THE MATH I PROMISED:
THE MATH:
32 symbols
10 numerals
26 lowercase
26 uppercase
= 94 possible characters each
94^64 = 1,906,262,174,603,609,240,179,178,656,657,625,086, 945,986,037,788,719,949,935,941,357,851,066,322,59 6,406,102,384,587,670,757,587,004,664,979,877,271, 875,661,328,285,696
possible combinations
19062621746036092401791786566576250869459860377887 19949935941357851066322596406102384587670757587004 664979877271875661328285696[possible combinations]/2800000000[number of passwords per second for one PC using software]
680,807,919,501,289,014,349,706,663,092,008,959,62 3,566,442,067,399,982,119,979,056,375,380,829,498, 716,465,137,352,739,556,281,073,094,635,670,454,24 1,307
seconds
seconds in one year: 31,556,926 (rounded up from 31,556,925.9936)
How many years would it take for one PC to crack a 64 character password (ONLY using the symbols on a keyboard, not counting other symbols), using commercial-grade top-of-the-line software on a single home PC (BARE PASSWORD, NOT INCLUDING WPA2 ALGORITHM)?
Answer: 68080791950128901434970666309200895962356644206739 99821199790563753808294987164651373527395562810730 94635670454241307[seconds to crack]/31556925.9936[seconds in one year] =
21,573,961,913,760,600,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000,000,000,000 years
THERE IS NOT A NAME FOR A NUMBER THAT LARGE!!! THE HIGHEST THE NUMERICAL SYSTEM GOES IS THE GOOGOL (where Google got its name). THE GOOGOL HAS 100 ZEROS AFTER IT. THIS NUMBER IS 21.5 x 10^108 - that is, 109 ZEROS AFTER 21 (36 SETS OF THREE). So let's just say it like this:
It would take 21,573,961,91 GOOGOL YEARS to crack the password.
PERSPECTIVE: The universe will cease to exist (big crunch) in 100 billion years.
So, 21573961913760600000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000[YEARS TO CRACK IT]/114000000000[time from big bang to big crunch]=
189,245,279,945,268,421,052,631,578,947,368,421,05 2,631,578,947,368,421,052,631,578,947,368,421,052, 631,578,947,368,421,052,631,578 TIMES FOR THE UNIVERSE TO EXPAND AND COLLAPSE BEFORE YOU COULD CRACK THE PASSWORD.
In other words, 1.8924528 x 10^98, in lamen terms:
IT WOULD TAKE ALMOST 19 MILLION GOOGOL (19 with 106 zeros after it) TIMES FOR THE UNIVERSE TO GO FROM THE BIG BANG TO THE BIG CRUNCH, IN ORDER TO CRACK THE PASSWORD!!!
AND THAT'S ***BEFORE*** WE HAD ANY KIND OF ALGORITHM LIKE WPA2!!!
Unfortunately this would actually even be possible because the proposed
HEAT DEATH OF THE UNIVERSE will be in 10^150 years from now.
--
NOW, let's calculate what it would be WITH WPA2:
WPA2 uses a military-grade 256-bit algorithm that uses a logarithmic scale. If you use the standard ASCII characters, then that leaves you with 94 possibilites for each of 64 characters.
In short, the same as the SSID and password themselves, since I used 32 characters each.
Thus, the solution is quite easy without delving into much math (we're not even going to delve into the other factors of WPA2 that would multiply this solution exponentially. the number would be so outrageously large it would be completely pointless to even write:
(94^64)[SSID+Password]^[To the POWER OF](94^64)[WPA2]
In short, (94^64)^(94^64)
As we know from before, this is 1,906,262,174,603,609,240,179,178,656,657,625,086, 945,986,037,788,719,949,935,941,357,851,066,322,59 6,406,102,384,587,670,757,587,004,664,979,877,271, 875,661,328,285,696 ^
1,906,262,174,603,609,240,179,178,656,657,625,086, 945,986,037,788,719,949,935,941,357,851,066,322,59 6,406,102,384,587,670,757,587,004,664,979,877,271, 875,661,328,285,696
SORRY, I HAD TO STOP. THE BIG NUMBER CALCULATOR GAVE ME AN ERROR, "SORRY, WE CAN'T CALCULATE NUMBERS THAT BIG!!!"
(Apparently even trying to calculate this would make such an outrageously large number that it would be completely pointless to even write))
http://s11.postimage.org/dfapnjzrn/Clipboard01.jpg
Now you see why you would have to be retarded to think you could crack it.