what makes things like SHA256, mathematically impossible to decrypt/decipher?

Question

i get that SHA256 isn’t considered “encryption”, it’s something to do with hashing. so, if i encrypt “hello” into a random string of characters, why is it said to be impossible to decrypt it back to “hello”? if you had a maths equation like P = (k * 10 / G) / (4x * 5gl), it’s possible to work backwards to find the value of k or g eventually. why not with SHA256? is it something to do with random numbers?

In: Mathematics

Answer 1

SHA is a Hashing function, SHA stands for Secure Hashing Algorithm.

Hashing functions are by definition a repeatable 1-way mathematical algorithm that creates an output of a set length.

The formulas are designed in such a way that you cannot reverse the process to run the output back into the input.

Meaning that a specific input into the function will always give the same answer (repeatable) and also for any given input a HASH function will always result in an output of the same number of characters or numbers in length.

This is important in cryptography because it allows you so store information like hashed passwords in a way that doesn’t allow the hacker to determine what the original password was. A database of hashed passwords will be a long list of seemingly random strings of digits and characters that are all the same length. So you can’t determine anything about the original password such as it’s length or what characters were in it.

BUT when you do a password lookup, you can take a password inputed, run it through the algorithm, and then compare the resulting hash to what’s stored in the database.

What this means is that to break a hash the only thing you can do is run different inputs into the hash and see what outputs they give until you find the correct answer. This is called Brute Forcing which is a long and convoluted process making it impractical.

This is also why hashing algorithms keep getting more complex. As computing power increases the ability for hackers to Brute Force passwords gets easier and easier, so by making the hashing algorithm take longer you are making it harder to Brute Force.

The actually maths behind a hashing algorithm are pretty complex and outside the scope of what I want to type. So if you want to learn more I suggest you watch numberfile: