# What math puzzle do miners actually solve?
***
In this post we will try to break down, in simpler terms, the mechanism of blockchain and bitcoin. Readers are assumed to be familiar with a few basic cryptography and blockchain related [terms][6]. Today, I'll specifically focus on transaction validation and mining rewards. Transactions are validated by miners by solving *complicated math puzzle* and the first miner to solve this puzzle is rewarded with brand new coins aka virgin coins. This creation of new coins is somewhat equivalent to printing paper money by a government, or as economists put it, [*quantitative easing*][5]. A government can print money at will resulting in inflation and currency's devaluation. But creation of money in bitcoin economy is pre-defined in such a way that the total supply approaches to **21 million** (20.99999998 million to be exact) by 2140. After that no coins will be created. It's not possible to manipulate supply and hence price. In the below figure, the green line indicates BTC supply over time.
<center>**Figure:** *bitcoin supply*</center>
https://bashco.github.io/Bitcoin_Monetary_Inflation/images/Bitcoin_Monetary_Inflation.png?raw=true
Image credit: https://bashco.github.io/

Divisibility, portability, fungibility, scarcity,  resistance to  manipulation of supply and distributed authority, among others, make bitcoin a superior form of currency to government issued paper (or digital) money.

Now, how is money created in bitcoin economy? The most common answer  I get is that *miners are rewarded with coins they add a new block to the bitcoin blockchain by solving a math puzzle*. What do we exactly mean by that math puzzle? We'll see by the end of this post. To find the answer in less technical terms, I particularly consulted these resources:

- [Mastering Bitcoin: Unlocking Digital Cryptocurrencies][1] by bitcoin guru [Andreas M. Antonopoulos][2]
- [bitcoin wiki][3]
- [StackExchange bitcoin site][4]

I would recommend Antonopoulos' book to anyone aspiring to learn about technical nitty gritty of bitcoin. And the following is a great video lecture series taught by Princeton professor and PhDs. It consists of 12 sessions (combined duration: 15-16 hours).

https://www.youtube.com/watch?v=fOMVZXLjKYo

An individual will ask these two basic questions to justify a currency' value:
1. Can I trust the money is authentic and not counterfeit?
2. Can I be sure that no one else can claim that this money belongs to them and not
me? (Aka the “double-spend” problem.)

In order to maintain integrity and prevent double spending, bitcoin implements consisting of:
 
- A decentralized peer-to-peer network (the bitcoin protocol)
- A public transaction ledger (the blockchain)
- A decentralized mathematical and deterministic currency issuance (distributed
mining)
- A decentralized transaction verification system (transaction script)

We'll briefly discuss point 2 (blockchain) and 3 (mining) to answer our question regarding bitcoin creation.
## Bitcoin overview
The below image illustrates the bitcoin peer-to-peer network and connected participants,  a transaction issued and relayed by a bitcoin user with his private key and  validation of that transaction by miners.
<center>**Figure:** *bitcoin overview*</center>
https://s11.postimg.org/6ta081ulf/bitcoin-overview.jpg
Image credit: *Mastering Bitcoin*

Below is an extended illustration of connected participants in bitcoin network:

<center>**Figure:** *The extended bitcoin network showing various node types, gateways, and
protocols*</center>
<center>https://s8.postimg.org/6b53zfi9x/btc-extended-network.jpg</center>
Image credit: *Mastering Bitcoin*

Suppose that Alice transfers 1 BTC to Bob in exchange for a high-end gaming laptop, Pete transfers 0.001 BTC for a pizza and there are many more such transactions. Currently a block consists of around 1000-2500 transaction. Now let's see how miners validate the transactions. In other words, miners check if the issuer is the rightful owner (holder of private key) of coins to associated bitcoin address. A miner verifies all such transactions  and includes in a block. If the miner can add this block to existing blocks, known as the blockchain, it is rewarded for the computation it did. Miners basically:

