Combinations

CremePuff · September 10, 2020

I have four folders on my computer with 10 keyfiles in each. I know if I use these like a normal 4-digit combination lock, where each folder is a place value, and each file is a digit, there would be 10,000 possible combinations. But what if you didn't have the files. Each keyfile is 1.00 MB in size (1,048,576 bytes to be exact). How many possible combinations would there be if you have to create each keyfile from scratch? Every single bit. How much data would that be?

TetraSky · September 10, 2020

So... If you have to create each files from scratch, it assume you don't know what's in the files?
A single character, like the letter "a", is 1 byte. But special characters, like "←" (3 bytes) or ŧ (2 bytes) use up more...

It could be as simple as 1x + 2y + 3z = 1,048,576 bytes... where x = single byte characters, y = 2 bytes characters and z = three bytes characters.

After that you can multiply by 10^4... There can be as many as 349,525 triple bytes characters + a single 1 byte character... Or 349,525 double digit characters... or 1,048,576 single digit.... per key files.

If we ignore dual bytes and triple bytes. You can basically just do :

lower case letters = 26

upper case letters = 26

digits = 10

single byte "special" = 20 (might be more)

+ space bar

total = 83

83^1048576 * 10^4 = HUGE NUMBER. So large that my calculator is just giving me the middle finger and saying "error".

Characters like ! @ $ % ? are also single byte, but I don't feel like finding out all of the various different ones.... So I just included the ones I tested quickly. It's missing a bunch of them.

There wouldn't be a single answer. You'd have a range of possible answer and I'm not even sure of the question to begin with. It's so vast that it is near impossible to find.

So...Yeah, overall... it would be so big that the universe is likely to end faster than anyone/any super computer, actually going through every single possible combinations.

To put it in perspective...

83^998 * 10^4

That would be if each files were 998 bytes (a long shot from 1,048,576).

The number of different combinations for that would be :

Spoiler

83,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

And that's with the biggest calculator I could find online! It didn't go further than 998 for the exponents.

That's 83 followed by 1002 zeroes.

To further put that in perspective... If that same document was only 200 bytes instead of the 998 above. (and much less an actual MB)

It would take over 300 years to crack.

For the actual answer with the right byte number, it would be 83 followed by 1048579 zeroes.... That, is almost 138 word document page, in Times New Roman, in character size 8, filled with zeroes(no comma, just zeroes).... And you know what the funniest thing is? That document was only 13.2KB according to Windows. So all of this. EVERYTHING.... IS POINTLESS.