You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.

It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

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? There is a clever solution.

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.

What is Bitcoin?

The blockchain is a shared, immutable ledger that helps businesses record transactions and track assets. The blockchain can track tangible assets like cars, houses, and land. Tangible assets like intellectual property can also be tracked on the blockchain.

Imagine a blockchain as a distributed database split among computer nodes. A blockchain stores data in blocks. When a block is full, it is closed and linked to the next. As a result, all subsequent information is compiled into a new block that will be added to the chain once it is filled.

The blockchain is designed so that adding a transaction requires consensus. That means a majority of network nodes must approve a transaction. No single authority can control transactions on the blockchain. The network nodes use cryptographic keys and passwords to validate each other's transactions.

Blockchain History

The blockchain was not as popular in 1991 when Stuart Haber and W. Scott Stornetta worked on it. The blocks were designed to prevent tampering with document timestamps. Stuart Haber and W. Scott Stornetta improved their work in 1992 by using Merkle trees to increase efficiency and collect more documents on a single block.

In 2004, he developed Reusable Proof of Work. This system allows users to verify token transfers in real time. Satoshi Nakamoto invented distributed blockchains in 2008. He improved the blockchain design so that new blocks could be added to the chain without being signed by trusted parties.

Satoshi Nakomoto mined the first Bitcoin block in 2009, earning 50 Bitcoins. Then, in 2013, Vitalik Buterin stated that Bitcoin needed a scripting language for building decentralized applications. He then created Ethereum, a new blockchain-based platform for decentralized apps. Since the Ethereum launch in 2015, different blockchain platforms have been launched: from Hyperledger by Linux Foundation, EOS.IO by block.one, IOTA, NEO and Monero dash blockchain. The block chain industry is still growing, and so are the businesses built on them.

Blockchain Components

The Blockchain is made up of many parts:

1. Node: The node is split into two parts: full and partial. The full node has the authority to validate, accept, or reject any transaction. Partial nodes or lightweight nodes only keep the transaction's hash value. It doesn't keep a full copy of the blockchain, so it has limited storage and processing power.

2. Ledger: A public database of information. A ledger can be public, decentralized, or distributed. Anyone on the blockchain can access the public ledger and add data to it. It allows each node to participate in every transaction. The distributed ledger copies the database to all nodes. A group of nodes can verify transactions or add data blocks to the blockchain.

3. Wallet: A blockchain wallet allows users to send, receive, store, and exchange digital assets, as well as monitor and manage their value. Wallets come in two flavors: hardware and software. Online or offline wallets exist. Online or hot wallets are used when online. Without an internet connection, offline wallets like paper and hardware wallets can store private keys and sign transactions. Wallets generally secure transactions with a private key and wallet address.

4. Nonce: A nonce is a short term for a "number used once''. It describes a unique random number. Nonces are frequently generated to modify cryptographic results. A nonce is a number that changes over time and is used to prevent value reuse. To prevent document reproduction, it can be a timestamp. A cryptographic hash function can also use it to vary input. Nonces can be used for authentication, hashing, or even electronic signatures.

5. Hash: A hash is a mathematical function that converts inputs of arbitrary length to outputs of fixed length. That is, regardless of file size, the hash will remain unique. A hash cannot generate input from hashed output, but it can identify a file. Hashes can be used to verify message integrity and authenticate data. Cryptographic hash functions add security to standard hash functions, making it difficult to decipher message contents or track senders.

Blockchain: Pros and Cons

The blockchain provides a trustworthy, secure, and trackable platform for business transactions quickly and affordably. The blockchain reduces paperwork, documentation errors, and the need for third parties to verify transactions.

Blockchain security relies on a system of unaltered transaction records with end-to-end encryption, reducing fraud and unauthorized activity. The blockchain also helps verify the authenticity of items like farm food, medicines, and even employee certification. The ability to control data gives users a level of privacy that no other platform can match.

In the case of Bitcoin, the blockchain can only handle seven transactions per second. Unlike Hyperledger and Visa, which can handle ten thousand transactions per second. Also, each participant node must verify and approve transactions, slowing down exchanges and limiting scalability.

The blockchain requires a lot of energy to run. In addition, the blockchain is not a hugely distributable system and it is destructible. The security of the block chain can be compromised by hackers; it is not completely foolproof. Also, since blockchain entries are immutable, data cannot be removed. The blockchain's high energy consumption and limited scalability reduce its efficiency.

Why Is Blockchain So Popular?
The blockchain is a technology giant. In 2018, 90% of US and European banks began exploring blockchain's potential. In 2021, 24% of companies are expected to invest $5 million to $10 million in blockchain. By the end of 2024, it is expected that corporations will spend $20 billion annually on blockchain technical services.

Blockchain is used in cryptocurrency, medical records storage, identity verification, election voting, security, agriculture, business, and many other fields. The blockchain offers a more secure, decentralized, and less corrupt system of making global payments, which cryptocurrency enthusiasts love. Users who want to save time and energy prefer it because it is faster and less bureaucratic than banking and healthcare systems.

Most organizations have jumped on the blockchain bandwagon, and for good reason: the blockchain industry has never had more potential. The launch of IBM's Blockchain Wire, Paystack, Aza Finance and Bloom are visible proof of the wonders that the blockchain has done. The blockchain's cryptocurrency segment may not be as popular in the future as the blockchain's other segments, as evidenced by the various industries where it is used. The blockchain is here to stay, and it will be discussed for a long time, not just in tech, but in many industries.

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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.