Number of possible password combinations

[Knot2Brite]

Hello,

A half-century ago I dozed during math class and now I regret it.

Assuming I have a computer password consisting of 31 digits. How many combinations are possible?

A formula to compute this would be well beyond my ability. Likewise, a very long number would not do much because after I get beyond a million I don't know the names of what follows.

I'm guessing it would be a very long number but for my purposes an answer such as "5 billion," will be adequate.

Thank you

K2B

 

[stapel]

Assuming I have a computer password consisting of 31 digits. How many combinations are possible?

Are the "digits" all numerical? Then there are only ten possibilities for each digit; namely, zero through nine. But if alphabetic characters are allowed, then there are 10 + 26 = 36 possibilities for each digit. If other characters, such as spaces are allowed, the number of possibilities for each digit grows.

So, in order to answer this exercise, you will first need to clarify what is the meaning of a "digit", and if there are any other rules which apply. (This information should be included in the instructions to the exercise.)

When you reply, please show everything you have tried so far. Thank you!

Eliz.

 

[Knot2Brite]

Hello and thank you for responding,

My ignorance is showing.

Each one of the 31 places can be an upper or lower case letter, a numeral zero to nine or any symbol that shows on a Western computer keyboard (&>~ etc.). Blank or empty spaces are not allowed.

I lack the technical education to know even where to begin so I have not any work to share.

Thank you

 

[Deleted member 4993]

Last time I counted - there were 47 character keys on the standard keyboard.

Then using <shift> we have possible 94 characters.

Is this a homework for class or just curiosity (or something else) question?

 

[Knot2Brite]

Hello,

I think general curiosity would be the most accurate description of my interest.

I got into a software program which generates passwords. Having read that there are software programs that will break passwords I thought one of an odd length, 31 digits, would make things tough on them.

The computer magazines say that the longer the password the better and if it is a mixed bag of letters and numbers and symbols your protection is greater. That got me thinking, how many calculations would a computer have to run to break my password.

Thank you

 

[pka]

Let’s assume that there are 92 possible symbols available to us to use in 31 spaces then there are \(\displaystyle {92}^{31} =7540890729115114577038236151386562505708947165995322056900608\) possible strings.

 

[Knot2Brite]

I sense that is a big, big, number.

Can you summarize or reduce it to something like "about 500 million" or "about 60 million" or "it would have 31 or 92 zeros"?

I am trying to get a "feel" for the work a hacker would have ahead of him if he tried to break my password. Rounding and drive by guesstimates are fine.

Thank you

 

[Deleted member 4993]

That number is ~\(\displaystyle 10^{61}\) - which like way way way more than 10 billion (which is \(\displaystyle 10^{10}\))

It would have ~61 zeros.

 

[Knot2Brite]

My screen just refreshed and I can view the entire message. Previously I only saw the formula. WOW!!!

Does a number of that length have a "name" like million or billion? I failed math 50 years ago and haven't got smarter since.

Looking at that number I am guessing it is like the number of stars or grains of sand on the beach. For people like me and someone trying to crack my password it represents an impossibility in a human lifetime.

Thanks to all for helping me get my mind around this.

Be well

 

[stapel]

Let’s assume that there are 92 possible symbols available to us to use in 31 spaces then there are \(\displaystyle {92}^{31} =7540890729115114577038236151386562505708947165995322056900608\) possible strings.

This number is about 75.4 novemdecillion. :wink:

This is larger than the number of atoms in our planet. :shock:

If you tried a trillion passwords a second, it would take you about 2.38 tridecillion years to test them all.

Eliz.

 

[Deleted member 4993]

The nearest number is called novemdecillion (by the way a googol is \(\displaystyle 10^{100}\))

There are about \(\displaystyle 10^8\) seconds in 3 years.

Suppose you have computer that generates and checks 10 billion \(\displaystyle 10^{10}\) passwords per second.

What the heck - make it 10 billion times faster - it can check \(\displaystyle 10^{20}\) passwords per second.

Then that computer will take \(\displaystyle 3 \cdot 10^{33}\) years to hit all the passwords

Age 0f universe is ~\(\displaystyle 10^{10}\) years.

So many many many (~ about \(\displaystyle 10^{24}\) - septillion ) universes can be created and destroyed in the mean time.

Stapel was \(\displaystyle 10^{-9}\) second faster than I was :evil: