# How long to crack an 8 character WPA2 hash if first char is known

I know the first char is A and it's all upper alphanumeric. Is there a way to estimate how long a mid level single GPU using hashcat would take to crack it?

• It would take the same amount of time as it takes to brute-force guess a 7 character uppercase alphanumeric password. It depends entirely on how many guesses your computer can make per second. Assuming 34 characters [A-Z0-9], it would take 7^34 operations at most, and (7^34)/2 operations on average. ("mid level single GPU" is not something that we can convert to operations/sec). Commented Aug 1, 2019 at 18:27
• Or is that 34^7... I never can remember, never needed to know for myself, and will only bother to remember when (if) I ever actually do need to know... ;-) Commented Aug 1, 2019 at 18:29
• @Ghedipunk it's 34^7. The way I remember it is with the extreme case. If I have only 1 possible letter there's only 1 possible guess (e.g. 1^7=1). The wrong alternative would be 7^1=7 which is intuitively wrong. Commented Aug 1, 2019 at 19:08
• A-Z0-9 is 36 characters, not 34. Commented Aug 1, 2019 at 19:14
• Digits are 0-9. I guess you mean "characters" then? Commented Aug 2, 2019 at 5:26

If the passphrase is exactly 8 characters long and the first character is known, then only 7 need to be brute forced. Assuming characters are 0‒9 and A‒Z, the maximum number of combinations is 367.

An AMD Radeon RX480 GPU can go through approximately 170,000 candidate WPA2 passwords per second. This means it will take around 367 / 170000 seconds at most to exhaust all possible 7 character upper alphanumeric passwords, and half that on average. This equates to an average of 2.5 days.

Note that higher-end GPUs and clusters of GPUs can crack such a password, and stronger ones, much more quickly. From Twitter, 8x 2080Ti GPUs can crack any 8 character password in ~2.5 hours!

• This may be relevant.
– user163495
Commented Aug 20, 2019 at 7:48
• @MechMK1 True, but 8 high-end GPUs probably don't qualify as "a mid-level single GPU" Commented Aug 20, 2019 at 7:48
• True, hence why it's more of a "further reading" kind of thing. But a 2080 can be gotten for around 700€, making the total cost of such a cracking rig around 6000€, which is totally affordable for an attacker. Even with just 4x2080's, it's take around 2 hours to crack.
– user163495
Commented Aug 20, 2019 at 7:53