Yes, if you only want to crack Alice's password, the salt will not slow you down. But if your goal is to crack a million, wouldn't the salt slow you down?
If I'm missing something, I would really like to know. Always good to learn something new!
Rainbow tables are useful if the time it takes to compute is big enough that storing a large list is useful.
The GPU crackers are so fast nowadays that that isn't the case. If you can try 500M per second, that's about 10 GB of SHA1 generated! Imagine storing a day's worth of work in a rainbow table :)
It's better to use a proper password hash, which will be slow, and will likely have per-user salting built in, anyway.
The hole in your logic is: there is no point in guarding against the case where, if two users share the same password, cracking one will crack the other, because the only time that two users share a password is when that password is really weak.
What are the odds that two users share the same password? If passwords were totally random and 24 characters long the answer would be "pretty low". And the odds of cracking one of these passwords by brute force would also be pretty low. If only we lived in that world.
In the real world the odds of two users sharing a password are frighteningly high, but that's because most passwords are awful: they are things like "pizzapizza" or even "password". The cracking programs can crack one of these in a millisecond, because they are equipped with lists of thousands of real-world weak passwords harvested from real websites. And then, if another user shares this awful weak password, that user will also get cracked, a few milliseconds later. There is no point in "parallelising cracking across users" because it's so easy to just guess all the weak passwords for every user.
Another way to think about it: A salt could only help in cases where (a) two users share the same password, but (b) that password doesn't appear in the list of several million other real-world passwords that is built into the password cracker. And that just isn't worth worrying about.
But if the database has individually salted hashes then you need to do each hash operation individually for each user. That means you have to do 1 quadrillion hashes. That will take 1,000 times longer.
Really. First, stare at this chart from the Ars Technica article:
http://cdn.arstechnica.net/wp-content/uploads/2012/08/expone...
This graph shows, roughly, that a short password can be brute forced in seconds using modern hardware. If it is just one character longer, it suddenly takes a week to brute-force. This is the miracle of exponential functions.
Now multiply the y axis by 1000. The long password now takes 1000 weeks. But the shorter one still only takes a few thousand seconds. If you are running your cracking program for a day, you'll get the same results you got before. The weak passwords are still weak enough to crack. The strong ones are still strong.
(Note, by the way, that it doesn't take 1000 times longer to guess 1000 salted passwords, because some of those passwords are super weak and will fall in seconds, after which one no longer needs to guess them. So, for example, once half the passwords have been broken, the new multiple is only 500. The Ars article explains this, but I didn't understand its wording at first.)
It is true that salt makes some difference. But it is not a meaningful difference. The difference between giving up 60% of your passwords and giving up 73% of your passwords is probably moot.
EDIT: And my example number of 73% is too low! That is bad news for MD5! Again, the article: they cracked 82% of a 16k-password file in one hour using only a single commodity GPU.
So the difficulty of the search is no longer proportional to the number of passwords tried, but rather proportional to the product of the number of users and number of passwords - a rather large increase!
They are compiled in a different way but serve the very same purpose as a rainbow table. A list of precompiled hashes.
Thus, they are just a kind of rainbow table.
Therefore, rainbow tables do matter.
But if the passwords were individually salted you would have to individually hash each dictionary item for each hash in the database. So that would be 1,000,000 hash operations.
1. If you're using salt, it implies you chose to roll your own key function using hashes. That's a bad idea, because:
2. GPUs can produce so many combinations per second that the difference between salted and unsalted is basically indistinguishable for smart attackers.