Question

I am curious about developing my own Simple Hashing mechanism.

I would like to know some math functions that are irreversible.

I know that raised to function and modulus are some functions that are irreversible in the sense that the reverse procedure gives two answers.

e.g.:- square root(4) = 2 or -2

I need a function that is not reversible because, even if anyone cracked my cipher, they should not be able to produce a decrypter, that can easily decrypt the passwords in my hashing.

Using this functions I can make my hashing more secure.

It would be helpful if someone could give more such functions with explanations.

Answer 1

Squaring in R is irreversible in the sense that it loses information. But that’s not at all what hash functions are about.

Cryptographic hash functions have two main properties:

1. It’s hard to find two inputs with the same output, called a collision
2. It’s hard to find an input matching a given output, called a pre-image

Squaring on R has neither of these properties:

1. Finding a collision is trivial. Given x just calculate -x, both of which square to x*x.
2. Finding a pre-image is easy. Calculate the square-root. There are efficient algorithms for this. (Ignoring the problem that you can’t output the infinite sequence of digits if the result is irrational)

Unfortunately there are no “simple” functions with these properties.

Related questions:

• Why are hash functions one way? If I know the algorithm, why can’t I calculate the input from it?