I know there are many discussions on salted hashes, and I understand that the purpose is to make it impossible to build a rainbow table of all possible hashes (generally up to 7 characters).

My understanding is that the random salted values are simply concatenated to the password hash. Why can a rainbow table not be used against the password hash and ignore the first X bits that are known to be the random salt hash?

Update

Thanks for the replies. I am guessing for this to work, the directory (LDAP, etc) has to store a salt specific to each user, or it seems like the salt would be "lost" and authentication could never occur.

It typically works like this:
Say your password is "baseball". I could simply store it raw, but anyone who gets my database gets the password. So instead I do an SHA1 hash on it, and get this:
$ echo -n baseball | sha1sum
a2c901c8c6dea98958c219f6f2d038c44dc5d362

Theoretically it's impossible to reverse a SHA1 hash. But go do a google search on that exact string, and you will have no trouble recovering the original password.
Plus, if two users in the database have the same password, then they'll have the same SHA1 hash. And if one of them has a password hint that says try "baseball" -- well now I know what both users' passwords are.
So before we hash it, we prepend a unique string. Not a secret, just something unique. How about WquZ012C. So now we're hashing the string WquZ012Cbaseball. That hashes to this:

c5e635ec235a51e89f6ed7d4857afe58663d54f5

Googling that string turns up nothing (except perhaps this page), so now we're on to something. And if person2 also uses "baseball" as his password, we use a different salt and get a different hash.
Of course, in order to test out your password, you have to know what the salt is. So we have to store that somewhere. Most implementations just tack it right on there with the hash, usually with some delimiter. Try this if you have openssl installed:
[tylerl ~]$ openssl passwd -1
Password: baseball
Verifying - Password: baseball
$1$oaagVya9$NMvf1IyubxEYvrZTRSLgk0

This gives us a hash using the standard crypt library. So our hash is $1$oaagVya9$NMvf1IyubxEYvrZTRSLgk0: it's actually 3 sections separated by $. I'll replace the delimiter with a space to make it more visually clear:
$1$oaagVya9$NMvf1IyubxEYvrZTRSLgk0
 1 oaagVya9 NMvf1IyubxEYvrZTRSLgk0


1 means "algorithm number 1" which is a little complicated, but uses MD5. There are plenty others which are much better, but this is our example.
oaagVya9 is our salt. Plunked down right there in with our hash.
NMvf1IyubxEYvrZTRSLgk0 is the actual MD5 sum, base64-encoded.

If I run the process again, I get a completely different hash with a different salt. In this example, there are about 1014 ways to store this one password. All of these are for the password "baseball":
$1$9XsNo9.P$kTPuyvrHqsJJuCci3zLwL.
$1$nLEOCtx6$uSnz6PF8q3YuUhB3rLTC3/
$1$/jZJXTF3$OqDuk8T/cEIGpeKWfsamf.
$1$2lC.Cb/U$KR0jkhpeb1sz.UIqvfYOR.

But, if I deliberately specify the salt I want to check, I'll get back my expected result:
[tylerl ~]$ openssl passwd -1 -salt oaagVya9
Password: baseball
Verifying - Password: baseball
$1$oaagVya9$NMvf1IyubxEYvrZTRSLgk0

And that's the test I run to check to see if the password is correct. Find the stored hash for the user, find the saved salt, re-run that same hash using saved salt, check to see if the result matches the original hash.
Implementing This Yourself
To be clear, this post is not an implementation guide. Don't simply salt your MD5 and call it good. That's not enough in today's risk climate. You'll instead want to run an iterative process which runs the hash function thousands of times. This has been explained elsewhere many times over, so I won't go over the "why" here.
There are several well-established and trusted options for doing this:

crypt: The function I used above is an older variation on the unix crypt password hashing mechanism built-in to all Unix/Linux operating systems. The original (DES-based) version is horribly insecure; don't even consider it. The one I showed (MD5-based) is better, but still shouldn't be used today. Later variations, including the SHA-256 and SHA-512 variations should be reasonable. All recent variants implement multiple rounds of hashes.

bcrypt: The blowfish version of the crypt functional call mentioned above. Capitalizes on the fact that blowfish has a very expensive key setup process, and takes a "cost" parameter which increases the key setup time accordingly.

PBKDF2: ("Password-based Key Derivation Function version 2") Created to produce strong cryptographic keys from simple passwords, this is the only function listed here that actually has an RFC. Runs a configurable number of rounds, with each round it hashes the password plus the previous round's result. The first round uses a salt. It's worth noting that its original intended purpose is creating strong keys, not storing passwords, but the overlap in goals makes this a well-trusted solution here as well. If you had no libraries available and were forced to implement something from scratch, this is the easiest and best-documented option. Though, obviously, using a well-vetted library is always best.

scrypt: A recently-introduced system designed specifically to be difficult to implement on dedicated hardware. In addition to requiring multiple rounds of a hashing function, scrypt also has a very large working memory state, so as to increase the RAM requirement for implementations. While very new and mostly unproven, it looks at least as secure as the others, and possibly the most secure of them all.


