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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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.