What is a hash?

In order to comprehend how Bitcoin mining works, it is important to understand what is hashing. Basically, it is the conversion of a string of digits into a shorter value or key of a fixed length that corresponds with the original string. The main aim of hashing lies in indexing and retrieving units in the database, since finding a unit with the help of a shorter hashed key is much faster than applying the initial value.
What is hash
The hashing algorithm is also known as a hash function, and the notion comes from the idea that the final hash value can be perceived as a mixed up variation of the represented value. The hash function takes a particular input of an arbitrary length, a message, and applies a set of mathematical transformations to produce a single output, also known as hash, tag or digest (earlier cryptographic hash function MD5 = Message Digest 5). A specific input cannot have two different outputs; therefore, the output of a hash function is always consistent. The same data will always bring out the same hash, but if even one digit of the data is modified, the hash will entirely altered.
The hash function, and more specifically the cryptographic hash function, has a number of properties that makes it distinctive. A cryptographic hash function is different from other hash functions as possesses critical design goals and specific properties such as high level of security, confidentiality, privacy, necessity of authentication, etc. First of all, it is crucial that a cryptographic hash function is computationally efficient, implying that it should not take a lot of time to compute the output from a given input. Secondly, since the input is of an arbitrary length and the output is of a fixed-length it is possible that two different inputs result in the same output. This process is called a collision, and the crypto-hash function should be collision resistant, meaning that it should take an astronomically long time for the processor to find a same output for two distinct inputs. Thirdly, the hash function should hide any relevant information or details, for example, whether the key is an even or an odd number. And finally, the output should be well distributed, and, therefore, it should look random as if you were flipping a coin. In any case, it should be impossible to predict the output. All of these properties are interrelated.
The hash function is commonly used to encrypt and decrypt data for information security in digital signatures as well as in e-commerce, message authentication protocols, password security, fingerprinting, etc. The Bitcoin system uses the SHA-256 hash algorithm to produce verifiably random key. In order to solve the block and gain the reward (Bitcoins), the miner must create an SHA-256 hash with a lower value than the current target.

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