functions that are essential for life. It's made up of four chemical letters, just like DNA, and can carry genetic information. RNA, like proteins, can catalyze chemical reactions that are necessary for life.

However, RNA can cause headaches. No one has yet discovered a set of plausible primordial conditions that would cause hundreds of RNA letters—each of which is a complicated molecule—to join together into strands long enough to support the intricate chemistry required to kick-start evolution.

Basaltic glasses may have played a role, according to Stephen Mojzsis, a geologist at the University of Colorado, Boulder. They're high in metals like magnesium and iron, which help to trigger a variety of chemical reactions. "Basaltic glass was omnipresent on Earth at the time," he adds.

He provided the Foundation for Applied Molecular Evolution samples of five different basalt glasses. Each sample was ground into a fine powder, sanitized, and combined with a solution of nucleoside triphosphates by molecular biologist Elisa Biondi and her colleagues. The RNA letters were unable to link up without the presence of glass powder. However, when the molecules were mixed with the glass particles, they formed long strands of hundreds of letters, according to the researchers, who published their findings in Astrobiology this week. There was no need for heat or light. Biondi explains, "All we had to do was wait." After only a day, little RNA strands produced, yet the strands continued to grow for months. Jan Paek, a molecular biologist at Firebird Biomolecular Sciences, says, "The beauty of this approach is its simplicity." "Mix the components together, wait a few days, and look for RNA."

Nonetheless, the findings pose a slew of problems. One of the questions is how nucleoside triphosphates came to be in the first place. Recent study by Biondi's colleague Steven Benner suggests that the same basaltic glasses may have aided in the creation and stabilization of individual RNA letters.

The form of the lengthy RNA strands, according to Szostak, is a significant challenge. Enzymes in modern cells ensure that most RNAs form long linear chains. RNA letters, on the other hand, can bind in complicated branching sequences. Szostak wants the researchers to reveal what kind of RNA was produced by the basaltic glasses. "It irritates me that the authors made an intriguing initial finding but then chose to follow the hype rather than the research," Szostak says.

Biondi acknowledges that her team's experiment almost probably results in some RNA branching. She does acknowledge, however, that some branched RNAs are seen in species today, and that analogous structures may have existed before the origin of life. Other studies carried out by the study also confirmed the presence of lengthy strands with connections, indicating that they are most likely linear. "It's a healthy argument," says Dieter Braun, a Ludwig Maximilian University origin-of-life chemist. "It will set off the next series of tests."

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.

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.