- collect all pending transactions
- verifies them
- bundles into a block
- guess a random number (aka nonce) such that **sha256(sha256(data+nonce)) less than difficulty** where
  - [SHA256][7] is the cryptographic hash function.  The SHA-256 algorithm is intended to take an arbitrary amount of input data and produce 256 bits of output, whilst also maintaining certain properties that make for an effective cryptographic hash.
  - **nonce** is a random integer. Miners try to "guess" the nonce; only way a miner can find the number is by brute-forcing, *i.e.* trying millions of random numbers.
  - **data** is a hash over the contents of the block (transactions) and the previous block's hash
  - **difficulty** is a measure of how difficult it is to find a hash below a given target 

The transaction created by Alice’s (or anyone else's) wallet application is 258 bytes long and contains everything necessary to confirm ownership of the funds and assign new owners. Now, the transaction must be transmitted to the bitcoin network where it will become part of the distributed ledger (the blockchain).

We now elaborate hashing in sketchy terms. As of now, the hash of  latest block in the blockchain, [Block #472391][8] is:
```0000000000000000014228823553852a90563fe84da5f0a5aa4832e85f68b1b5```
Note the bunch of zero's at the beginning. Simply put,  miners need to choose a random number (nonce) such that the hash generated by sha256(sha256(data+nonce)) begins with a number (thirteen) of 0's. This difficulty level changes based on how much time, on average, is required to find a block. As the network combined mining capacity increases, difficulty too increases and vice versa. The below figure illustrates block formation:

<center>https://s1.postimg.org/uaww0h7lb/btc-block.jpg</center>
Image credit: *Mastering Bitcoin*

We now take a look at hashes of pending transactions:

```
2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824   -transaction 1
91e9240f415223982edc345532630710e94a7f52cd5f48f5ee1afc555078f0ab   -transaction 2
87298cc2f31fba73181ea2a9e6ef10dce21ed95e98bdac9c4e1504ea16f486e4   -transaction 3

... ...
... ...
```
Now miner creates a transaction root (aka Merkle root) which essentially is hash of all transaction combined. The process is illustrated below:

<center> https://s18.postimg.org/p4di6a18p/Bitcoin_Block_Data.jpg </center>

Image credit: Wikipedia 

[Block 472391][8]'s Merkle root is:
```
d29b40ec75fe295493398f4675b60633a9d5a6a20e2914df9a0b353e2a742a2a
```

Suppose that we'd like to find the next block (Block 472392). So we take hash of Block 472391, transaction root (of all the transactions waiting to be included in Block 472392, timestamp (we'll ignore in illustration). We have (scroll right to see entire line):

```
0000000000000000014228823553852a90563fe84da5f0a5aa4832e85f68b1b5--e361a57a7406adee653f1dcff660d84f0ca302907747af2a387f67821acfce33
```
Now concatenate 1 to the above string (shortened it for the sake of readability):
```
00000000000000000142288--e361a57a7406adee653f1-1
```
Run it through SA256, and see if it meets difficulty requirement, *i.e.*, begin with a bunch of 0's. Try 2, 3, 4, and so on until you find a number that satisfies the difficulty condition. I'm not how computers (miners) approach this random number guessing. This random number in Block 472391 is **1900492548** and was found by [F2Pool][9]. 
### Guessing the number 1900492548 is solving the complicated math problem
This nonce is not unique,*i.e*, it is possible to find more than 1 number (nonce) that satisfies difficulty  condition. The block is added to the blockchain and miner is awarded with 12.5 BTC.

[1]: https://www.amazon.com/Mastering-Bitcoin-Unlocking-Digital-Cryptocurrencies/dp/1449374042
[2]: https://antonopoulos.com
[3]: https://en.bitcoin.it/wiki/Main_Page
[4]: https://bitcoin.stackexchange.com/
[5]: http://www.economist.com/blogs/economist-explains/2015/03/economist-explains-5
[6]: https://en.bitcoin.it/wiki/Vocabulary
[7]: https://en.wikipedia.org/wiki/SHA-2
[8]: https://blockchain.info/block/0000000000000000014228823553852a90563fe84da5f0a5aa4832e85f68b1b5
[9]: https://www.f2pool.com/