1. Nov 8, 2007

### Omnis

How do I work out password combination probabilities?

For example, I'm looking for a password between 10-15 characters in length, the password can contain any alpha-numeric character (lower/upper alphabet character and 0-9 digits). How would I find out how many possible combinations there are?

2. Nov 8, 2007

### DaveC426913

What would you make for an answer as your first try? What logic did you use?

Hint:
How many possibilities are there for the first number in the sequence?
How many possibilities are there for the second number in the sequence?
Hw many times do you have to do this?

What is a really compact way representing that as a generalized formula?

Last edited: Nov 8, 2007
3. Nov 9, 2007

### Omnis

62

62

10-15 times depending on the password length

I have no idea, thats why I came here, I'm wondering if its possible to recover a zip password on one of my files but I need to know how many possiblilities there are and I also like to know how to work it out for myself :)

4. Nov 9, 2007

### DaveC426913

OK, well there's
62x62x62x62x62x62x62x62x62x62
+
62x62x62x62x62x62x62x62x62x62x62
+
62x62x62x62x62x62x62x62x62x62x62x62
+
62x62x62x62x62x62x62x62x62x62x62x62x62
+
62x62x62x62x62x62x62x62x62x62x62x62x62x62
+
62x62x62x62x62x62x62x62x62x62x62x62x62x62x62

or

62^10 + 62^11 + 62^12 + 62^13 + 62^14 + 62^15

or

a little more than 781 septillion

combinations.

At one try per second, it will take you a mere 24 quadrillion years, a mere 1.8 billion times longer than the universe has existed to-date.

Don't try to do them all in one sitting.

Last edited: Nov 9, 2007
5. Nov 9, 2007

### CRGreathouse

If you try ten billion passwords in a second with a given computer, and you use a million computers, it would take 1238 years on average.

6. Nov 10, 2007

### JasonRox

After the 10th character the user has the option not choose at all, so that is 63 choices.

7. Nov 10, 2007

### ben328i

isn't there a formula for that from allg or something.
what is the equation not worked out like in a, b c, etc. form.

8. Nov 10, 2007

### HallsofIvy

The "formula" DaveC426913 was using earlier is often referred to as simply "The Fundamental Counting Principle": If you can do A in "n" ways and you can do B in "m" ways, then you can do A and B together in "mn" ways.

If you have 62 symbols you can use and there are no restrictions on how they can be used, then you have 62 ways you can write each of the, say, 10 symbols and so have

Altogether, then, there are a total of 6210+ 6211+6212+6213+6214+_6215 "passwords". That's the figure DaveC426913 gave.

But if the user chose no character for the 11th choice, he must make the same choice for the 12th, 13th 14th, and 15th. I don't think that simplifies anything.

Last edited by a moderator: Nov 16, 2008
9. Nov 10, 2007

### ben328i

ha good luck if this is really a problem not just a question.

10. Nov 10, 2007

### DaveC426913

What? No.

If the pw is 10 characters long, there are 62^10 possible combinations.
If the pw is 11 characters long, there are 62^11 possible combinations.
etc.

Add them together and you get all possible combinations within the parameters set.

So, your scenario where the user decides to not choose at all after the tenth character (or more accurataly: hits return), is simply the scenario where the pw is only 10 characters long.

11. Nov 12, 2007

### Omnis

Thanks to everyone for the help

It is a problem, I'm trying to recover a password for a zip file, but the luck is much appreciated

12. Nov 12, 2007

### JasonRox

You're right!

13. Nov 12, 2007

### DaveC426913

If it's your password, that should eliminate about 99.999999% of the possibilities, shrinking it to ones you would have come up with.

14. Nov 12, 2007

### JasonRox

Yeah, you can eliminate the characters you know for sure you didn't use!

15. Nov 13, 2007

### wysard

Assuming order is important, ie:that "BAT" is not the same as "TAB"

then the general answer is n!/r! or:

62!/ (pwd length)! Where "!" means the factorial function.

Just like picking a lottery number.

PS. It's easier to break the password encryption scheme than guess the actual password.

16. Nov 15, 2008

### Dantie Neit

Figured I'd use this one. I'm trying to crack my password for something I got years ago, but I don't know how worth it it is. I need to know the number of possibilities for a 4 character password which has 6 characters to use. Basically 1111 to 6666. I'm good at maths, but that's only at a low level still. If someone can just work out what it is, that would be great.

Cheers!!!

17. Nov 16, 2008

### slider142

Use the Multiplication Principle of Counting: You have 6 choices for the first character, 6 choices for the second character, 6 for the third, and 6 for the fourth, so altogether you have 6*6*6*6 choices for a string of 4 characters.
The principle comes from the following thought experiment. If you have a string of two characters with m choices for the first character and n choices for the second character, then first counting all possible strings starting with characters in the first space. For each character in the first space, there will be n possibilities for the second space. Ie., if the first character can be any letter in the alphabet, you would have sets like {A_, A_, ...}, {B_, B_, ...}, ... ,{Z_, Z_, ...} where the underscores are replaced by characters from the second set (of size n). Thus, you should have m sets of n strings, or m*n total strings.

18. Nov 16, 2008

### HallsofIvy

No. That would be true if the same letter or numeral could not be used twice in the same password and that is not true.

19. Nov 18, 2008

### soandos

If there are any files in the zip archive that you have unencrypted, or it is encrypted using any early version (as you seem to suggest), then there are flaws in the scheme that have been exploited, and can recover the password near instantaneously. if there is an unencrypted files that is also present in the archive, then there is something that is called a plain text attack that can be used. basically, is uses patterns between the encrypted and unencrypted copies to get the password. gets an alphanumeric 10 character password in about an hour on an average desktop.

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