## Math Problem Clock Cycles

For the discussion of math. Duh.

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Iankap99
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### Math Problem Clock Cycles

So I got a problem, duel sided.

For this problem, assume the program used to decrypt the document used 4 operations per attempt at the codebreak.

1) How long will it take the average computer, lets assume 3 ghz processor. To solve a pdf password of 24 characters, case sensitive, all keys on keyboard used).
Conversely the fastest supercomputer in the world of 2.566 petaFLOPS, how long would it take that to solve the same encrypted document.

2) Assuming a doubling of processor speed each year. Compounded annually. How long would it take for a current 3ghz processor to solve it.
Again, the supercomputer of 2.566petaFLOPS, how long would it take, doubling processor power each year.

So there you go, difficult problem. I actually would like the answer to this as would several friends.

masher
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### Re: Math Problem Clock Cycles

Iankap99 wrote:So I got a problem, duel sided.

For this problem, assume the program used to decrypt the document used 4 operations per attempt at the codebreak.

1) How long will it take the average computer, lets assume 3 ghz processor. To solve a pdf password of 24 characters, case sensitive, all keys on keyboard used).

On my keyboard, there are 47 keys, so 94 possible characters. That means there are 94^24 (~2.265×10^47) possible passwords.

For a 3 GHz computer, assuming ideal conditions (and your limit of 4 operations per attempt), this is equivelant to 0.75×10^9 passwords tested per second.

So, 2.265×10^47 divided by 0.75×10^9 is 3.020×10^38 seconds, or 9.570×10^30 years

So, quite a while.

Wash, rinse, repeat for the others...

gmalivuk
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### Re: Math Problem Clock Cycles

This looks suspiciously homework-like in its wording, so for now I think that should be all the specific math help offered in this thread. (Specific as in using the OP's numbers. Other discussion is still fine.)

Speaking of other discussion, suppose the doubling period is D, and suppose the number of operations in a problem would take T on the current generation of machines. Then if we started at future time t, with the faster machines available then, it would only take 2^-(t/D)*T to complete the problem. So the total time to complete the problem is t+2^-(t/D)*T, which is optimized at
$t=\frac{\log \left(\frac{T\log (2)}{D}\right)}{\log (2)}\times D$
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Iankap99
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### Re: Math Problem Clock Cycles

gmalivuk wrote:This looks suspiciously homework-like in its wording, so for now I think that should be all the specific math help offered in this thread. (Specific as in using the OP's numbers. Other discussion is still fine.)

Speaking of other discussion, suppose the doubling period is D, and suppose the number of operations in a problem would take T on the current generation of machines. Then if we started at future time t, with the faster machines available then, it would only take 2^-(t/D)*T to complete the problem. So the total time to complete the problem is t+2^-(t/D)*T, which is optimized at
$t=\frac{\log \left(\frac{T\log (2)}{D}\right)}{\log (2)}\times D$

Actually not homework. A curious argument with a friend about cracking a pdf we get each year in the two weak alloted period before we get the password to it. One friend suggested it would take an hour if a server was rented. One suggested we would never see the completion of this problem in our lifetime.

Cursory calculations suggest that the supercomputer would also take a ridiculous amount of time to solve this problem. So about the doubling problem, I have no idea how to use a log. I'll see if I can find a friend who would know how to use a log with the information.

Thanks for the help and if you decide to give me the answer to the doubling problem.

gmalivuk
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### Re: Math Problem Clock Cycles

Log is logarithm. Any scientific calculator (or Wolfram|Alpha) will know how to compute one. (And so I did give you the answer to the doubling problem. You just need to put in your own values for T and D.)
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### Re: Math Problem Clock Cycles

Iankap99 wrote:2) Assuming a doubling of processor speed each year. Compounded annually. How long would it take for a current 3ghz processor to solve it.
Again, the supercomputer of 2.566petaFLOPS, how long would it take, doubling processor power each year.

Hertz measures clock cycles per second, while FLOPS measures floating point operations, so the two aren't directly comparable. To convert from one to the other, you would need to know how many clock cycles per floating point operation, which presumably depends on processor architecture.
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WarDaft
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### Re: Math Problem Clock Cycles

Brute forcing it would of course take longer than is practical.

If you know anything about how the .pdf is encrypted however, vastly (well, compared to brute force) more efficient attacks may be possible. So both your friends are partially right.
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