I was wondering if I could reasons or links to resources explaining why SHA512 is a superior hashing algorithm to MD5.
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There are a couple of points not being addressed here, and I feel it is from a lack of understanding about what a hash is, how it works, and how long it takes to successfully attack them, using rainbow or any other method currently known to man...
Mathematically speaking, MD5 is not "broken" if you salt the hash and throttle attempts (even by 1 second), your security would be just as "broken" as it would by an attacker slowly pelting away at your 1ft solid steel wall with a wooden spoon:
It will take thousands of years, and by then everyone involved will be dead; there are more important things to worry about.
If you lock their account by the 20th attempt... problem solved. 20 hits on your wall = 0.0000000001% chance they got through. There is literally a better statistical chance you are in fact Jesus.
It's also important to note that absolutely any hash function is going to be vulnerable to collisions by virtue of what a hash is: "a (small) unique id of something else".
When you increase the bit space you decrease collision rates, but you also increase the size of the id and the time it takes to compute it.
Let's do a tiny thought experiment...
SHA-2, if it existed, would have 4 total possible unique IDs for something else... 00, 01, 10 & 11. It will produce collisions, obviously. Do you see the issue here? A hash is just a generated ID of what you're trying to identify.
MD5 is actually really, really good at randomly choosing a number based on an input. SHA is actually not that much better at it; SHA just has massive more space for IDs.
The method used is about 0.1% of the reason the collisions are less likely. The real reason is the larger bit space.
This is literally the only reason SHA-256 and SHA-512 are less vulnerable to collisions; because they use a larger space for a unique id.
The actual methods SHA-256 and SHA-512 use to generate the hash are in fact better, but not by much; the same rainbow attacks would work on them if they had fewer bits in their IDs, and files and even passwords can have identical IDs using SHA-256 and SHA-512, it's just a lot less likely because it uses more bits.
If you allow automated attacks to hit your authentication endpoint 1,000 times per second, you're going to get broken into. If you throttle to 1 attempt per 3 seconds and lock the account for 24 hours after the 10th attempt, you're not.
If you store the passwords without salt (a salt is just an added secret to the generator, making it harder to identify bad passwords like "31337" or "password") and have a lot of users, you're going to get hacked. If you salt them, even if you use MD5, you're not.
Considering MD5 uses 128 bits (32 bytes in HEX, 16 bytes in binary), and SHA 512 is only 4x the space but virtually eliminates the collision ratio by giving you 2^384 more possible IDs... Go with SHA-512, every time.
But if you're worried about what is really going to happen if you use MD5, and you don't understand the real, actual differences, you're still probably going to get hacked, make sense?