Hashing functions

Hashing functions are algorithms that work on data of an arbitrary length to produce a fixed length output. Given the same input, the output is always the same and for different input values, the output is always different. These functions are one way, which means that the reverse operation on data is not possible.

In mathematical terms, a one-way hash function can be defined as follows:

Given a message M, and a one-way hash function H, it is easy to compute x such that H(M) = x. But given x and H, it is infeasible to get the message M. This can be shown mathematically as follows:

H(M) = x

H(x) ≠ M

Another property of hash functions is low collision probability. This means that given a message M, it is hard to find another message M, such that:

H(M) ≠ H(M')

One-way hash functions can be used for various applications. They are used to create a fixed size output for a variable length string. Using a hash, a value can be securely stored as given by the hash; it is unfeasible to retrieve...