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.

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.

Six Thinking Hats was written by Dr. Edward de Bono. "Six Thinking Hats" and parallel thinking allow groups to plan thinking processes in a detailed and cohesive way, improving collaboration.

Fundamental ideas

In order to develop strategies for thinking about specific issues, the method assumes that the human brain thinks in a variety of ways that can be intentionally challenged. De Bono identifies six brain-challenging directions. In each direction, the brain brings certain issues into conscious thought (e.g. gut instinct, pessimistic judgement, neutral facts). Some may find wearing hats unnatural, uncomfortable, or counterproductive.

The example of "mismatch" sensitivity is compelling. In the natural world, something out of the ordinary may be dangerous. This mode causes negative judgment and critical thinking.

Colored hats represent each direction. Putting on a colored hat symbolizes changing direction, either literally or metaphorically. De Bono first used this metaphor in his 1971 book "Lateral Thinking for Management" to describe a brainstorming framework. These metaphors allow more complete and elaborate thought separation. Six thinking hats indicate ideas' problems and solutions.

Similarly, his CoRT Thinking Programme introduced "The Five Stages of Thinking" method in 1973.

HAT	OVERVIEW	TECHNIQUE
BLUE	"The Big Picture" & Managing	CAF (Consider All Factors); FIP (First Important Priorities)
WHITE	"Facts & Information"	Information
RED	"Feelings & Emotions"	Emotions and Ego
BLACK	"Negative"	PMI (Plus, Minus, Interesting); Evaluation
YELLOW	"Positive"	PMI
GREEN	"New Ideas"	Concept Challenge; Yes, No, Po

Strategies and programs

After identifying the six thinking modes, programs can be created. These are groups of hats that encompass and structure the thinking process. Several of these are included in the materials for franchised six hats training, but they must often be adapted. Programs are often "emergent," meaning the group plans the first few hats and the facilitator decides what to do next.

The group agrees on how to think, then thinks, then evaluates the results and decides what to do next. Individuals or groups can use sequences (and indeed hats). Each hat is typically used for 2 minutes at a time, although an extended white hat session is common at the start of a process to get everyone on the same page. The red hat is recommended to be used for a very short period to get a visceral gut reaction – about 30 seconds, and in practice often takes the form of dot-voting.

ACTIVITY	HAT SEQUENCE
Initial Ideas	Blue, White, Green, Blue
Choosing between alternatives	Blue, White, (Green), Yellow, Black, Red, Blue
Identifying Solutions	Blue, White, Black, Green, Blue
Quick Feedback	Blue, Black, Green, Blue
Strategic Planning	Blue, Yellow, Black, White, Blue, Green, Blue
Process Improvement	Blue, White, White (Other People's Views), Yellow, Black, Green, Red, Blue
Solving Problems	Blue, White, Green, Red, Yellow, Black, Green, Blue
Performance Review	Blue, Red, White, Yellow, Black, Green, Blue

Use

Speedo's swimsuit designers reportedly used the six thinking hats. "They used the "Six Thinking Hats" method to brainstorm, with a green hat for creative ideas and a black one for feasibility.

Typically, a project begins with extensive white hat research. Each hat is used for a few minutes at a time, except the red hat, which is limited to 30 seconds to ensure an instinctive gut reaction, not judgement. According to Malcolm Gladwell's "blink" theory, this pace improves thinking.

De Bono believed that the key to a successful Six Thinking Hats session was focusing the discussion on a particular approach. A meeting may be called to review and solve a problem. The Six Thinking Hats method can be used in sequence to explore the problem, develop a set of solutions, and choose a solution through critical examination.

Everyone may don the Blue hat to discuss the meeting's goals and objectives. The discussion may then shift to Red hat thinking to gather opinions and reactions. This phase may also be used to determine who will be affected by the problem and/or solutions. The discussion may then shift to the (Yellow then) Green hat to generate solutions and ideas. The discussion may move from White hat thinking to Black hat thinking to develop solution set criticisms.

Because everyone is focused on one approach at a time, the group is more collaborative than if one person is reacting emotionally (Red hat), another is trying to be objective (White hat), and another is critical of the points which emerge from the discussion (Black hat). The hats help people approach problems from different angles and highlight problem-solving flaws.