Mfcttrf

I generated a password recently for a new account and the first three characters were "aa1".

After exhausting all other attacks, a cracker would start brute forcing. On the assumption they'd start from "a", my password of "aa1" would be cracked faster than, say, "ba1", and that faster than, say, "za1".

This password was very long so this question is more theoretical than practical. (Unless password lengths are limited, of course...) Are my assumptions right about brute-forcing and passwords?

It would seem that it depends on how exactly the attacker is going to bruteforce your password. However, my opinion is that in the end it doesn't matter.

A serious attacker will never start from the beginning in alphanumeric order, from aaaaaaaa to 99999999, unless they know they can do that in a reasonable time. If that's going to take them a thousand years, why should they use that method, knowing they will necessarily have to stop at, say, cccccccc? But if the attacker knows that they can try all the possibilities in a reasonable time, then it doesn't matter whether your password is among the first combinations or among the last, because in the end they will find it anyway (in a reasonable time).

Most passwords are still weak (say, your dog's name, plus maybe your date of birth, etc.) and the attackers don't like wasting too much time, let alone years to crack passwords. So what attackers normally do is use dictionaries and patterns. They will first try passwords like: pass123, 123pass, john90, john91, John92, JOHN93, suckmyd1ck, l1nux4dm1n, etc. If every attempt with dictionaries and patterns fails, they might move on and assume that the password looks truly random. How long will it take to try all the possible passwords? If that can be done in a reasonable time, they might try them all (for example from aaaaaaaa to 99999999). Otherwise if the attacker assumes that they will never be able to try them all, they might try to bruteforce the password with some random guesses (random strings, not ordered): 12hrisn589sjlf, 9f2jcvew85hdye, otnwc739vhe82b, etc. If the attacker is lucky they might find the password, sooner or later. However if the password is too strong, such that it would take them too many years to guess it, they had better give up or think of an alternative attack (phishing, shoulder surfing, keyloggers, etc.)

Entropy is really the biggest concern, and entropy is determined by the amount of randomness in your password generation process.

Let's use an 18 character password as an example. We'll look at alphanumeric characters only (62 possible characters). This gives:

log2(62**18) = 107 bits of entropy

If you decide to always convert the first 3 characters to Z to make it harder to bruteforce then you have effectively removed 3 random characters from your password, leaving you with:

log2(62**15) = 89 bits of entropy

Which is about a factor of 1,000,000 weaker. Of course, both are still absolutely and completely impossible to bruteforce, so if someone is trying to brute force your password I wouldn't worry. However, it's worth emphasizing how impossible it is to brute force such a password (just in case my links didn't convince you). A top of the line MD5 hashing rig can try 200 billion hashes per second. It's blazing fast (which is why MD5 isn't supposed to be used for passwords). Even your weaker password (when you replaced the first three characters with z) has 7.6e26 possible combinations. At 200 billion hashes per second it will only take 120 MILLION years to try all password possibilities if the password was hashed with MD5. I don't think you have anything to worry about.

So, is it better to start with "higher" characters to make it harder for someone to brute force your password? Maybe, maybe not. It depends on how someone actually tries to crack the password (and there aren't any guarantees about what direction they might work in). Either way though, if you use a long random password, there is absolutely zero chance that it will get hacked. So I wouldn't worry about it. When it comes to passwords length is king.