How long it will take to crack a RAR password?

I wonder how long it will take to crack 16 character alphanumeric WinRAR password for a mini supercomputer. As far as I know graphic cards are preferred over CPUs to crack passwords nowadays. If we consider that the cracker (law enforcment) uses the latest technologies to crack the RAR password and has pretty much computing power how long it will take for him to crack the password?

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If you mean 16 completely random alphanumeric characters, then it's infeasible even for state level adversaries. I'd estimate a ~112 bit security level, which should be good for several decades. – CodesInChaos Mar 26 '13 at 18:10
With a policy which mandates a password change every one week , now top this with what @CodesInChaos said its just become very impractical. – Saladin Mar 26 '13 at 18:22
@Saladin A password-change policy wouldn't actually have any effect at all, since we're talking about a password on a file. At any given point in time the file has a password that can't be invalidated if the file is copied, so the frequency with which it is changed is immaterial to the feasibility of a brute-force attack. – Xander Mar 26 '13 at 18:27
@Xander okay i was thinking somewhere along the lines of a static file kept on a secure server (without any copies rights) which the attacker is trying to bruteforce. If it has been already copied (e.g in usb) then you are right, it wouldn't have any effect. Thanks for clarifying. – Saladin Mar 26 '13 at 18:32
@kasperd 95 bits of entropy + 17 bits of iterated hashing = 112 bits of security. See my answer. – CodesInChaos Oct 31 '15 at 21:55

A completely random alphanumeric password of length 16 has an entropy of 95 bits (16*log2(2*26+10)). I forgot the exact value, but I think rar uses around 100k iterations for its KDF, increasing the security level by about 17 bits, resulting in an effective security level of 112 bits.

With standard GPUs breaking this would cost around \$1019. Custom hardware shaves off a factor 100 or so, still giving you a cost of \$1017. Even if Moore's law continues, it'll take several decades until this is remotely feasible.

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I just would like to mention that RAR uses 262144 SHA-1 iterations in its KDF. – Adi Mar 26 '13 at 22:48
For anyone wondering the significance of that number, it's just `0x40000`, or 2^18. – Polynomial Mar 27 '13 at 0:42

A 17 DIGIT PASSWORD LIKE 1234567890ABCDEFG

HAS POSSIBLE COMBINATION TO CRACK A PASSWORD = 9637684994875392000

SO IT IS VERY TEDIOUS TO CRACK A THIS TYPES OF PASSWORD.

OFTEN A TOTAL OF 4GHZ COMPUTER TAKES TIME TO CRACK A ONLY 6 NUMBER(1,2,3) PASSWORD= LESS THAN 3 HOURS ,

A TOTAL OF 4GHZ COMPUTER TAKES TIME TO CRACK A ONLY 6 ALPHABETS (A,B,C) PASSWORD= LESS THAN 10 HOURS ,

A TOTAL OF 4GHZ COMPUTER TAKES TIME TO CRACK A ONLY 6 NUMBER+ ALPHABET(1,2,3,A,B) PASSWORD= LESS THAN 4 DAYS,

A TOTAL OF 1000GHZ=1 TERA-HERTZ COMPUTER TAKES TIME TO CRACK A 6 NUMBER(1,2,3) PASSWORD= 3/4X1000=TIME,

SO VIA THIS YOU CAN CALCULATE THAT, HOW MUCH TIME WILL TAKEN TO CRACK THE TOTAL OF PASSWORD WITH OTHER SYMBOL EXCEPT ONLY TAKE THE DIGITS OR WORDS OR BOTH. THE RATIO WILL TAKE TO CRACK 16 DIGIT PASSWORD WILL BE 3 YEARS FOR SUPERCOMPUTER.

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Rage Mode or broken Caps Lock? – John Oct 31 '15 at 18:41
Severe formatting problems. I sense a disturbance in the Force as if all minuscules have been simultaneously stolen. – Deer Hunter Oct 31 '15 at 18:49
this answer assumes an offline attack - you also do not provide evidence or backup to your statements – schroeder Oct 31 '15 at 22:14